Compartmental modeling and tracer kinetics
Anderson, David H
1983-01-01
This monograph is concerned with mathematical aspects of compartmental an alysis. In particular, linear models are closely analyzed since they are fully justifiable as an investigative tool in tracer experiments. The objective of the monograph is to bring the reader up to date on some of the current mathematical prob lems of interest in compartmental analysis. This is accomplished by reviewing mathematical developments in the literature, especially over the last 10-15 years, and by presenting some new thoughts and directions for future mathematical research. These notes started as a series of lectures that I gave while visiting with the Division of Applied ~1athematics, Brown University, 1979, and have developed in to this collection of articles aimed at the reader with a beginning graduate level background in mathematics. The text can be used as a self-paced reading course. With this in mind, exercises have been appropriately placed throughout the notes. As an aid in reading the material, the e~d of a ...
Compartmental modelling for magnetic resonance renography.
Sourbron, Steven
2010-01-01
A basic formalism is presented for generating and interpreting compartmental models for dynamic contrast-enhanced MRI data in the kidney. A graphical convention is introduced to represent and design compartmental models in a transparent and physically intuitive manner. A systematic system of notations and a simple set of rules allows direct translation of the graphical representation into a mathematical solution. The rules are derived from the physical principle of mass conservation, and the interpretation provided by the general tracer-kinetic theory of linear and stationary systems. The power of the formalism is illustrated using examples of models that have been proposed in the literature on perfusion MRI, and by generating a number of advanced models that may be of use in the kidney.
Compartmental analysis of dynamic nuclear medicine data: models and identifiability
Delbary, Fabrice; Garbarino, Sara; Vivaldi, Valentina
2016-12-01
Compartmental models based on tracer mass balance are extensively used in clinical and pre-clinical nuclear medicine in order to obtain quantitative information on tracer metabolism in the biological tissue. This paper is the first of a series of two that deal with the problem of tracer coefficient estimation via compartmental modelling in an inverse problem framework. Specifically, here we discuss the identifiability problem for a general n-dimension compartmental system and provide uniqueness results in the case of two-compartment and three-compartment compartmental models. The second paper will utilize this framework in order to show how nonlinear regularization schemes can be applied to obtain numerical estimates of the tracer coefficients in the case of nuclear medicine data corresponding to brain, liver and kidney physiology.
A Calculus for Modelling, Simulating and Analysing Compartmentalized Biological Systems
DEFF Research Database (Denmark)
Mardare, Radu Iulian; Ihekwaba, Adoha
2007-01-01
A. Ihekwaba, R. Mardare. A Calculus for Modelling, Simulating and Analysing Compartmentalized Biological Systems. Case study: NFkB system. In Proc. of International Conference of Computational Methods in Sciences and Engineering (ICCMSE), American Institute of Physics, AIP Proceedings, N 2...
A Calculus for Modelling, Simulating and Analysing Compartmentalized Biological Systems
DEFF Research Database (Denmark)
Mardare, Radu Iulian; Ihekwaba, Adoha
2007-01-01
A. Ihekwaba, R. Mardare. A Calculus for Modelling, Simulating and Analysing Compartmentalized Biological Systems. Case study: NFkB system. In Proc. of International Conference of Computational Methods in Sciences and Engineering (ICCMSE), American Institute of Physics, AIP Proceedings, N 2...
Compartmentalization analysis using discrete fracture network models
Energy Technology Data Exchange (ETDEWEB)
La Pointe, P.R.; Eiben, T.; Dershowitz, W. [Golder Associates, Redmond, VA (United States); Wadleigh, E. [Marathon Oil Co., Midland, TX (United States)
1997-08-01
This paper illustrates how Discrete Fracture Network (DFN) technology can serve as a basis for the calculation of reservoir engineering parameters for the development of fractured reservoirs. It describes the development of quantitative techniques for defining the geometry and volume of structurally controlled compartments. These techniques are based on a combination of stochastic geometry, computational geometry, and graph the theory. The parameters addressed are compartment size, matrix block size and tributary drainage volume. The concept of DFN models is explained and methodologies to compute these parameters are demonstrated.
Dynamic behaviors of a class of HIV compartmental models
Chen, Xiaoyan; Huang, Lihong; Yu, Pei
2015-06-01
Based on heterogeneities in drug efficacy (either spatial or phenotypic), two HIV compartmental models were proposed in Callaway and Perelson (2002) to study the HIV virus dynamics under drug treatment. In this paper, we provide a global analysis on the two models, including the positivity and boundedness of solutions and the global stability of equilibrium solutions. In particular, we show that when the basic reproduction number R0 ⩽ 1 (for which the infection equilibrium does not exist), the infection-free equilibrium is globally asymptotically stable; while when R0 > 1 (for which the infection equilibrium exists), the infection equilibrium is globally asymptotically stable.
Analytical properties of a three-compartmental dynamical demographic model
Postnikov, E. B.
2015-07-01
The three-compartmental demographic model by Korotaeyv-Malkov-Khaltourina, connecting population size, economic surplus, and education level, is considered from the point of view of dynamical systems theory. It is shown that there exist two integrals of motion, which enables the system to be reduced to one nonlinear ordinary differential equation. The study of its structure provides analytical criteria for the dominance ranges of the dynamics of Malthus and Kremer. Additionally, the particular ranges of parameters enable the derived general ordinary differential equations to be reduced to the models of Gompertz and Thoularis-Wallace.
Pharmacokinetics of Remifentanil: a three-compartmental modeling approach
Cascone, Sara; Lamberti, Gaetano; Titomanlio, Giuseppe; Piazza, Ornella
Remifentanil is a new opioid derivative drug characterized by a fast onset and by a short time of action, since it is rapidly degraded by esterases in blood and other tissues. Its pharmacokinetic and pharmacodynamics properties make remifentanil a very interesting molecule in the field of 0anesthesia. However a complete and versatile pharmacokinetic description of remifentanil still lacks. In this work a three-compartmental model has been developed to describe the pharmacokinetics of remifentanil both in the case in which it is administered by intravenous constant-rate infusion and by bolus injection. The model curves have been compared with experimental data published in scientific papers and the model parameters have been optimized to describe both ways of administration. The ad hoc model is adaptable and potentially useful for predictive purposes. PMID:24251247
Menzies, T; Compton, P
1997-06-01
It is difficult to assess hypothetical models in poorly measured domains such as neuroendocrinology. Without a large library of observations to constrain inference, the execution of such incomplete models implies making assumptions. Mutually exclusive assumptions must be kept in separate worlds. We define a general abductive multiple-worlds engine that assesses such models by (i) generating the worlds and (ii) tests if these worlds contain known behaviour. World generation is constrained via the use of relevant envisionment. We describe QCM, a modeling language for compartmental models that can be processed by this inference engine. This tool has been used to find faults in theories published in international refereed journals; i.e. QCM can detect faults which are invisible to other methods. The generality and computational limits of this approach are discussed. In short, this approach is applicable to any representation that can be compiled into an and-or graph, provided the graphs are not too big or too intricate (fanout < 7).
A compartmental model for post-Chernobyl resuspension
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Dovlete, C. [Institute of Environmental Research and Engineering, Bucharest (Romania); Osvath, I. [Institute of Environmental Research and Engineering, Bucharest (Romania)
1993-12-31
A simple compartmental model is proposed to describe the transfer of Cs-137 between the lower (boundary) layer of the atmosphere and the ground for short and long term. The experimental basis for the evaluation of the model parameters (the exchange rates between the compartments), consists of the monthly deposition data sequences between 1986 - 1992 for 16 sampling stations on Romanian territory, as well as the data regarding the immediate impact (May 1986) of the Chernobyl accident on the atmosphere in Romania As a result of fitting the experimental data, the model parameters have been estimated and an analytical expression has been found for Cs-137 concentration in air as a function of these parameters and time. The site dependence of each parameter (exchange rate) has been studied. As a conclusion a new analytic expression for the resuspension factor is proposed, containing its dependence on initial conditions and the exchange rates between the model compartments. The theoretical predictions regarding the resuspension factor are in good agreement with the experimental results obtained using air concentration data from the respective sites. (orig.)
Efficient Vaccine Distribution Based on a Hybrid Compartmental Model.
Directory of Open Access Journals (Sweden)
Zhiwen Yu
Full Text Available To effectively and efficiently reduce the morbidity and mortality that may be caused by outbreaks of emerging infectious diseases, it is very important for public health agencies to make informed decisions for controlling the spread of the disease. Such decisions must incorporate various kinds of intervention strategies, such as vaccinations, school closures and border restrictions. Recently, researchers have paid increased attention to searching for effective vaccine distribution strategies for reducing the effects of pandemic outbreaks when resources are limited. Most of the existing research work has been focused on how to design an effective age-structured epidemic model and to select a suitable vaccine distribution strategy to prevent the propagation of an infectious virus. Models that evaluate age structure effects are common, but models that additionally evaluate geographical effects are less common. In this paper, we propose a new SEIR (susceptible-exposed-infectious šC recovered model, named the hybrid SEIR-V model (HSEIR-V, which considers not only the dynamics of infection prevalence in several age-specific host populations, but also seeks to characterize the dynamics by which a virus spreads in various geographic districts. Several vaccination strategies such as different kinds of vaccine coverage, different vaccine releasing times and different vaccine deployment methods are incorporated into the HSEIR-V compartmental model. We also design four hybrid vaccination distribution strategies (based on population size, contact pattern matrix, infection rate and infectious risk for controlling the spread of viral infections. Based on data from the 2009-2010 H1N1 influenza epidemic, we evaluate the effectiveness of our proposed HSEIR-V model and study the effects of different types of human behaviour in responding to epidemics.
Global identifiability of linear compartmental models--a computer algebra algorithm.
Audoly, S; D'Angiò, L; Saccomani, M P; Cobelli, C
1998-01-01
A priori global identifiability deals with the uniqueness of the solution for the unknown parameters of a model and is, thus, a prerequisite for parameter estimation of biological dynamic models. Global identifiability is however difficult to test, since it requires solving a system of algebraic nonlinear equations which increases both in nonlinearity degree and number of terms and unknowns with increasing model order. In this paper, a computer algebra tool, GLOBI (GLOBal Identifiability) is presented, which combines the topological transfer function method with the Buchberger algorithm, to test global identifiability of linear compartmental models. GLOBI allows for the automatic testing of a priori global identifiability of general structure compartmental models from general multi input-multi output experiments. Examples of usage of GLOBI to analyze a priori global identifiability of some complex biological compartmental models are provided.
Yang, Pei-Chi; Boras, Britton W; Jeng, Mao-Tsuen; Docken, Steffen S; Lewis, Timothy J; McCulloch, Andrew D; Harvey, Robert D; Clancy, Colleen E
2016-07-01
Subcellular compartmentation of the ubiquitous second messenger cAMP has been widely proposed as a mechanism to explain unique receptor-dependent functional responses. How exactly compartmentation is achieved, however, has remained a mystery for more than 40 years. In this study, we developed computational and mathematical models to represent a subcellular sarcomeric space in a cardiac myocyte with varying detail. We then used these models to predict the contributions of various mechanisms that establish subcellular cAMP microdomains. We used the models to test the hypothesis that phosphodiesterases act as functional barriers to diffusion, creating discrete cAMP signaling domains. We also used the models to predict the effect of a range of experimentally measured diffusion rates on cAMP compartmentation. Finally, we modeled the anatomical structures in a cardiac myocyte diad, to predict the effects of anatomical diffusion barriers on cAMP compartmentation. When we incorporated experimentally informed model parameters to reconstruct an in silico subcellular sarcomeric space with spatially distinct cAMP production sites linked to caveloar domains, the models predict that under realistic conditions phosphodiesterases alone were insufficient to generate significant cAMP gradients. This prediction persisted even when combined with slow cAMP diffusion. When we additionally considered the effects of anatomic barriers to diffusion that are expected in the cardiac myocyte dyadic space, cAMP compartmentation did occur, but only when diffusion was slow. Our model simulations suggest that additional mechanisms likely contribute to cAMP gradients occurring in submicroscopic domains. The difference between the physiological and pathological effects resulting from the production of cAMP may be a function of appropriate compartmentation of cAMP signaling. Therefore, understanding the contribution of factors that are responsible for coordinating the spatial and temporal
Sartori, F.; Sericano, J. L.; Wade, T. L.; Mohanty, B. P.
2012-12-01
Knowledge about the mobilization of polycyclic aromatic hydrocarbons (PAH) from PAH-laden soils or sediments is important to understand their bioavailability, and ultimately assess the environmental risk of PAH transport from surface soils into the groundwater. The transport and kinetics of three PAH from a spiked soil layer (2-3 cm soil depth), Phenanthrene-d10 (1900 ng/g), Naphthalene-d8 (1500 ng/g), and Pyrene-d10 (1800 ng/g), were investigated by performing a series of 8 rainfall events during 25 days in two large, replicate soil columns (length: 35 cm; diameter: 14.5 cm; 1 Pore Volume [PV]=2.29 L) under variably-saturated flow conditions. The water-methanol displacing solutions were at volumetric fractions of 0.3 and 0.6 during day 1 (E1) through E8 and E12-E22, respectively. Soil matric potential (h) was monitored at 5-cm and 20-cm depth and volumetric water content (θ) at 12.5-cm and 27.5-cm depth. Soil solution was sampled at 5 cm- (n=46) and 27.5-cm depth (n=46), and the effluent at the bottom of the column (n=163). HYDRUS-1D was used for inverse modeling of h and θ data and to predict θ at specific times and soil depth increments. First-order kinetics, compartmental models describing the transfer of PAH from the soil compartment to the soil solution compartment (desorption) and vice versa (sorption), were used to estimate mass transfer rates (φs, sorption; φd, desorption; φe, elimination), PAH mass in each compartment, and partition coefficients (Kd). Phenanthrene breakthrough curve could be interpreted through a two-parameter, two-compartment model corresponding to the common two-site sorption model, whose parameter estimates (and 95% confidence intervals) were φd=2.72 (2.31, 3.19) PV-1 and φe=4.67 (3.82, 5.7 ) PV-1. Naphthalene breakthrough curve followed a simple one-compartment elimination model, φe=2.0 (1.9, 2.1) PV-1, and that of Pyrene a three-parameter, two-compartment model, φs=0.0454 (0.00853, 0.0603) PV-1, φd=0.165 (0.0319, 0.855) PV
Compartmental models: theory and practice using the SAAM II software system.
Cobelli, C; Foster, D M
1998-01-01
Understanding in vivo the functioning of metabolic systems at the whole-body or regional level requires one to make some assumptions on how the system works and to describe them mathematically, that is, to postulate a model of the system. Models of systems can have different characteristics depending on the properties of the system and the database available for their study; they can be deterministic or stochastic, dynamic or static, with lumped or distributed parameters. Metabolic systems are dynamic systems and we focus here on the most widely used class of dynamic (differential equation) models: compartmental models. This is a class of models for which the governing law is conservation of mass. It is a very attractive class to users because it formalizes physical intuition in a simple and reasonable way. Compartmental models are lumped parameter models, in that the events in the system are described by a finite number of changing variables, and are thus described by ordinary differential equations. While stochastic compartment models can also be defined, we discuss here the deterministic versions--those that can work with exact relationships between model variables. These are the models most widely used in discussions of endocrinology and metabolism. In this chapter, we will discuss the theory of compartmental models, and then discuss how the SAAM II software system, a system designed specifically to aid in the development and testing of multicompartmental models, can be used.
Riml, J.; Wörman, A.
2009-12-01
Knowledge about both hydrochemical processes and watershed characteristics are key factors when trying to model transportation and retention of nutrients in a river system. The proposed parameterization method opens for the possibility to introduce independently measured parameters in lumped (compartmental) models. The analysis provides a better understanding of the model structure and aids in the calculation of optimal parameter values. The investigation uses a 1D distributed network model and parameterizes the result in a form appropriate for a compartmental model structure that has been developed for Swedish conditions during decades. The main tool for the analysis is the comparison of temporal moments between the two model structures. The parameterization gives information about the importance of river hydraulics but also about the effect of geomorphological processes such as the river network structure and parameter variability within the watershed. The methodology does also reveal information about predominating processes during distinctive hydrological conditions.
Robust global identifiability theory using potentials--Application to compartmental models.
Wongvanich, N; Hann, C E; Sirisena, H R
2015-04-01
This paper presents a global practical identifiability theory for analyzing and identifying linear and nonlinear compartmental models. The compartmental system is prolonged onto the potential jet space to formulate a set of input-output equations that are integrals in terms of the measured data, which allows for robust identification of parameters without requiring any simulation of the model differential equations. Two classes of linear and non-linear compartmental models are considered. The theory is first applied to analyze the linear nitrous oxide (N2O) uptake model. The fitting accuracy of the identified models from differential jet space and potential jet space identifiability theories is compared with a realistic noise level of 3% which is derived from sensor noise data in the literature. The potential jet space approach gave a match that was well within the coefficient of variation. The differential jet space formulation was unstable and not suitable for parameter identification. The proposed theory is then applied to a nonlinear immunological model for mastitis in cows. In addition, the model formulation is extended to include an iterative method which allows initial conditions to be accurately identified. With up to 10% noise, the potential jet space theory predicts the normalized population concentration infected with pathogens, to within 9% of the true curve. Copyright © 2015 Elsevier Inc. All rights reserved.
Multi-scale hierarchical approach for parametric mapping: assessment on multi-compartmental models.
Rizzo, G; Turkheimer, F E; Bertoldo, A
2013-02-15
This paper investigates a new hierarchical method to apply basis function to mono- and multi-compartmental models (Hierarchical-Basis Function Method, H-BFM) at a voxel level. This method identifies the parameters of the compartmental model in its nonlinearized version, integrating information derived at the region of interest (ROI) level by segmenting the cerebral volume based on anatomical definition or functional clustering. We present the results obtained by using a two tissue-four rate constant model with two different tracers ([(11)C]FLB457 and [carbonyl-(11)C]WAY100635), one of the most complex models used in receptor studies, especially at the voxel level. H-BFM is robust and its application on both [(11)C]FLB457 and [carbonyl-(11)C]WAY100635 allows accurate and precise parameter estimates, good quality parametric maps and a low percentage of voxels out of physiological bound (approach for PET quantification by using compartmental modeling at the voxel level. In particular, different from other proposed approaches, this method can also be used when the linearization of the model is not appropriate. We expect that applying it to clinical data will generate reliable parametric maps. Copyright © 2012 Elsevier Inc. All rights reserved.
Similarity transformation approach to identifiability analysis of nonlinear compartmental models.
Vajda, S; Godfrey, K R; Rabitz, H
1989-04-01
Through use of the local state isomorphism theorem instead of the algebraic equivalence theorem of linear systems theory, the similarity transformation approach is extended to nonlinear models, resulting in finitely verifiable sufficient and necessary conditions for global and local identifiability. The approach requires testing of certain controllability and observability conditions, but in many practical examples these conditions prove very easy to verify. In principle the method also involves nonlinear state variable transformations, but in all of the examples presented in the paper the transformations turn out to be linear. The method is applied to an unidentifiable nonlinear model and a locally identifiable nonlinear model, and these are the first nonlinear models other than bilinear models where the reason for lack of global identifiability is nontrivial. The method is also applied to two models with Michaelis-Menten elimination kinetics, both of considerable importance in pharmacokinetics, and for both of which the complicated nature of the algebraic equations arising from the Taylor series approach has hitherto defeated attempts to establish identifiability results for specific input functions.
Davidson, Natalie R; Godfrey, Keith R; Alquaddoomi, Faisal; Nola, David; DiStefano, Joseph J
2017-05-01
We describe and illustrate use of DISTING, a novel web application for computing alternative structurally identifiable linear compartmental models that are input-output indistinguishable from a postulated linear compartmental model. Several computer packages are available for analysing the structural identifiability of such models, but DISTING is the first to be made available for assessing indistinguishability. The computational algorithms embedded in DISTING are based on advanced versions of established geometric and algebraic properties of linear compartmental models, embedded in a user-friendly graphic model user interface. Novel computational tools greatly speed up the overall procedure. These include algorithms for Jacobian matrix reduction, submatrix rank reduction, and parallelization of candidate rank computations in symbolic matrix analysis. The application of DISTING to three postulated models with respectively two, three and four compartments is given. The 2-compartment example is used to illustrate the indistinguishability problem; the original (unidentifiable) model is found to have two structurally identifiable models that are indistinguishable from it. The 3-compartment example has three structurally identifiable indistinguishable models. It is found from DISTING that the four-compartment example has five structurally identifiable models indistinguishable from the original postulated model. This example shows that care is needed when dealing with models that have two or more compartments which are neither perturbed nor observed, because the numbering of these compartments may be arbitrary. DISTING is universally and freely available via the Internet. It is easy to use and circumvents tedious and complicated algebraic analysis previously done by hand. Copyright © 2017 Elsevier B.V. All rights reserved.
Electrophysiological properties of inferior olive neurons: A compartmental model.
Schweighofer, N; Doya, K; Kawato, M
1999-08-01
As a step in exploring the functions of the inferior olive, we constructed a biophysical model of the olivary neurons to examine their unique electrophysiological properties. The model consists of two compartments to represent the known distribution of ionic currents across the cell membrane, as well as the dendritic location of the gap junctions and synaptic inputs. The somatic compartment includes a low-threshold calcium current (I(Ca_l)), an anomalous inward rectifier current (I(h)), a sodium current (I(Na)), and a delayed rectifier potassium current (I(K_dr)). The dendritic compartment contains a high-threshold calcium current (I(Ca_h)), a calcium-dependent potassium current (I(K_Ca)), and a current flowing into other cells through electrical coupling (I(c)). First, kinetic parameters for these currents were set according to previously reported experimental data. Next, the remaining free parameters were determined to account for both static and spiking properties of single olivary neurons in vitro. We then performed a series of simulated pharmacological experiments using bifurcation analysis and extensive two-parameter searches. Consistent with previous studies, we quantitatively demonstrated the major role of I(Ca_l) in spiking excitability. In addition, I(h) had an important modulatory role in the spike generation and period of oscillations, as previously suggested by Bal and McCormick. Finally, we investigated the role of electrical coupling in two coupled spiking cells. Depending on the coupling strength, the hyperpolarization level, and the I(Ca_l) and I(h) modulation, the coupled cells had four different synchronization modes: the cells could be in-phase, phase-shifted, or anti-phase or could exhibit a complex desynchronized spiking mode. Hence these simulation results support the counterintuitive hypothesis that electrical coupling can desynchronize coupled inferior olive cells.
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Greiter, Matthias B., E-mail: matthias.greiter@helmholtz-muenchen.de; Giussani, Augusto, E-mail: AGiussani@BfS.de; Hoellriegl, Vera, E-mail: vera.hoellriegl@helmholtz-muenchen.de; Li Weibo, E-mail: wli@helmholtz-muenchen.de; Oeh, Uwe, E-mail: uwe.oeh@helmholtz-muenchen.de
2011-09-01
Biokinetic models describing the uptake, distribution and excretion of trace elements are an essential tool in nutrition, toxicology, or internal dosimetry of radionuclides. Zirconium, especially its radioisotope {sup 95}Zr, is relevant to radiation protection due to its production in uranium fission and neutron activation of nuclear fuel cladding material. We present a comprehensive set of human data from a tracer study with stable isotopes of zirconium. The data are used to refine a biokinetic model of zirconium. Six female and seven male healthy adult volunteers participated in the study. It includes 16 complete double tracer investigations with oral ingestion and intravenous injection, and seven supplemental investigations. Tracer concentrations were measured in blood plasma and urine collected up to 100 d after tracer administration. The four data sets (two chemical tracer forms in plasma and urine) each encompass 105-240 measured concentration values above detection limits. Total fractional absorption of ingested zirconium was found to be 0.001 for zirconium in citrate-buffered drinking solution and 0.007 for zirconium oxalate solution. Biokinetic models were developed based on the linear first-order kinetic compartmental model approach used by the International Commission on Radiological Protection (ICRP). The main differences of the optimized systemic model of zirconium to the current ICRP model are (1) recycling into the transfer compartment made necessary by the observed tracer clearance from plasma, (2) different parameters related to fractional absorption for each form of the ingested tracer, and (3) a physiologically based excretion pathway to urine. The study considerably expands the knowledge on the biokinetics of zirconium, which was until now dominated by data from animal studies. The proposed systemic model improves the existing ICRP model, yet is based on the same principles and fits well into the ICRP radiation protection approach. - Research
A compartmental model of the cAMP/PKA/MAPK pathway in Bio-PEPA
Directory of Open Access Journals (Sweden)
Federica Ciocchetta
2009-11-01
Full Text Available The vast majority of biochemical systems involve the exchange of information between different compartments, either in the form of transportation or via the intervention of membrane proteins which are able to transmit stimuli between bordering compartments. The correct quantitative handling of compartments is, therefore, extremely important when modelling real biochemical systems. The Bio-PEPA process algebra is equipped with the capability of explicitly defining quantitative information such as compartment volumes and membrane surface areas. Furthermore, the recent development of the Bio-PEPA Eclipse Plug-in allows us to perform a correct stochastic simulation of multi-compartmental models. Here we present a Bio-PEPA compartmental model of the cAMP/PKA/MAPK pathway. We analyse the system using the Bio-PEPA Eclipse Plug-in and we show the correctness of our model by comparison with an existing ODE model. Furthermore, we perform computational experiments in order to investigate certain properties of the pathway. Specifically, we focus on the system response to the inhibition and strengthening of feedback loops and to the variation in the activity of key pathway reactions and we observe how these modifications affect the behaviour of the pathway. These experiments are useful to understand the control and regulatory mechanisms of the system.
DEFF Research Database (Denmark)
Vahidi, O; Kwok, K E; Gopaluni, R B
2016-01-01
We have expanded a former compartmental model of blood glucose regulation for healthy and type 2 diabetic subjects. The former model was a detailed physiological model which considered the interactions of three substances, glucose, insulin and glucagon on regulating the blood sugar. The main...... drawback of the former model was its restriction on the route of glucose entrance to the body which was limited to the intravenous glucose injection. To handle the oral glucose intake, we have added a model of glucose absorption in the gastrointestinal tract to the former model to address the resultant...... variations of blood glucose concentrations following an oral glucose intake. Another model representing the incretins production in the gastrointestinal tract along with their hormonal effects on boosting pancreatic insulin production is also added to the former model. We have used two sets of clinical data...
Xia, Binfeng; Yang, Zhen; Zhou, Haiying; Lukacova, Viera; Zhu, Wei; Milewski, Mikolaj; Kesisoglou, Filippos
2015-05-01
Intraoral (IO) delivery is an alternative administration route to deliver a drug substance via the mouth that provides several advantages over conventional oral dosage forms. The purpose of this work was to develop and evaluate a novel, physiologically based oral cavity model for projection and mechanistic analysis of the clinical pharmacokinetics of intraoral formulations. The GastroPlus™ Oral Cavity Compartmental Absorption and Transit (OCCAT™) model was used to simulate the plasma concentration versus time profiles and the fraction and rate of intraoral drug transit/absorption for Intermezzo® sublingual tablets (zolpidem tartrate). The model was evaluated by the goodness-of-fit between simulated and observed concentrations and the deviation of key PK parameters (e.g., C max, T max, and AUC). In addition, a sensitivity analysis was conducted to demonstrate the interplay and impact of key modeling parameters on the fraction absorbed via oral mucosa (F a_IO). The OCCAT™ model captured the observed pharmacokinetics for Intermezzo® sublingual tablets (R (2) > 0.9). The predicted deviations (%) for C max, AUC0-inf, AUC0-20 min, and T max were 5.7, 28.0, 11.8, and 28.6%, respectively, indicating good prediction accuracy. The model also estimated ~18% of total drug was absorbed via the IO route. Furthermore, the sensitivity analysis indicated that the F a_IO was not only associated with drug diffusivity and unbound fraction in epithelium tissue (f ut) but also depended on the physicochemical properties of compounds for IO delivery (e.g., solubility and logD pH = 7.4). The novel physiologically based IO absorption OCCAT™ model showed satisfactory performance and will be helpful to guide development of future intraoral formulations.
Willats, Adam; Ivanova, Tamara; Prinz, Astrid; Liu, Robert
2015-03-01
Immediate Early Genes (IEGs) are rapidly and transiently transcribed in neurons after a sensory experience. Some of these genes act as effector IEGs, which mediate specific effects on cellular function. Arc is one such effector IEG that is essential for synaptic plasticity and memory consolidation in hippocampus and cortex. The expression of Arc in neurons has previously been examined using an imaging method known as Compartmental Analysis of Temporal Fluorescent In-Situ Hybridization. Previous work found that the time course of Arc expression within the nuclear and perinuclear cytoplasmic compartments of a neuron is altered by prior sensory experience. We explore a simple model of the kinetics of IEG transcription and nuclear export, with the aim of eventually uncovering possible mechanisms for how experience alters expression kinetics. Thus far, we characterize our compartmental model using phase-plane analysis and validate it against several IEG expression data sets, including one where prior experience with vocalizing mice alters the time course of call-induced Arc expression in the auditory cortex of a listening mouse. Our model provides a framework to explore why Arc expression may change depending on a receiver's past sound experience and internal state. Adam Willats was supported by NIH Training Grant 5T90DA032466. This research was also supported by NIDCD R01 DC8343.
Koldsø, Heidi; Reddy, Tyler; Fowler, Philip W; Duncan, Anna L; Sansom, Mark S P
2016-09-01
The cytoskeleton underlying cell membranes may influence the dynamic organization of proteins and lipids within the bilayer by immobilizing certain transmembrane (TM) proteins and forming corrals within the membrane. Here, we present coarse-grained resolution simulations of a biologically realistic membrane model of asymmetrically organized lipids and TM proteins. We determine the effects of a model of cytoskeletal immobilization of selected membrane proteins using long time scale coarse-grained molecular dynamics simulations. By introducing compartments with varying degrees of restraints within the membrane models, we are able to reveal how compartmentalization caused by cytoskeletal immobilization leads to reduced and anomalous diffusional mobility of both proteins and lipids. This in turn results in a reduced rate of protein dimerization within the membrane and of hopping of membrane proteins between compartments. These simulations provide a molecular realization of hierarchical models often invoked to explain single-molecule imaging studies of membrane proteins.
Predictions of Radionuclide Dose Rates from Sellafield Discharges using a Compartmental Model
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McCubbin, D.; Leonard, K.S.; Gurbutt, P.A.; Round, G.D
1998-07-01
A multi-compartmental model (MIRMAID) of the Irish Sea has been used to predict radionuclide dose rates to the public, via seafood consumption pathways. Radionuclides originate from the authorised discharge of low level liquid effluent from the BNF plc nuclear reprocessing plant at Sellafield. The model has been used to predict combined annual doses, the contribution of dose from individual radionuclides and to discriminate dose between present day and historic discharges. An assessment has been carried out to determine the sensitivity of the predictions to changes in various model parameters. The predicted dose to the critical group from seafood consumption in 1995 ranged from 37-96 {mu}Sv of which the majority originated from current discharges. The contribution from {sup 99}Tc was predicted to have increased from 0.2% in 1993 up to 20% in 1995. The predicted contribution of Pu and Am from historic discharges is underestimated in the model. (author)
Information Processing in Single Cells and Small Networks: Insights from Compartmental Models
Poirazi, Panayiota
2009-03-01
The goal of this paper is to present a set of predictions generated by detailed compartmental models regarding the ways in which information may be processed, encoded and propagated by single cells and neural assemblies. Towards this goal, I will review a number of modelling studies from our lab that investigate how single pyramidal neurons and small neural networks in different brain regions process incoming signals that are associated with learning and memory. I will first discuss the computational capabilities of individual pyramidal neurons in the hippocampus [1-3] and how these properties may allow a single cell to discriminate between different memories [4]. I will then present biophysical models of prefrontal layer V neurons and small networks that exhibit sustained activity under realistic synaptic stimulation and discuss their potential role in working memory [5].
The construction of next-generation matrices for compartmental epidemic models.
Diekmann, O; Heesterbeek, J A P; Roberts, M G
2010-06-06
The basic reproduction number (0) is arguably the most important quantity in infectious disease epidemiology. The next-generation matrix (NGM) is the natural basis for the definition and calculation of (0) where finitely many different categories of individuals are recognized. We clear up confusion that has been around in the literature concerning the construction of this matrix, specifically for the most frequently used so-called compartmental models. We present a detailed easy recipe for the construction of the NGM from basic ingredients derived directly from the specifications of the model. We show that two related matrices exist which we define to be the NGM with large domain and the NGM with small domain. The three matrices together reflect the range of possibilities encountered in the literature for the characterization of (0). We show how they are connected and how their construction follows from the basic model ingredients, and establish that they have the same non-zero eigenvalues, the largest of which is the basic reproduction number (0). Although we present formal recipes based on linear algebra, we encourage the construction of the NGM by way of direct epidemiological reasoning, using the clear interpretation of the elements of the NGM and of the model ingredients. We present a selection of examples as a practical guide to our methods. In the appendix we present an elementary but complete proof that (0) defined as the dominant eigenvalue of the NGM for compartmental systems and the Malthusian parameter r, the real-time exponential growth rate in the early phase of an outbreak, are connected by the properties that (0) > 1 if and only if r > 0, and (0) = 1 if and only if r = 0.
Australia's Next Top Fraction Model
Gould, Peter
2013-01-01
Peter Gould suggests Australia's next top fraction model should be a linear model rather than an area model. He provides a convincing argument and gives examples of ways to introduce a linear model in primary classrooms.
Proposing a Compartmental Model for Leprosy and Parameterizing Using Regional Incidence in Brazil.
Directory of Open Access Journals (Sweden)
Rebecca Lee Smith
2016-08-01
Full Text Available Hansen's disease (HD, or leprosy, is still considered a public health risk in much of Brazil. Understanding the dynamics of the infection at a regional level can aid in identification of targets to improve control. A compartmental continuous-time model for leprosy dynamics was designed based on understanding of the biology of the infection. The transmission coefficients for the model and the rate of detection were fit for each region using Approximate Bayesian Computation applied to paucibacillary and multibacillary incidence data over the period of 2000 to 2010, and model fit was validated on incidence data from 2011 to 2012. Regional variation was noted in detection rate, with cases in the Midwest estimated to be infectious for 10 years prior to detection compared to 5 years for most other regions. Posterior predictions for the model estimated that elimination of leprosy as a public health risk would require, on average, 44-45 years in the three regions with the highest prevalence. The model is easily adaptable to other settings, and can be studied to determine the efficacy of improved case finding on leprosy control.
Proposing a Compartmental Model for Leprosy and Parameterizing Using Regional Incidence in Brazil.
Smith, Rebecca Lee
2016-08-01
Hansen's disease (HD), or leprosy, is still considered a public health risk in much of Brazil. Understanding the dynamics of the infection at a regional level can aid in identification of targets to improve control. A compartmental continuous-time model for leprosy dynamics was designed based on understanding of the biology of the infection. The transmission coefficients for the model and the rate of detection were fit for each region using Approximate Bayesian Computation applied to paucibacillary and multibacillary incidence data over the period of 2000 to 2010, and model fit was validated on incidence data from 2011 to 2012. Regional variation was noted in detection rate, with cases in the Midwest estimated to be infectious for 10 years prior to detection compared to 5 years for most other regions. Posterior predictions for the model estimated that elimination of leprosy as a public health risk would require, on average, 44-45 years in the three regions with the highest prevalence. The model is easily adaptable to other settings, and can be studied to determine the efficacy of improved case finding on leprosy control.
A multi-stage compartmental model for HIV-infected individuals: I--waiting time approach.
Billard, L; Dayananda, P W A
2014-03-01
Traditionally, epidemic processes have focused on establishing systems of differential-difference equations governing the number of individuals at each stage of the epidemic. Except for simple situations such as when transition rates are linear, these equations are notoriously intractable mathematically. In this work, the process is described as a compartmental model. The model also allows for individuals to go directly from any prior compartment directly to a final stage corresponding to death. This allows for the possibility that individuals can die earlier due to some non-disease related cause. Then, the model is based on waiting times in each compartment. Survival probabilities of moving from a given compartment to another compartment are established. While our approach can be used for general epidemic processes, our framework is for the HIV/AIDS process. It is then possible to establish the impact of the HIV/AIDS epidemic process on, e.g., insurance premiums and payouts and health-care costs. The effect of changing model parameter values on these entities is investigated.
Linear least squares compartmental-model-independent parameter identification in PET.
Thie, J A; Smith, G T; Hubner, K F
1997-02-01
A simplified approach involving linear-regression straight-line parameter fitting of dynamic scan data is developed for both specific and nonspecific models. Where compartmental-model topologies apply, the measured activity may be expressed in terms of: its integrals, plasma activity and plasma integrals--all in a linear expression with macroparameters as coefficients. Multiple linear regression, as in spreadsheet software, determines parameters for best data fits. Positron emission tomography (PET)-acquired gray-matter images in a dynamic scan are analyzed: both by this method and by traditional iterative nonlinear least squares. Both patient and simulated data were used. Regression and traditional methods are in expected agreement. Monte-Carlo simulations evaluate parameter standard deviations, due to data noise, and much smaller noise-induced biases. Unique straight-line graphical displays permit visualizing data influences on various macroparameters as changes in slopes. Advantages of regression fitting are: simplicity, speed, ease of implementation in spreadsheet software, avoiding risks of convergence failures or false solutions in iterative least squares, and providing various visualizations of the uptake process by straight line graphical displays. Multiparameter model-independent analyses on lesser understood systems is also made possible.
A Compartmental Model for Zika Virus with Dynamic Human and Vector Populations.
Lee, Eva K; Liu, Yifan; Pietz, Ferdinand H
2016-01-01
The Zika virus (ZIKV) outbreak in South American countries and its potential association with microcephaly in newborns and Guillain-Barré Syndrome led the World Health Organization to declare a Public Health Emergency of International Concern. To understand the ZIKV disease dynamics and evaluate the effectiveness of different containment strategies, we propose a compartmental model with a vector-host structure for ZIKV. The model utilizes logistic growth in human population and dynamic growth in vector population. Using this model, we derive the basic reproduction number to gain insight on containment strategies. We contrast the impact and influence of different parameters on the virus trend and outbreak spread. We also evaluate different containment strategies and their combination effects to achieve early containment by minimizing total infections. This result can help decision makers select and invest in the strategies most effective to combat the infection spread. The decision-support tool demonstrates the importance of "digital disease surveillance" in response to waves of epidemics including ZIKV, Dengue, Ebola and cholera.
A Compartmental Model for Zika Virus with Dynamic Human and Vector Populations
Lee, Eva K; Liu, Yifan; Pietz, Ferdinand H
2016-01-01
The Zika virus (ZIKV) outbreak in South American countries and its potential association with microcephaly in newborns and Guillain-Barré Syndrome led the World Health Organization to declare a Public Health Emergency of International Concern. To understand the ZIKV disease dynamics and evaluate the effectiveness of different containment strategies, we propose a compartmental model with a vector-host structure for ZIKV. The model utilizes logistic growth in human population and dynamic growth in vector population. Using this model, we derive the basic reproduction number to gain insight on containment strategies. We contrast the impact and influence of different parameters on the virus trend and outbreak spread. We also evaluate different containment strategies and their combination effects to achieve early containment by minimizing total infections. This result can help decision makers select and invest in the strategies most effective to combat the infection spread. The decision-support tool demonstrates the importance of “digital disease surveillance” in response to waves of epidemics including ZIKV, Dengue, Ebola and cholera. PMID:28269870
Compartmental and Data-Based Modeling of Cerebral Hemodynamics: Nonlinear Analysis.
Henley, Brandon; Shin, Dae; Zhang, Rong; Marmarelis, Vasilis
2016-07-09
Objective-As an extension to our study comparing a putative compartmental and data-based model of linear dynamic cerebral autoregulation (CA) and CO2-vasomotor reactivity (VR), we study the CA-VR process in a nonlinear context. Methods- We use the concept of Principal Dynamic Modes (PDM) in order to obtain a compact and more easily interpretable input-output model. This in silico study permits the use of input data with a dynamic range large enough to simulate the classic homeostatic CA and VR curves using a putative structural model of the regulatory control of the cerebral circulation. The PDM model obtained using theoretical and experimental data are compared. Results- It was found that the PDM model was able to reflect accurately both the simulated static CA and VR curves in the Associated Nonlinear Functions (ANFs). Similar to experimental observations, the PDM model essentially separates the pressure-flow relationship into a linear component with fast dynamics and nonlinear components with slow dynamics. In addition, we found good qualitative agreement between the PDMs representing the dynamic theoretical and experimental CO2-flow relationship. Conclusion- Under the modeling assumption and in light of other experimental findings, we hypothesize that PDMs obtained from experimental data correspond with passive fluid dynamical and active regulatory mechanisms. Significance- Both hypothesis-based and data-based modeling approaches can be combined to offer some insight into the physiological basis of PDM model obtained from human experimental data. The PDM modeling approach potentially offers a practical way to quantify the status of specific regulatory mechanisms in the CA-VR process.
The Arab Spring: A Simple Compartmental Model for the Dynamics of a Revolution
Lang, John
2012-01-01
The self-immolation of Mohamed Bouazizi on December 17, 2011 in the small Tunisian city of Sidi Bouzid, set off a sequence of events culminating in the revolutions of the Arab Spring. It is widely believed that the Internet and social media played a critical role in the growth and success of protests that led to the downfall of the regimes in Egypt and Tunisia. However, the precise mechanisms by which these new media affected the course of events remain unclear. We introduce a simple compartmental model for the dynamics of a revolution in a dictatorial regime such as Tunisia or Egypt which takes into account the role of the Internet and social media. An elementary mathematical analysis of the model identifies four main parameter regions: stable police state, meta-stable police state, unstable police state, and failed state. We illustrate how these regions capture, at least qualitatively, a wide range of scenarios observed in the context of revolutionary movements by considering the revolutions in Tunisia and ...
A Likelihood Approach for Real-Time Calibration of Stochastic Compartmental Epidemic Models
Zimmer, Christoph; Cohen, Ted
2017-01-01
Stochastic transmission dynamic models are especially useful for studying the early emergence of novel pathogens given the importance of chance events when the number of infectious individuals is small. However, methods for parameter estimation and prediction for these types of stochastic models remain limited. In this manuscript, we describe a calibration and prediction framework for stochastic compartmental transmission models of epidemics. The proposed method, Multiple Shooting for Stochastic systems (MSS), applies a linear noise approximation to describe the size of the fluctuations, and uses each new surveillance observation to update the belief about the true epidemic state. Using simulated outbreaks of a novel viral pathogen, we evaluate the accuracy of MSS for real-time parameter estimation and prediction during epidemics. We assume that weekly counts for the number of new diagnosed cases are available and serve as an imperfect proxy of incidence. We show that MSS produces accurate estimates of key epidemic parameters (i.e. mean duration of infectiousness, R0, and Reff) and can provide an accurate estimate of the unobserved number of infectious individuals during the course of an epidemic. MSS also allows for accurate prediction of the number and timing of future hospitalizations and the overall attack rate. We compare the performance of MSS to three state-of-the-art benchmark methods: 1) a likelihood approximation with an assumption of independent Poisson observations; 2) a particle filtering method; and 3) an ensemble Kalman filter method. We find that MSS significantly outperforms each of these three benchmark methods in the majority of epidemic scenarios tested. In summary, MSS is a promising method that may improve on current approaches for calibration and prediction using stochastic models of epidemics. PMID:28095403
A Likelihood Approach for Real-Time Calibration of Stochastic Compartmental Epidemic Models.
Zimmer, Christoph; Yaesoubi, Reza; Cohen, Ted
2017-01-01
Stochastic transmission dynamic models are especially useful for studying the early emergence of novel pathogens given the importance of chance events when the number of infectious individuals is small. However, methods for parameter estimation and prediction for these types of stochastic models remain limited. In this manuscript, we describe a calibration and prediction framework for stochastic compartmental transmission models of epidemics. The proposed method, Multiple Shooting for Stochastic systems (MSS), applies a linear noise approximation to describe the size of the fluctuations, and uses each new surveillance observation to update the belief about the true epidemic state. Using simulated outbreaks of a novel viral pathogen, we evaluate the accuracy of MSS for real-time parameter estimation and prediction during epidemics. We assume that weekly counts for the number of new diagnosed cases are available and serve as an imperfect proxy of incidence. We show that MSS produces accurate estimates of key epidemic parameters (i.e. mean duration of infectiousness, R0, and Reff) and can provide an accurate estimate of the unobserved number of infectious individuals during the course of an epidemic. MSS also allows for accurate prediction of the number and timing of future hospitalizations and the overall attack rate. We compare the performance of MSS to three state-of-the-art benchmark methods: 1) a likelihood approximation with an assumption of independent Poisson observations; 2) a particle filtering method; and 3) an ensemble Kalman filter method. We find that MSS significantly outperforms each of these three benchmark methods in the majority of epidemic scenarios tested. In summary, MSS is a promising method that may improve on current approaches for calibration and prediction using stochastic models of epidemics.
Cosmological Models with Fractional Derivatives and Fractional Action Functional
Institute of Scientific and Technical Information of China (English)
V.K. Shchigolev
2011-01-01
Cosmological models of a scalar field with dynamical equations containing fractional derivatives or derived from the Einstein-Hilbert action of fractional order, are constructed. A number of exact solutions to those equations of fractional cosmological models in both eases is given.
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Stefano eMasoli
2015-02-01
Full Text Available The Purkinje cell (PC is among the most complex neurons in the brain and plays a critical role for cerebellar functioning. PCs operate as fast pacemakers modulated by synaptic inputs but can switch from simple spikes to complex bursts and, in some conditions, show bistability. In contrast to original works emphasizing dendritic Ca-dependent mechanisms, recent experiments have supported a primary role for axonal Na-dependent processing, which could effectively regulate spike generation and transmission to deep cerebellar nuclei (DCN. In order to account for the numerous ionic mechanisms involved (at present including Nav1.6, Cav2.1, Cav3.1, Cav3.2, Cav3.3, Kv1.1, Kv1.5, Kv3.3, Kv3.4, Kv4.3, KCa1.1, KCa2.2, KCa3.1, Kir2.x, HCN1, we have elaborated a multicompartmental model incorporating available knowledge on localization and gating of PC ionic channels. The axon, including initial segment (AIS and Ranvier nodes (RNs, proved critical to obtain appropriate pacemaking and firing frequency modulation. Simple spikes initiated in the AIS and protracted discharges were stabilized in the soma through Na-dependent mechanisms, while somato-dendritic Ca channels contributed to sustain pacemaking and to generate complex bursting at high discharge regimes. Bistability occurred only following Na and Ca channel down-regulation. In addition, specific properties in RNs K currents were required to limit spike transmission frequency along the axon. The model showed how organized electroresponsive functions could emerge from the molecular complexity of PCs and showed that the axon is fundamental to complement ionic channel compartmentalization enabling action potential processing and transmission of specific spike patterns to DCN.
Linear regressive model structures for estimation and prediction of compartmental diffusive systems
Vries, D.; Keesman, K.J.; Zwart, H.
2006-01-01
Abstract In input-output relations of (compartmental) diffusive systems, physical parameters appear non-linearly, resulting in the use of (constrained) non-linear parameter estimation techniques with its short-comings regarding global optimality and computational effort. Given a LTI system in state
Linear regressive model structures for estimation and prediction of compartmental diffusive systems
Vries, D.; Keesman, K.J.; Zwart, H.J.
2006-01-01
In input-output relations of (compartmental) diffusive systems, physical parameters appear non-linearly, resulting in the use of (constrained) non-linear parameter estimation techniques with its short-comings regarding global optimality and computational effort. Given a LTI system in state space for
Generaux, Claudia N; Ainslie, Garrett R; Bridges, Arlene S; Ismail, Mohamed A; Boykin, David W; Tidwell, Richard R; Thakker, Dhiren R; Paine, Mary F
2013-02-01
DB868 [2,5-bis [5-(N-methoxyamidino)-2-pyridyl] furan], a prodrug of the diamidine DB829 [2,5-bis(5-amidino-2-pyridyl) furan], has demonstrated efficacy in murine models of human African trypanosomiasis. A cross-species evaluation of prodrug bioconversion to the active drug is required to predict the disposition of prodrug, metabolites, and active drug in humans. The phase I biotransformation of DB868 was elucidated using liver microsomes and sandwich-cultured hepatocytes from humans and rats. All systems produced four NADPH-dependent metabolites via O-demethylation (M1, M2) and N-dehydroxylation (M3, M4). Compartmental kinetic modeling of the DB868 metabolic pathway suggested an unusual N-demethoxylation reaction that was supported experimentally. A unienzyme Michaelis-Menten model described the kinetics of M1 formation by human liver microsomes (HLMs) (K(m), 11 μM; V(max), 340 pmol/min/mg), whereas a two-enzyme model described the kinetics of M1 formation by rat liver microsomes (RLMs) (K(m1), 0.5 μM; V(max1), 12 pmol/min/mg; K(m2), 27 μM; V(max2), 70 pmol/min/mg). Human recombinant CYP1A2, CYP3A4, and CYP4F2, rat recombinant Cyp1a2 and Cyp2d2, and rat purified Cyp4f1 catalyzed M1 formation. M2 formation by HLMs exhibited allosteric kinetics (S(50), 18 μM; V(max), 180 pmol/mg), whereas M2 formation by RLMs was negligible. Recombinant CYP1A2/Cyp1a2 catalyzed M2 formation. DB829 was detected in trace amounts in HLMs at the end of the 180-min incubation and was detected readily in sandwich-cultured hepatocytes from both species throughout the 24-h incubation. These studies demonstrated that DB868 biotransformation to DB829 is conserved between humans and rats. An improved understanding of species differences in the kinetics of DB829 formation would facilitate preclinical development of a promising antitrypanosomal prodrug.
Computer Modeling of Sand Transport on Mars Using a Compart-Mentalized Fluids Algorithm (CFA)
Marshall, J.; Stratton, D.
1999-01-01
of sand comminution on Mars. A multiple-grain transport model using just the equations of grain motion describing lift and drag is impossible to develop owing to stochastic effects --the very effects we wish to model. Also, unless we were to employ supercomputing techniques and extremely complex computer codes that could deal with millions of grains simultaneously, it would also be difficult to model grain transport if we attempted to consider every grain in motion. No existing computer models were found that satisfactorily used the equations of motion to arrive at transport flux numbers for the different populations of saltation and reptation. Modeling all the grains in a transport system was an intractable problem within our resources, and thus we developed what we believe to be a new modeling approach to simulating grain transport. The CFA deals with grain populations, but considers them to belong to various compartmentalized fluid units in the boundary layer. In this way, the model circumvents the multigrain problem by dealing primarily with the consequences of grain transport --momentum transfer between air and grains, which is the physical essence of a dynamic grain-fluid mixture. We thus chose to model the aeolian transport process as a superposition of fluids. These fluids include the air as well as particle populations of various properties. The prime property distinguishing these fluids is upward and downward grain motion. In a normal saltation trajectory, a grain's downwind velocity increases with time, so a rising grain will have a smaller downwind velocity than a failing grain. Because of this disparity in rising and falling grain proper-ties, it seemed appropriate to track these as two separate grain populations within the same physical space. The air itself can be considered a separate fluid superimposed within and interacting with the various grain-cloud "fluids". Additional informaiton is contained in the original.
Radical pathway in catecholase activity with zinc-based model complexes of compartmental ligands.
Guha, Averi; Chattopadhyay, Tanmay; Paul, Nanda Dulal; Mukherjee, Madhuparna; Goswami, Somen; Mondal, Tapan Kumar; Zangrando, Ennio; Das, Debasis
2012-08-20
Four dinuclear and three mononuclear Zn(II) complexes of phenol-based compartmental ligands (HL(1)-HL(7)) have been synthesized with the aim to investigate the viability of a radical pathway in catecholase activity. The complexes have been characterized by routine physicochemical studies as well as X-ray single-crystal structure analysis: [Zn(2)(H(2)L(1))(OH)(H(2)O)(NO(3))](NO(3))(3) (1), [Zn(2)L(2)Cl(3)] (2), [Zn(2)L(3)Cl(3)] (3), [Zn(2)(L(4))(2)(CH(3)COO)(2)] (4), [Zn(HL(5))Cl(2)] (5), [Zn(HL(6))Cl(2)] (6), and [Zn(HL(7))Cl(2)] (7) [L(1)-L(3) and L(5)-L(7) = 2,6-bis(R-iminomethyl)-4-methylphenolato, where R= N-ethylpiperazine for L(1), R = 2-(N-ethyl)pyridine for L(2), R = N-ethylpyrrolidine for L(3), R = N-methylbenzene for L(5), R = 2-(N-methyl)thiophene for L(6), R = 2-(N-ethyl)thiophene for L(7), and L(4) = 2-formyl-4-methyl-6-N-methylbenzene-iminomethyl-phenolato]. Catecholase-like activity of the complexes has been investigated in methanol medium by UV-vis spectrophotometric study using 3,5-di-tert-butylcatechol as model substrate. All complexes are highly active in catalyzing the aerobic oxidation of 3,5-di-tert-butylcatechol (3,5-DTBC) to 3,5-di-tert-butylbenzoquinone (3,5-DTBQ). Conversion of 3,5-DTBC to 3,5-DTBQ catalyzed by mononuclear complexes (5-7) is observed to proceed via formation of two enzyme-substrate adducts, ES1 and ES2, detected spectroscopically, a finding reported for the first time in any Zn(II) complex catalyzed oxidation of catechol. On the other hand, no such enzyme-substrate adduct has been identified, and 3,5-DTBC to 3,5-DTBQ conversion is observed to be catalyzed by the dinuclear complexes (1-4) very smoothly. EPR experiment suggests generation of radicals in the presence of 3,5-DTBC, and that finding has been strengthened by cyclic voltammetric study. Thus, it may be proposed that the radical pathway is probably responsible for conversion of 3,5-DTBC to 3,5-DTBQ promoted by complexes of redox-innocent Zn(II) ion. The ligand
Directory of Open Access Journals (Sweden)
Valdur Saks
2011-12-01
Full Text Available In this review we analyze the recent important and remarkable advancements in studies of compartmentation of adenine nucleotides in muscle cells due to their binding to macromolecular complexes and cellular structures, which results in non-equilibrium steady state of the creatine kinase reaction. We discuss the problems of measuring the energy fluxes between different cellular compartments and their simulation by using different computer models. Energy flux determinations by 18O transfer method have shown that in heart about 80% of energy is carried out of mitochondrial intermembrane space into cytoplasm by phosphocreatine fluxes generated by mitochondrial creatine kinase from adenosine triphosphate (ATP, produced by ATP Synthasome. We have applied the mathematical model of compartmentalized energy transfer for analysis of experimental data on the dependence of oxygen consumption rate on heart workload in isolated working heart reported by Williamson et al. The analysis of these data show that even at the maximal workloads and respiration rates, equal to 174 µmol O2 per min per g dry weight, phosphocreatine flux, and not ATP, carries about 80–85% percent of energy needed out of mitochondria into the cytosol. We analyze also the reasons of failures of several computer models published in the literature to correctly describe the experimental data.
A compartmental model predicts that dietary potassium affects lithium dynamics in rats.
Everts, H B; Jang, H; Boston, R C; Canolty, N L
1996-05-01
Lithium is the treatment of choice for manic depression, but therapy often results in nephrogenic diabetes insipidus and lithium intoxication. To investigate the effects of dietary potassium on potential side effects of lithium therapy, a mathematical model was built using the modeling program SAAM (Simulation, Analysis, And Modeling). Experimental data modeled were from adult male Sprague-Dawley rats fed diets with or without lithium and one of three levels of potassium for 17 d. A five-compartment model of lithium dynamics was built that was consistent with data from rats fed a lithium-containing diet adequate in potassium. This model was then compared with data from rats fed the other two lithium-containing diets. The model predicts that both the fractional transfer coefficient and rate of transport of lithium to the serum compartment from the kidney compartment are lower in rats fed the potassium-adequate diet than in those fed the potassium-deficient diet, and even lower in those fed the potassium-supplemented diet. In addition, fractional transfer coefficients into the serum compartment from the sampled and simulated tissue compartments changed differently with time depending on the amount of dietary potassium. The model also predicts that there would be less accumulation of lithium in the kidney, sampled tissue and simulated tissue compartments with supplemental dietary potassium. The model suggests that potassium supplementation, after a 7-d delay, protects against nephrogenic diabetes insipidus and the potentially toxic accumulation of lithium by decreasing the reabsorption of lithium from the kidneys and increasing lithium efflux from the tissues.
A fractional model for dye removal
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Ji-Huan He
2016-01-01
Full Text Available The adsorption process has a fractional property, and a fractional model is suggested to study a transport model of direct textile industry wastewater. An approximate solution of the concentration is obtained by the variational iteration method.
DEFF Research Database (Denmark)
Parlesak, Alexandr; Haller, D.; Brinz, S.
2004-01-01
To further investigate the interaction between human mononuclear leucocytes [peripheral blood mononuclear cells (PBMC)] and enterocytes, the effect of a confluent layer of differentiated CACO-2 cells on cytokine kinetics during challenge with bacteria in a compartmentalized coculture model...... cells when leucocytes were stimulated directly with bacteria. This suppression was not paralleled by changes in the production of IL-10, IL-6 and transforming growth factor (TGF)-beta. When the bacteria were applied apically to the CACO-2 cell layer, the production of TNF-alpha, IL-12, IL-1beta, IL-8...... analysis revealed that IL-8 gene expression was equally induced in both CACO-2 and PBMC after apical stimulation with bacteria. Of note, bacteria-stimulated CACO-2 cells produced little or no cytokines in the absence of leucocytes, supporting the concept of leucocyte-epithelial cell cross...
McMurtrey, Richard J
2016-01-01
Biomaterials are becoming an essential tool in the study and application of stem cell research. Various types of biomaterials enable three-dimensional culture of stem cells, and, more recently, also enable high-resolution patterning and organization of multicellular architectures. Biomaterials also hold potential to provide many additional advantages over cell transplants alone in regenerative medicine. This article describes novel designs for functionalized biomaterial constructs that guide tissue development to targeted regional identities and structures. Such designs comprise compartmentalized regions in the biomaterial structure that are functionalized with molecular factors that form concentration gradients through the construct and guide stem cell development, axis patterning, and tissue architecture, including rostral/caudal, ventral/dorsal, or medial/lateral identities of the central nervous system. The ability to recapitulate innate developmental processes in a three-dimensional environment and under specific controlled conditions has vital application to advanced models of neurodevelopment and for repair of specific sites of damaged or diseased neural tissue.
Mathematical modelling of fractional order circuits
Moreles, Miguel Angel
2016-01-01
In this work a classical derivation of fractional order circuits models is presented. Generalized constitutive equations in terms of fractional Riemann-Liouville derivatives are introduced in the Maxwell's equations. Next the Kirchhoff voltage law is applied in a RCL circuit configuration. A fractional differential equation model is obtained with Caputo derivatives. Thus standard initial conditions apply.
Fractional constant elasticity of variance model
Ngai Hang Chan; Chi Tim Ng
2007-01-01
This paper develops a European option pricing formula for fractional market models. Although there exist option pricing results for a fractional Black-Scholes model, they are established without accounting for stochastic volatility. In this paper, a fractional version of the Constant Elasticity of Variance (CEV) model is developed. European option pricing formula similar to that of the classical CEV model is obtained and a volatility skew pattern is revealed.
Brenner, F.; Hoffmann, P.; Marwan, N.
2016-12-01
Infectious diseases are a major threat to human health. The spreading of airborne diseases has become fast and hard to predict. Global air travelling created a network which allows a pathogen to migrate worldwide in only a few days. Pandemics of SARS (2002/03) and H1N1 (2009) have impressively shown the epidemiological danger in a strongly connected world. In this study we simulate the outbreak of an airborne infectious disease that is directly transmitted from human to human. We use a regular Susceptible-Infected-Recovered (SIR) model and a modified Susceptible-Exposed-Infected-Recovered (SEIR) compartmental approach with the basis of a complex network built by global air traffic data (from openflights.org). Local Disease propagation is modeled with a global population dataset (from SEDAC and MaxMind) and parameterizations of human behavior regarding mobility, contacts and awareness. As a final component we combine the worldwide outbreak simulation with daily averaged climate data from WATCH-Forcing-Data-ERA-Interim (WFDEI) and Coupled Model Intercomparison Project Phase 5 (CMIP5). Here we focus on Influenza-like illnesses (ILI), whose transmission rate has a dependency on relative humidity and temperature. Even small changes in relative humidity are sufficient to trigger significant differences in the global outbreak behavior. Apart from the direct effect of climate change on the transmission of airborne diseases, there are indirect ramifications that alter spreading patterns. For example seasonal changing human mobility is influenced by climate settings.
Fractional Order Models of Industrial Pneumatic Controllers
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Abolhassan Razminia
2014-01-01
Full Text Available This paper addresses a new approach for modeling of versatile controllers in industrial automation and process control systems such as pneumatic controllers. Some fractional order dynamical models are developed for pressure and pneumatic systems with bellows-nozzle-flapper configuration. In the light of fractional calculus, a fractional order derivative-derivative (FrDD controller and integral-derivative (FrID are remodeled. Numerical simulations illustrate the application of the obtained theoretical results in simple examples.
Review of Some Promising Fractional Physical Models
Tarasov, Vasily E
2015-01-01
Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law non-locality, power-law long-term memory or fractal properties by using integrations and differentiation of non-integer orders, i.e., by methods of the fractional calculus. This paper is a review of physical models that look very promising for future development of fractional dynamics. We suggest a short introduction to fractional calculus as a theory of integration and differentiation of non-integer order. Some applications of integro-differentiations of fractional orders in physics are discussed. Models of discrete systems with memory, lattice with long-range inter-particle interaction, dynamics of fractal media are presented. Quantum analogs of fractional derivatives and model of open nano-system systems with memory are also discussed.
Liu, Huolong; Li, Mingzhong
2014-11-20
In this work a two-compartmental population balance model (TCPBM) was proposed to model a pulsed top-spray fluidized bed granulation. The proposed TCPBM considered the spatially heterogeneous granulation mechanisms of the granule growth by dividing the granulator into two perfectly mixed zones of the wetting compartment and drying compartment, in which the aggregation mechanism was assumed in the wetting compartment and the breakage mechanism was considered in the drying compartment. The sizes of the wetting and drying compartments were constant in the TCPBM, in which 30% of the bed was the wetting compartment and 70% of the bed was the drying compartment. The exchange rate of particles between the wetting and drying compartments was determined by the details of the flow properties and distribution of particles predicted by the computational fluid dynamics (CFD) simulation. The experimental validation has shown that the proposed TCPBM can predict evolution of the granule size and distribution within the granulator under different binder spray operating conditions accurately. Copyright © 2014 Elsevier B.V. All rights reserved.
Wang, Kai; Riera, Jorge; Enjieu-Kadji, Herve; Kawashima, Ryuta
2013-07-01
With the rapid increase in the number of technologies aimed at observing electric activity inside the brain, scientists have felt the urge to create proper links between intracellular- and extracellular-based experimental approaches. Biophysical models at both physical scales have been formalized under assumptions that impede the creation of such links. In this work, we address this issue by proposing a multicompartment model that allows the introduction of complex extracellular and intracellular resistivity profiles. This model accounts for the geometrical and electrotonic properties of any type of neuron through the combination of four devices: the integrator, the propagator, the 3D connector, and the collector. In particular, we applied this framework to model the tufted pyramidal cells of layer 5 (PCL5) in the neocortex. Our model was able to reproduce the decay and delay curves of backpropagating action potentials (APs) in this type of cell with better agreement with experimental data. We used the voltage drops of the extracellular resistances at each compartment to approximate the local field potentials generated by a PCL5 located in close proximity to linear microelectrode arrays. Based on the voltage drops produced by backpropagating APs, we were able to estimate the current multipolar moments generated by a PCL5. By adding external current sources in parallel to the extracellular resistances, we were able to create a sensitivity profile of PCL5 to electric current injections from nearby microelectrodes. In our model for PCL5, the kinetics and spatial profile of each ionic current were determined based on a literature survey, and the geometrical properties of these cells were evaluated experimentally. We concluded that the inclusion of the extracellular space in the compartmental models of neurons as an extra electrotonic medium is crucial for the accurate simulation of both the propagation of the electric potentials along the neuronal dendrites and the
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Silva, Joao Eduardo Maeda Moreira da; Furuie, Sergio Shiguemi [Universidade de Sao Paulo (USP), SP (Brazil). Dept. de Engenharia de Telecomunicacoes e Controle. Lab. de Engenharia Biomedica
2011-12-15
The objective of this work is the determination of the most adequate compartmental model for the study of physiological dynamics based on positron emission tomography exams. We propose the use of Akaike's information criterion for the optimal model selection, and Levenberg-Marquardt algorithm with sensitivity equations for the task of estimating the characteristic parameters of the differential equations describing the models. We have considered three compartmental structures represented, respectively, by two compartments and two characteristic constants, three compartments and four characteristic constants and four compartments and six characteristics constants. The data considered in this work were synthesized taking into account key features of a real tomography exam, such as type and level of noise and morphology of the input function of the system. Applying the proposed methodology with three noise levels (low, medium and high), we obtained agreement of the best model with strong and considerable degrees (with Kappa indexes equal to 0.95, 0.93 and 0.63, respectively). It was observed that, with high noise level and more complex models (four compartments), the classification is deteriorated due to lack of data for the decision. Programs have been developed and a graphical interface that can be used in research, development, simulation and parameter identification of compartmental models, supporting analysis of clinical diagnostics and scientific practices. (author)
A Fractionally Integrated Wishart Stochastic Volatility Model
M. Asai (Manabu); M.J. McAleer (Michael)
2013-01-01
textabstractThere has recently been growing interest in modeling and estimating alternative continuous time multivariate stochastic volatility models. We propose a continuous time fractionally integrated Wishart stochastic volatility (FIWSV) process. We derive the conditional Laplace transform of
McMurtrey, Richard J
2016-01-01
Biomaterials are becoming an essential tool in the study and application of stem cell research. Various types of biomaterials enable three-dimensional culture of stem cells, and, more recently, also enable high-resolution patterning and organization of multicellular architectures. Biomaterials also hold potential to provide many additional advantages over cell transplants alone in regenerative medicine. This article describes novel designs for functionalized biomaterial constructs that guide tissue development to targeted regional identities and structures. Such designs comprise compartmentalized regions in the biomaterial structure that are functionalized with molecular factors that form concentration gradients through the construct and guide stem cell development, axis patterning, and tissue architecture, including rostral/caudal, ventral/dorsal, or medial/lateral identities of the central nervous system. The ability to recapitulate innate developmental processes in a three-dimensional environment and under specific controlled conditions has vital application to advanced models of neurodevelopment and for repair of specific sites of damaged or diseased neural tissue. PMID:27766141
Directory of Open Access Journals (Sweden)
Richard J McMurtrey
2016-10-01
Full Text Available Biomaterials are becoming an essential tool in the study and application of stem cell research. Various types of biomaterials enable three-dimensional culture of stem cells, and, more recently, also enable high-resolution patterning and organization of multicellular architectures. Biomaterials also hold potential to provide many additional advantages over cell transplants alone in regenerative medicine. This article describes novel designs for functionalized biomaterial constructs that guide tissue development to targeted regional identities and structures. Such designs comprise compartmentalized regions in the biomaterial structure that are functionalized with molecular factors that form concentration gradients through the construct and guide stem cell development, axis patterning, and tissue architecture, including rostral/caudal, ventral/dorsal, or medial/lateral identities of the central nervous system. The ability to recapitulate innate developmental processes in a three-dimensional environment and under specific controlled conditions has vital application to advanced models of neurodevelopment and for repair of specific sites of damaged or diseased neural tissue.
Kendrick, Felicity; Evans, Neil D.; Arnulf, Bertrand; Avet-Loiseau, Hervé; Decaux, Olivier; Dejoie, Thomas; Fouquet, Guillemette; Guidez, Stéphanie; Harel, Stéphanie; Hebraud, Benjamin; Javaugue, Vincent; Richez, Valentine; Schraen, Susanna; Touzeau, Cyrille; Moreau, Philippe; Leleu, Xavier; Harding, Stephen; Chappell, Michael J.
2017-01-01
Immunoglobulin G (IgG) metabolism has received much attention in the literature for two reasons: (i) IgG homeostasis is regulated by the neonatal Fc receptor (FcRn), by a pH-dependent and saturable recycling process, which presents an interesting biological system; (ii) the IgG-FcRn interaction may be exploitable as a means for extending the plasma half-life of therapeutic monoclonal antibodies, which are primarily IgG-based. A less-studied problem is the importance of endogenous IgG metabolism in IgG multiple myeloma. In multiple myeloma, quantification of serum monoclonal immunoglobulin plays an important role in diagnosis, monitoring and response assessment. In order to investigate the dynamics of IgG in this setting, a mathematical model characterizing the metabolism of endogenous IgG in humans is required. A number of authors have proposed a two-compartment nonlinear model of IgG metabolism in which saturable recycling is described using Michaelis–Menten kinetics; however it may be difficult to estimate the model parameters from the limited experimental data that are available. The purpose of this study is to analyse the model alongside the available data from experiments in humans and estimate the model parameters. In order to achieve this aim we linearize the model and use several methods of model and parameter validation: stability analysis, structural identifiability analysis, and sensitivity analysis based on traditional sensitivity functions and generalized sensitivity functions. We find that all model parameters are identifiable, structurally and taking into account parameter correlations, when several types of model output are used for parameter estimation. Based on these analyses we estimate parameter values from the limited available data and compare them with previously published parameter values. Finally we show how the model can be applied in future studies of treatment effectiveness in IgG multiple myeloma with simulations of serum monoclonal
Directory of Open Access Journals (Sweden)
Vladimir E Bondarenko
Full Text Available The β1-adrenergic signaling system plays an important role in the functioning of cardiac cells. Experimental data shows that the activation of this system produces inotropy, lusitropy, and chronotropy in the heart, such as increased magnitude and relaxation rates of [Ca(2+]i transients and contraction force, and increased heart rhythm. However, excessive stimulation of β1-adrenergic receptors leads to heart dysfunction and heart failure. In this paper, a comprehensive, experimentally based mathematical model of the β1-adrenergic signaling system for mouse ventricular myocytes is developed, which includes major subcellular functional compartments (caveolae, extracaveolae, and cytosol. The model describes biochemical reactions that occur during stimulation of β1-adrenoceptors, changes in ionic currents, and modifications of Ca(2+ handling system. Simulations describe the dynamics of major signaling molecules, such as cyclic AMP and protein kinase A, in different subcellular compartments; the effects of inhibition of phosphodiesterases on cAMP production; kinetics and magnitudes of phosphorylation of ion channels, transporters, and Ca(2+ handling proteins; modifications of action potential shape and duration; magnitudes and relaxation rates of [Ca(2+]i transients; changes in intracellular and transmembrane Ca(2+ fluxes; and [Na(+]i fluxes and dynamics. The model elucidates complex interactions of ionic currents upon activation of β1-adrenoceptors at different stimulation frequencies, which ultimately lead to a relatively modest increase in action potential duration and significant increase in [Ca(2+]i transients. In particular, the model includes two subpopulations of the L-type Ca(2+ channels, in caveolae and extracaveolae compartments, and their effects on the action potential and [Ca(2+]i transients are investigated. The presented model can be used by researchers for the interpretation of experimental data and for the developments of
Giraudeau, Céline; Leporq, Benjamin; Doblas, Sabrina; Lagadec, Matthieu; Pastor, Catherine M; Daire, Jean-Luc; Van Beers, Bernard E
2017-05-01
Changes in the expression of hepatocyte membrane transporters in advanced fibrosis decrease the hepatic transport function of organic anions. The aim of our study was to assess if these changes can be evaluated with pharmacokinetic analysis of the hepatobiliary transport of the MR contrast agent gadoxetate. Dynamic gadoxetate-enhanced MRI was performed in 17 rats with advanced fibrosis and 8 normal rats. After deconvolution, hepatocyte three-compartmental analysis was performed to calculate the hepatocyte influx, biliary efflux and sinusoidal backflux rates. The expression of Oatp1a1, Mrp2 and Mrp3 organic anion membrane transporters was assessed with reverse transcription polymerase chain reaction. In the rats with advanced fibrosis, the influx and efflux rates of gadoxetate decreased and the backflux rate increased significantly (p = 0.003, 0.041 and 0.010, respectively). Significant correlations were found between influx and Oatp1a1 expression (r = 0.78, p liver fibrosis can be assessed with compartmental analysis of gadoxetate-enhanced MRI. • Expression of hepatocyte transporters is modified in rats with advanced liver fibrosis. • Kinetic parameters at gadoxetate-enhanced MRI are correlated with hepatocyte transporter expression. • Hepatocyte transport function can be assessed with compartmental analysis of gadoxetate-enhanced MRI. • Compartmental analysis of gadoxetate-enhanced MRI might provide biomarkers in advanced liver fibrosis.
Multi-Fraction Bayesian Sediment Transport Model
Directory of Open Access Journals (Sweden)
Mark L. Schmelter
2015-09-01
Full Text Available A Bayesian approach to sediment transport modeling can provide a strong basis for evaluating and propagating model uncertainty, which can be useful in transport applications. Previous work in developing and applying Bayesian sediment transport models used a single grain size fraction or characterized the transport of mixed-size sediment with a single characteristic grain size. Although this approach is common in sediment transport modeling, it precludes the possibility of capturing processes that cause mixed-size sediments to sort and, thereby, alter the grain size available for transport and the transport rates themselves. This paper extends development of a Bayesian transport model from one to k fractional dimensions. The model uses an existing transport function as its deterministic core and is applied to the dataset used to originally develop the function. The Bayesian multi-fraction model is able to infer the posterior distributions for essential model parameters and replicates predictive distributions of both bulk and fractional transport. Further, the inferred posterior distributions are used to evaluate parametric and other sources of variability in relations representing mixed-size interactions in the original model. Successful OPEN ACCESS J. Mar. Sci. Eng. 2015, 3 1067 development of the model demonstrates that Bayesian methods can be used to provide a robust and rigorous basis for quantifying uncertainty in mixed-size sediment transport. Such a method has heretofore been unavailable and allows for the propagation of uncertainty in sediment transport applications.
Fractionally Integrated Models With ARCH Errors
Hauser, Michael A.; Kunst, Robert M.
1993-01-01
Abstract: We introduce ARFIMA-ARCH models which simultaneously incorporate fractional differencing and conditional heteroskedasticity. We develop the likelihood function and a numerical estimation procedure for this model class. Two ARCH models - Engle- and Weiss-type - are explicitly treated and stationarity conditions are derived. Finite-sample properties of the estimation procedure are explored by Monte Carlo simulation. An application to the Standard & Poor 500 Index indicates existence o...
A Fractional Micro-Macro Model for Crowds of Pedestrians based on Fractional Mean Field Games
Cao, Ke-cai; Stuart, Dan
2016-01-01
Modeling of crowds of pedestrians has been considered in this paper from different aspects. Based on fractional microscopic model that may be much more close to reality, a fractional macroscopic model has been proposed using conservation law of mass. Then in order to characterize the competitive and cooperative interactions among pedestrians, fractional mean field games are utilized in the modeling problem when the number of pedestrians goes to infinity and fractional dynamic model composed of fractional backward and fractional forward equations are constructed in macro scale. Fractional micro-macro model for crowds of pedestrians are obtained in the end. Simulation results are also included to illustrate the proposed fractional microscopic model and fractional macroscopic model respectively.
Modeling Students' Mathematics Using Steffe's Fraction Schemes
Norton, Anderson H.; McCloskey, Andrea V.
2008-01-01
Each year, more teachers learn about the successful intervention program known as Math Recovery (USMRC 2008; Wright 2003). The program uses Steffe's whole-number schemes to model, understand, and support children's development of whole-number reasoning. Readers are probably less familiar with Steffe's fraction schemes, which have proven similarly…
Berglund, Martin; Sunnåker, Mikael; Adiels, Martin; Jirstrand, Mats; Wennberg, Bernt
2012-12-01
Non-linear mixed effects (NLME) models represent a powerful tool to simultaneously analyse data from several individuals. In this study, a compartmental model of leucine kinetics is examined and extended with a stochastic differential equation to model non-steady-state concentrations of free leucine in the plasma. Data obtained from tracer/tracee experiments for a group of healthy control individuals and a group of individuals suffering from diabetes mellitus type 2 are analysed. We find that the interindividual variation of the model parameters is much smaller for the NLME models, compared to traditional estimates obtained from each individual separately. Using the mixed effects approach, the population parameters are estimated well also when only half of the data are used for each individual. For a typical individual, the amount of free leucine is predicted to vary with a standard deviation of 8.9% around a mean value during the experiment. Moreover, leucine degradation and protein uptake of leucine is smaller, proteolysis larger and the amount of free leucine in the body is much larger for the diabetic individuals than the control individuals. In conclusion, NLME models offers improved estimates for model parameters in complex models based on tracer/tracee data and may be a suitable tool to reduce data sampling in clinical studies.
Fractional dynamical model for neurovascular coupling
Belkhatir, Zehor
2014-08-01
The neurovascular coupling is a key mechanism linking the neural activity to the hemodynamic behavior. Modeling of this coupling is very important to understand the brain function but it is at the same time very complex due to the complexity of the involved phenomena. Many studies have reported a time delay between the neural activity and the cerebral blood flow, which has been described by adding a delay parameter in some of the existing models. An alternative approach is proposed in this paper, where a fractional system is used to model the neurovascular coupling. Thanks to its nonlocal property, a fractional derivative is suitable for modeling the phenomena with delay. The proposed model is coupled with the first version of the well-known balloon model, which relates the cerebral blood flow to the Blood Oxygen Level Dependent (BOLD) signal measured using functional Magnetic Resonance Imaging (fMRI). Through some numerical simulations, the properties of the fractional model are explained and some preliminary comparisons to a real BOLD data set are provided. © 2014 IEEE.
Dynamical models of happiness with fractional order
Song, Lei; Xu, Shiyun; Yang, Jianying
2010-03-01
This present study focuses on a dynamical model of happiness described through fractional-order differential equations. By categorizing people of different personality and different impact factor of memory (IFM) with different set of model parameters, it is demonstrated via numerical simulations that such fractional-order models could exhibit various behaviors with and without external circumstance. Moreover, control and synchronization problems of this model are discussed, which correspond to the control of emotion as well as emotion synchronization in real life. This study is an endeavor to combine the psychological knowledge with control problems and system theories, and some implications for psychotherapy as well as hints of a personal approach to life are both proposed.
Evolution of intracellular compartmentalization.
Diekmann, Yoan; Pereira-Leal, José B
2013-01-15
Cells compartmentalize their biochemical functions in a variety of ways, notably by creating physical barriers that separate a compartment via membranes or proteins. Eukaryotes have a wide diversity of membrane-based compartments, many that are lineage- or tissue-specific. In recent years, it has become increasingly evident that membrane-based compartmentalization of the cytosolic space is observed in multiple prokaryotic lineages, giving rise to several types of distinct prokaryotic organelles. Endosymbionts, previously believed to be a hallmark of eukaryotes, have been described in several bacteria. Protein-based compartments, frequent in bacteria, are also found in eukaryotes. In the present review, we focus on selected intracellular compartments from each of these three categories, membrane-based, endosymbiotic and protein-based, in both prokaryotes and eukaryotes. We review their diversity and the current theories and controversies regarding the evolutionary origins. Furthermore, we discuss the evolutionary processes acting on the genetic basis of intracellular compartments and how those differ across the domains of life. We conclude that the distinction between eukaryotes and prokaryotes no longer lies in the existence of a compartmentalized cell plan, but rather in its complexity.
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Giraudeau, Celine; Leporq, Benjamin; Doblas, Sabrina [University Paris Diderot, Sorbonne Paris Cite, Hopital Beaujon, Laboratory of Imaging Biomarkers, UMR1149 Inserm, Clichy (France); Lagadec, Matthieu; Daire, Jean-Luc; Van Beers, Bernard E. [University Paris Diderot, Sorbonne Paris Cite, Hopital Beaujon, Laboratory of Imaging Biomarkers, UMR1149 Inserm, Clichy (France); Beaujon University Hospital Paris Nord, Department of Radiology, Clichy (France); Pastor, Catherine M. [University Paris Diderot, Sorbonne Paris Cite, Hopital Beaujon, Laboratory of Imaging Biomarkers, UMR1149 Inserm, Clichy (France); Hopitaux Universitaires de Geneve, Departement d' Imagerie et des Sciences de l' Information Medicale, Geneva (Switzerland)
2017-05-15
Changes in the expression of hepatocyte membrane transporters in advanced fibrosis decrease the hepatic transport function of organic anions. The aim of our study was to assess if these changes can be evaluated with pharmacokinetic analysis of the hepatobiliary transport of the MR contrast agent gadoxetate. Dynamic gadoxetate-enhanced MRI was performed in 17 rats with advanced fibrosis and 8 normal rats. After deconvolution, hepatocyte three-compartmental analysis was performed to calculate the hepatocyte influx, biliary efflux and sinusoidal backflux rates. The expression of Oatp1a1, Mrp2 and Mrp3 organic anion membrane transporters was assessed with reverse transcription polymerase chain reaction. In the rats with advanced fibrosis, the influx and efflux rates of gadoxetate decreased and the backflux rate increased significantly (p = 0.003, 0.041 and 0.010, respectively). Significant correlations were found between influx and Oatp1a1 expression (r = 0.78, p < 0.001), biliary efflux and Mrp2 (r = 0.50, p = 0.016) and sinusoidal backflux and Mrp3 (r = 0.61, p = 0.002). These results show that changes in the bidirectional organic anion hepatocyte transport function in rats with advanced liver fibrosis can be assessed with compartmental analysis of gadoxetate-enhanced MRI. (orig.)
Modeling electron fractionalization with unconventional Fock spaces
Cobanera, Emilio
2017-08-01
It is shown that certain fractionally-charged quasiparticles can be modeled on D-dimensional lattices in terms of unconventional yet simple Fock algebras of creation and annihilation operators. These unconventional Fock algebras are derived from the usual fermionic algebra by taking roots (the square root, cubic root, etc) of the usual fermionic creation and annihilation operators. If the fermions carry non-Abelian charges, then this approach fractionalizes the Abelian charges only. In particular, the mth-root of a spinful fermion carries charge e/m and spin 1/2. Just like taking a root of a complex number, taking a root of a fermion yields a mildly non-unique result. As a consequence, there are several possible choices of quantum exchange statistics for fermion-root quasiparticles. These choices are tied to the dimensionality D=1,2,3,\\ldots of the lattice by basic physical considerations. One particular family of fermion-root quasiparticles is directly connected to the parafermion zero-energy modes expected to emerge in certain mesoscopic devices involving fractional quantum Hall states. Hence, as an application of potential mesoscopic interest, I investigate numerically the hybridization of Majorana and parafermion zero-energy edge modes caused by fractionalizing but charge-conserving tunneling.
Positive roles of compartmentalization in internal reactions.
Ichihashi, Norikazu; Yomo, Tetsuya
2014-10-01
Recently, many researchers have attempted to construct artificial cell models using a bottom-up approach in which various biochemical reactions that involve a defined set of molecules are reconstructed in cell-like compartments, such as liposomes and water-in-oil droplets. In many of these studies, the cell-like compartments have acted only as containers for the encapsulated biochemical reactions, whereas other studies have indicated that compartmentalization improves the rates and yields of these reactions. Here, we introduce two ways in which compartmentalization can improve internal reactions: the isolation effect and the condensation effect. These positive effects of compartmentalization might have played an important role in the genesis of the first primitive cell on early Earth.
State-Space Modelling of Loudspeakers using Fractional Derivatives
DEFF Research Database (Denmark)
King, Alexander Weider; Agerkvist, Finn T.
2015-01-01
This work investigates the use of fractional order derivatives in modeling moving-coil loudspeakers. A fractional order state-space solution is developed, leading the way towards incorporating nonlinearities into a fractional order system. The method is used to calculate the response....... It is shown that the identified parameters can be used in a linear fractional order state-space model to simulate the loudspeakers’ time domain response...... of a fractional harmonic oscillator, representing the mechanical part of a loudspeaker, showing the effect of the fractional derivative and its relationship to viscoelasticity. Finally, a loudspeaker model with a fractional order viscoelastic suspension and fractional order voice coil is fit to measurement data...
Billard, L; Dayananda, P W A
2014-03-01
Stochastic population processes have received a lot of attention over the years. One approach focuses on compartmental modeling. Billard and Dayananda (2012) developed one such multi-stage model for epidemic processes in which the possibility that individuals can die at any stage from non-disease related causes was also included. This extra feature is of particular interest to the insurance and health-care industries among others especially when the epidemic is HIV/AIDS. Rather than working with numbers of individuals in each stage, they obtained distributional results dealing with the waiting time any one individual spent in each stage given the initial stage. In this work, the impact of the HIV/AIDS epidemic on several functions relevant to these industries (such as adjustments to premiums) is investigated. Theoretical results are derived, followed by a numerical study.
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Zanzonico, Pat; O' Donoghue, Joseph A.; Humm, John L. [Memorial Sloan Kettering Cancer Center, Department of Medical Physics, New York, NY (United States); Carrasquillo, Jorge A.; Pandit-Taskar, Neeta; Ruan, Shutian; Larson, Steven M. [Memorial Sloan Kettering Cancer Center, Department of Radiology, New York, NY (United States); Smith-Jones, Peter [Memorial Sloan Kettering Cancer Center, Department of Radiology, New York, NY (United States); Stony Brook School of Medicine, Departments of Psychiatry and Radiology, Stony Brook, NY (United States); Divgi, Chaitanya [Columbia University Medical Center, New York, NY (United States); Scott, Andrew M. [La Trobe University, Olivia Newton-John Cancer Research Institute, Melbourne (Australia); Kemeny, Nancy E.; Wong, Douglas; Scheinberg, David [Memorial Sloan Kettering Cancer Center, Department of Medicine, New York, NY (United States); Fong, Yuman [Memorial Sloan Kettering Cancer Center, Department of Surgery, New York, NY (United States); City of Hope, Department of Surgery, Duarte, CA (United States); Ritter, Gerd; Jungbluth, Achem; Old, Lloyd J. [Memorial Sloan Kettering Cancer Center, Ludwig Institute for Cancer Research, New York, NY (United States)
2015-10-15
The molecular specificity of monoclonal antibodies (mAbs) directed against tumor antigens has proven effective for targeted therapy of human cancers, as shown by a growing list of successful antibody-based drug products. We describe a novel, nonlinear compartmental model using PET-derived data to determine the ''best-fit'' parameters and model-derived quantities for optimizing biodistribution of intravenously injected {sup 124}I-labeled antitumor antibodies. As an example of this paradigm, quantitative image and kinetic analyses of anti-A33 humanized mAb (also known as ''A33'') were performed in 11 colorectal cancer patients. Serial whole-body PET scans of {sup 124}I-labeled A33 and blood samples were acquired and the resulting tissue time-activity data for each patient were fit to a nonlinear compartmental model using the SAAM II computer code. Excellent agreement was observed between fitted and measured parameters of tumor uptake, ''off-target'' uptake in bowel mucosa, blood clearance, tumor antigen levels, and percent antigen occupancy. This approach should be generally applicable to antibody-antigen systems in human tumors for which the masses of antigen-expressing tumor and of normal tissues can be estimated and for which antibody kinetics can be measured with PET. Ultimately, based on each patient's resulting ''best-fit'' nonlinear model, a patient-specific optimum mAb dose (in micromoles, for example) may be derived. (orig.)
Fractional Langevin model of gait variability
Directory of Open Access Journals (Sweden)
Latka Miroslaw
2005-08-01
Full Text Available Abstract The stride interval in healthy human gait fluctuates from step to step in a random manner and scaling of the interstride interval time series motivated previous investigators to conclude that this time series is fractal. Early studies suggested that gait is a monofractal process, but more recent work indicates the time series is weakly multifractal. Herein we present additional evidence for the weakly multifractal nature of gait. We use the stride interval time series obtained from ten healthy adults walking at a normal relaxed pace for approximately fifteen minutes each as our data set. A fractional Langevin equation is constructed to model the underlying motor control system in which the order of the fractional derivative is itself a stochastic quantity. Using this model we find the fractal dimension for each of the ten data sets to be in agreement with earlier analyses. However, with the present model we are able to draw additional conclusions regarding the nature of the control system guiding walking. The analysis presented herein suggests that the observed scaling in interstride interval data may not be due to long-term memory alone, but may, in fact, be due partly to the statistics.
Directory of Open Access Journals (Sweden)
Martin Čulen
2015-01-01
Full Text Available Different batches of atorvastatin, represented by two immediate release formulation designs, were studied using a novel dynamic dissolution apparatus, simulating stomach and small intestine. A universal dissolution method was employed which simulated the physiology of human gastrointestinal tract, including the precise chyme transit behavior and biorelevant conditions. The multicompartmental dissolution data allowed direct observation and qualitative discrimination of the differences resulting from highly pH dependent dissolution behavior of the tested batches. Further evaluation of results was performed using IVIVC/IVIVR development. While satisfactory correlation could not be achieved using a conventional deconvolution based-model, promising results were obtained through the use of a nonconventional approach exploiting the complex compartmental dissolution data.
Discrete model of dislocations in fractional nonlocal elasticity
National Research Council Canada - National Science Library
Tarasov, Vasily E
2016-01-01
Discrete models of dislocations in fractional nonlocal materials are suggested. The proposed models are based on fractional-order differences instead of finite differences of integer orders that are usually used...
Directory of Open Access Journals (Sweden)
Yi-Fei Pu
2013-01-01
Full Text Available The traditional integer-order partial differential equation-based image denoising approaches often blur the edge and complex texture detail; thus, their denoising effects for texture image are not very good. To solve the problem, a fractional partial differential equation-based denoising model for texture image is proposed, which applies a novel mathematical method—fractional calculus to image processing from the view of system evolution. We know from previous studies that fractional-order calculus has some unique properties comparing to integer-order differential calculus that it can nonlinearly enhance complex texture detail during the digital image processing. The goal of the proposed model is to overcome the problems mentioned above by using the properties of fractional differential calculus. It extended traditional integer-order equation to a fractional order and proposed the fractional Green’s formula and the fractional Euler-Lagrange formula for two-dimensional image processing, and then a fractional partial differential equation based denoising model was proposed. The experimental results prove that the abilities of the proposed denoising model to preserve the high-frequency edge and complex texture information are obviously superior to those of traditional integral based algorithms, especially for texture detail rich images.
Discrete model of dislocations in fractional nonlocal elasticity
Directory of Open Access Journals (Sweden)
Vasily E. Tarasov
2016-01-01
Full Text Available Discrete models of dislocations in fractional nonlocal materials are suggested. The proposed models are based on fractional-order differences instead of finite differences of integer orders that are usually used. The fractional differences allow us to describe long-range interactions in materials. In continuous limit the suggested discrete models give continuum models of dislocations in nonlocal continua. Fractional generalization of the Frenkel–Kontorova model by using long-range interactions is suggested. We also propose a fractional generalization of interacting atomic chains (IAC model of dislocations by considering long-range interacting chains.
Engaging Students with Multiple Models of Fractions
Zhang, Xiaofen; Clements, M. A.; Ellerton, Nerida F.
2015-01-01
An understanding of unit fractions, and especially of one-half, one-third, and one-fourth, is crucially important for elementary school children's development of number sense (CCSSI 2010). We describe multimodal activities designed to assist elementary school students in gaining a rich understanding of unit fractions. Research has shown (Zhang,…
Energy Technology Data Exchange (ETDEWEB)
Schmidt, K.; Lucignani, G.; Mori, K.; Jay, T.; Palombo, E.; Nelson, T.; Pettigrew, K.; Holden, J.E.; Sokoloff, L.
1989-06-01
A translocase to transport hexose phosphate formed in the cytosol into the cisterns of the endoplasmic reticulum, where the phosphatase resides, is absent in brain. 2-Deoxyglucose-6-phosphate (DG-6-P) may therefore have limited access to glucose-6-phosphatase (G-6-Pase), and transport of the DG-6-P across the endoplasmic reticular membrane may be rate limiting to its dephosphorylation. To take this compartmentation into account, a five-rate constant (5K) model was developed to describe the kinetic behavior of 2-deoxyglucose (DG) and its phosphorylated product in brain. Loss of DG-6-P was modeled as a two-step process: (a) transfer of DG-6-P from the cytosol into the cisterns of the endoplasmic reticulum; (b) hydrolysis of DG-6-P by G-6-Pase and subsequent return of the free DG to the precursor pool. Local CMRglc (LCMRglc) was calculated in the rat on the basis of this model and compared with values calculated on the basis of the three-rate constant (3K) and the four-rate constant (4K) models of the DG method. The results show that under normal physiological conditions all three models yield values of LCMRglc that are essentially equivalent for experimental periods between 25 and 45 min. Therefore, the simplest model, the 3K model, is sufficient. For experimental periods from 60 to 120 min, the 4K and 5K models do not correct completely for loss of product, but the 5K model does yield estimates of LCMRglc that are closer to the values at 45 min than those obtained with the 3K and 4K models.
Likelihood Inference for a Nonstationary Fractional Autoregressive Model
DEFF Research Database (Denmark)
Johansen, Søren; Nielsen, Morten Ørregaard
This paper discusses model based inference in an autoregressive model for fractional processes based on the Gaussian likelihood. The model allows for the process to be fractional of order d or d - b; where d = b > 1/2 are parameters to be estimated. We model the data X¿, ..., X¿ given the initial...
Fractional-Order Nonlinear Systems Modeling, Analysis and Simulation
Petráš, Ivo
2011-01-01
"Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation" presents a study of fractional-order chaotic systems accompanied by Matlab programs for simulating their state space trajectories, which are shown in the illustrations in the book. Description of the chaotic systems is clearly presented and their analysis and numerical solution are done in an easy-to-follow manner. Simulink models for the selected fractional-order systems are also presented. The readers will understand the fundamentals of the fractional calculus, how real dynamical systems can be described using fractional derivatives and fractional differential equations, how such equations can be solved, and how to simulate and explore chaotic systems of fractional order. The book addresses to mathematicians, physicists, engineers, and other scientists interested in chaos phenomena or in fractional-order systems. It can be used in courses on dynamical systems, control theory, and applied mathematics at graduate or postgraduate level. ...
Survey on modeling methods for single compartmental spiking neuron%单房室脉冲神经元建模方法综述
Institute of Scientific and Technical Information of China (English)
蔺想红; 巩祖正
2011-01-01
要通过人工神经网络来模拟神经系统的功能并对实际问题进行求解,构建合适的脉冲神经元模型非常重要.为了使研究者了解此问题的研究进展,对目前的单房室脉冲神经元建模方法进行了综述.根据复杂程度将这些模型分为三类:具有生物可解释性的生理模型,具有脉冲生成机制的非线性模型和具有固定阈值的线性模型,对各类不同建模方法进行了阐述和分析,并讨论了各自的优缺点.%To simulate the function of the nervous system and solve practical problems using artificial neural networks,modeling suitable spiking neuron models is very importantAn overview is provided for the researchers to catch up with the lately research progress of the modeling methods of single compartmental spiking neuron.According to the complexity,these models will be divided into three categories:physiological models with biologically plausibility,nonlinear models with spiking mecha nism and linear models with fixed threshold.Different methods are described and analyzed respectively, and their advantages and disadvantages are discussed.
Modeling Persistence In Hydrological Time Series Using Fractional Differencing
Hosking, J. R. M.
1984-12-01
The class of autoregressive integrated moving average (ARIMA) time series models may be generalized by permitting the degree of differencing d to take fractional values. Models including fractional differencing are capable of representing persistent series (d > 0) or short-memory series (d = 0). The class of fractionally differenced ARIMA processes provides a more flexible way than has hitherto been available of simultaneously modeling the long-term and short-term behavior of a time series. In this paper some fundamental properties of fractionally differenced ARIMA processes are presented. Methods of simulating these processes are described. Estimation of the parameters of fractionally differenced ARIMA models is discussed, and an approximate maximum likelihood method is proposed. The methodology is illustrated by fitting fractionally differenced models to time series of streamflows and annual temperatures.
Likelihood Inference for a Fractionally Cointegrated Vector Autoregressive Model
DEFF Research Database (Denmark)
Johansen, Søren; Nielsen, Morten Ørregaard
We consider model based inference in a fractionally cointegrated (or cofractional) vector autoregressive model based on the conditional Gaussian likelihood. The model allows the process X(t) to be fractional of order d and cofractional of order d-b; that is, there exist vectors ß for which ß...
Cellular compartmentalization of secondary metabolism
Directory of Open Access Journals (Sweden)
H. Corby eKistler
2015-02-01
Full Text Available Fungal secondary metabolism is often considered apart from the essential housekeeping functions of the cell. However, there are clear links between fundamental cellular metabolism and the biochemical pathways leading to secondary metabolite synthesis. Besides utilizing key biochemical precursors shared with the most essential processes of the cell (e.g. amino acids, acetyl CoA, NADPH, enzymes for secondary metabolite synthesis are compartmentalized at conserved subcellular sites that position pathway enzymes to use these common biochemical precursors. Co-compartmentalization of secondary metabolism pathway enzymes also may function to channel precursors, promote pathway efficiency and sequester pathway intermediates and products from the rest of the cell. In this review we discuss the compartmentalization of three well-studied fungal secondary metabolite biosynthetic pathways for penicillin G, aflatoxin and deoxynivalenol, and summarize evidence used to infer subcellular localization. We also discuss how these metabolites potentially are trafficked within the cell and may be exported.
Nonnegative and Compartmental Dynamical Systems
Haddad, Wassim M; Hui, Qing
2010-01-01
This comprehensive book provides the first unified framework for stability and dissipativity analysis and control design for nonnegative and compartmental dynamical systems, which play a key role in a wide range of fields, including engineering, thermal sciences, biology, ecology, economics, genetics, chemistry, medicine, and sociology. Using the highest standards of exposition and rigor, the authors explain these systems and advance the state of the art in their analysis and active control design. Nonnegative and Compartmental Dynamical Systems presents the most complete treatment available o
Research on Modeling of Hydropneumatic Suspension Based on Fractional Order
Junwei Zhang; Sizhong Chen; Yuzhuang Zhao; Jianbo Feng; Chang Liu; Ying Fan
2015-01-01
With such excellent performance as nonlinear stiffness, adjustable vehicle height, and good vibration resistance, hydropneumatic suspension (HS) has been more and more applied to heavy vehicle and engineering vehicle. Traditional modeling methods are still confined to simple models without taking many factors into consideration. A hydropneumatic suspension model based on fractional order (HSM-FO) is built with the advantage of fractional order (FO) in viscoelastic material modeling considerin...
Fractional Differencing Modeling and Forecasting of Eurocurrency Deposit Rates
John Barkoulas; Baum, Christopher F
1996-01-01
We investigate the low frequency properties of three- and six- month rates for Eurocurrency deposits denominated in eight major currencies with specific emphasis on fractional dynamics. Using the fractional integration testing procedure suggested by Geweke and Porter-Hudak (1983), we find that several of the Eurocurrency deposit rates are fractionally integrated processes with long memory. These findings have important implications for econometric modeling, forecasting, and cointegration test...
2012-02-12
based upon the premises of information theory, is found in the Akaike Information Criterion (AIC). Briefly, for models with independent, homoscedastic...we can compute the Akaike weights wr = exp ( −∆r 2 ) ∑ r exp ( −∆r 2 ) . (26) It can be shown (either by likelihood ratio tests or in a Bayesian ...No. 0704-0188 Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing
Transit times and mean ages for nonautonomous and autonomous compartmental systems
Energy Technology Data Exchange (ETDEWEB)
Rasmussen, Martin; Hastings, Alan; Smith, Matthew J.; Agusto, Folashade B.; Chen-Charpentier, Benito M.; Hoffman, Forrest M.; Jiang, Jiang; Todd-Brown, Katherine E. O.; Wang, Ying; Wang, Ying-Ping; Luo, Yiqi
2016-04-01
We develop a theory for residence times and mean ages for nonautonomous compartmental systems. Using the McKendrick–von Forster equation, we show that the mean ages of mass in a compartmental system satisfy a linear nonautonomous ordinary differential equation that is exponentially stable. We then define a nonautonomous version of residence time as the mean age of mass leaving the compartmental system at a particular time and show that our nonautonomous theory is consistent with the autonomous case. We apply these results to study a nine-dimensional nonautonomous compartmental system modeling the carbon cycle, which is a simplified version of the Carnegie–Ames–Stanford approach (CASA) model.
An efficient method for solving fractional Hodgkin-Huxley model
Nagy, A. M.; Sweilam, N. H.
2014-06-01
In this paper, we present an accurate numerical method for solving fractional Hodgkin-Huxley model. A non-standard finite difference method (NSFDM) is implemented to study the dynamic behaviors of the proposed model. The Grünwald-Letinkov definition is used to approximate the fractional derivatives. Numerical results are presented graphically reveal that NSFDM is easy to implement, effective and convenient for solving the proposed model.
The fractional-nonlinear robotic manipulator: Modeling and dynamic simulations
David, S. A.; Balthazar, J. M.; Julio, B. H. S.; Oliveira, C.
2012-11-01
In this paper, we applied the Riemann-Liouville approach and the fractional Euler-Lagrange equations in order to obtain the fractional-order nonlinear dynamics equations of a two link robotic manipulator. The aformentioned equations have been simulated for several cases involving: integer and non-integer order analysis, with and without external forcing acting and some different initial conditions. The fractional nonlinear governing equations of motion are coupled and the time evolution of the angular positions and the phase diagrams have been plotted to visualize the effect of fractional order approach. The new contribution of this work arises from the fact that the dynamics equations of a two link robotic manipulator have been modeled with the fractional Euler-Lagrange dynamics approach. The results reveal that the fractional-nonlinear robotic manipulator can exhibit different and curious behavior from those obtained with the standard dynamical system and can be useful for a better understanding and control of such nonlinear systems.
Fractional-order in a macroeconomic dynamic model
David, S. A.; Quintino, D. D.; Soliani, J.
2013-10-01
In this paper, we applied the Riemann-Liouville approach in order to realize the numerical simulations to a set of equations that represent a fractional-order macroeconomic dynamic model. It is a generalization of a dynamic model recently reported in the literature. The aforementioned equations have been simulated for several cases involving integer and non-integer order analysis, with some different values to fractional order. The time histories and the phase diagrams have been plotted to visualize the effect of fractional order approach. The new contribution of this work arises from the fact that the macroeconomic dynamic model proposed here involves the public sector deficit equation, which renders the model more realistic and complete when compared with the ones encountered in the literature. The results reveal that the fractional-order macroeconomic model can exhibit a real reasonable behavior to macroeconomics systems and might offer greater insights towards the understanding of these complex dynamic systems.
Likelihood Inference for a Nonstationary Fractional Autoregressive Model
DEFF Research Database (Denmark)
Johansen, Søren; Nielsen, Morten Ørregaard
values Xº-n, n = 0, 1, ..., under the assumption that the errors are i.i.d. Gaussian. We consider the likelihood and its derivatives as stochastic processes in the parameters, and prove that they converge in distribution when the errors are i.i.d. with suitable moment conditions and the initial values......This paper discusses model based inference in an autoregressive model for fractional processes based on the Gaussian likelihood. The model allows for the process to be fractional of order d or d - b; where d = b > 1/2 are parameters to be estimated. We model the data X¿, ..., X¿ given the initial...... are bounded. We use this to prove existence and consistency of the local likelihood estimator, and to ?find the asymptotic distribution of the estimators and the likelihood ratio test of the associated fractional unit root hypothesis, which contains the fractional Brownian motion of type II...
Likelihood inference for a nonstationary fractional autoregressive model
DEFF Research Database (Denmark)
Johansen, Søren; Nielsen, Morten Ørregaard
values X0-n, n = 0, 1,...,under the assumption that the errors are i.i.d. Gaussian. We consider the likelihood and its derivatives as stochastic processes in the parameters, and prove that they converge in distribution when the errors are i.i.d. with suitable moment conditions and the initial values......This paper discusses model based inference in an autoregressive model for fractional processes based on the Gaussian likelihood. The model allows for the process to be fractional of order d or d-b; where d ≥ b > 1/2 are parameters to be estimated. We model the data X1,...,XT given the initial...... are bounded. We use this to prove existence and consistency of the local likelihood estimator, and to find the asymptotic distribution of the estimators and the likelihood ratio test of the associated fractional unit root hypothesis, which contains the fractional Brownian motion of type II....
Application of Integer and Fractional Models in Electrochemical Systems
Directory of Open Access Journals (Sweden)
Isabel S. Jesus
2012-01-01
Full Text Available This paper describes the use of integer and fractional electrical elements, for modelling two electrochemical systems. A first type of system consists of botanical elements and a second type is implemented by electrolyte processes with fractal electrodes. Experimental results are analyzed in the frequency domain, and the pros and cons of adopting fractional-order electrical components for modelling these systems are compared.
A Fractional Order Recovery SIR Model from a Stochastic Process.
Angstmann, C N; Henry, B I; McGann, A V
2016-03-01
Over the past several decades, there has been a proliferation of epidemiological models with ordinary derivatives replaced by fractional derivatives in an ad hoc manner. These models may be mathematically interesting, but their relevance is uncertain. Here we develop an SIR model for an epidemic, including vital dynamics, from an underlying stochastic process. We show how fractional differential operators arise naturally in these models whenever the recovery time from the disease is power-law distributed. This can provide a model for a chronic disease process where individuals who are infected for a long time are unlikely to recover. The fractional order recovery model is shown to be consistent with the Kermack-McKendrick age-structured SIR model, and it reduces to the Hethcote-Tudor integral equation SIR model. The derivation from a stochastic process is extended to discrete time, providing a stable numerical method for solving the model equations. We have carried out simulations of the fractional order recovery model showing convergence to equilibrium states. The number of infecteds in the endemic equilibrium state increases as the fractional order of the derivative tends to zero.
Directory of Open Access Journals (Sweden)
Edgar O. Oviedo-Rondón
2007-07-01
Full Text Available Esta palestra tem o objetivo de apresentar e discutir metodologias utilizadas para modelar e integrar o conhecimento clássico em nutrição animal, e o produzido por novas ciências moleculares como nutrigenoma, proteoma e metaboloma. Estas ciências e a bioinformática estão ajudando a expandir rapidamente o conhecimento dos sistemas biológicos de interesse em nutrição animal. Na palestra discutirei como é importante dedicar parte de nosso tempo a integrar o conhecimento existente para esclarecer os problemas em pesquisa, utilizando as ferramentas mais adequadas para evitar duplicação de pesquisas, que causam desperdício de recursos humanos, econômicos, e de tempo. A modelagem matemática por compartimentos utilizando programas de computador pode ser a melhor maneira de acumular estas informações, integrar diferentes descobertas, e comunicar o conhecimento atual dos sistemas, e do metabolismo de nutrientes às novas gerações, e avançar na determinação mais adequada das exigências nutricionais.This presentation aims to present and discuss methodologies used to model and integrate classical knowledge in animal nutrition, and new discoveries produced by new molecular sciences like nutrigenomics, proteomics and metabolomics. These sciences and bioinformatics are helping to expand >very quickly the knowledge of the biological systems of interest in animal nutrition. I will discuss the importance of dedicating part of our efforts to integrate current knowledge to prioritize research problems using the most adequate tools. This will help to avoid research duplication that causes waste of valuable resources. Compartmental mathematical modeling using computer software could be one of the best ways to accumulate this information. It can help to integrate new discoveries, communicate the knowledge about animal systems and nutrient metabolism to a new generation of scientists, and advance to more accurate determination of nutrient
Fractional and multivariable calculus model building and optimization problems
Mathai, A M
2017-01-01
This textbook presents a rigorous approach to multivariable calculus in the context of model building and optimization problems. This comprehensive overview is based on lectures given at five SERC Schools from 2008 to 2012 and covers a broad range of topics that will enable readers to understand and create deterministic and nondeterministic models. Researchers, advanced undergraduate, and graduate students in mathematics, statistics, physics, engineering, and biological sciences will find this book to be a valuable resource for finding appropriate models to describe real-life situations. The first chapter begins with an introduction to fractional calculus moving on to discuss fractional integrals, fractional derivatives, fractional differential equations and their solutions. Multivariable calculus is covered in the second chapter and introduces the fundamentals of multivariable calculus (multivariable functions, limits and continuity, differentiability, directional derivatives and expansions of multivariable ...
An efficient method for solving fractional Hodgkin–Huxley model
Energy Technology Data Exchange (ETDEWEB)
Nagy, A.M., E-mail: abdelhameed_nagy@yahoo.com [Department of Mathematics, Faculty of Science, Benha University, 13518 Benha (Egypt); Sweilam, N.H., E-mail: n_sweilam@yahoo.com [Department of Mathematics, Faculty of Science, Cairo University, 12613 Giza (Egypt)
2014-06-13
In this paper, we present an accurate numerical method for solving fractional Hodgkin–Huxley model. A non-standard finite difference method (NSFDM) is implemented to study the dynamic behaviors of the proposed model. The Grünwald–Letinkov definition is used to approximate the fractional derivatives. Numerical results are presented graphically reveal that NSFDM is easy to implement, effective and convenient for solving the proposed model. - Highlights: • An accurate numerical method for solving fractional Hodgkin–Huxley model is given. • Non-standard finite difference method (NSFDM) is implemented to the proposed model. • NSFDM can solve differential equations involving derivatives of non-integer order. • NDFDM is very powerful and efficient technique for solving the proposed model.
On an Estimation Method for an Alternative Fractionally Cointegrated Model
DEFF Research Database (Denmark)
Carlini, Federico; Łasak, Katarzyna
In this paper we consider the Fractional Vector Error Correction model proposed in Avarucci (2007), which is characterized by a richer lag structure than models proposed in Granger (1986) and Johansen (2008, 2009). We discuss the identification issues of the model of Avarucci (2007), following...
Atmospheric Turbulence Modeling for Aerospace Vehicles: Fractional Order Fit
Kopasakis, George (Inventor)
2015-01-01
An improved model for simulating atmospheric disturbances is disclosed. A scale Kolmogorov spectral may be scaled to convert the Kolmogorov spectral into a finite energy von Karman spectral and a fractional order pole-zero transfer function (TF) may be derived from the von Karman spectral. Fractional order atmospheric turbulence may be approximated with an integer order pole-zero TF fit, and the approximation may be stored in memory.
Drivers of compartmentalization in a Mediterranean pollination network
DEFF Research Database (Denmark)
Gonzalez, Ana M. Martin; Allesina, Stefano; Rodrigo, Anselm
2012-01-01
We study compartmentalization in a Mediterranean pollination network using three different analytical approaches: unipartite modularity (UM), bipartite modularity (BM) and the group model (GM). Our objectives are to compare compartments obtained with these three approaches and to explore the role...... of several species attributes related to pollination syndromes, species phenology, abundance and connectivity in structuring compartmentalization. BM could not identify compartments in our network. By contrast, UM revealed four modules composed of plants and pollinators, and GM four groups of plants and five...... of pollinators. Phenology had a major influence on compartmentalization, and compartments (both UM and GM) had distinct phenophases. Compartments were also strongly characterized by species degree (number of connections) and betweenness centrality. These two attributes were highly related to each other...
Directory of Open Access Journals (Sweden)
Bashir Ahmad
2013-02-01
Full Text Available In this article, we discuss the existence of solutions for a boundary-value problem of integro-differential equations of fractional order with nonlocal fractional boundary conditions by means of some standard tools of fixed point theory. Our problem describes a more general form of fractional stochastic dynamic model for financial asset. An illustrative example is also presented.
Fractional Heat Conduction Models and Thermal Diffusivity Determination
Directory of Open Access Journals (Sweden)
Monika Žecová
2015-01-01
Full Text Available The contribution deals with the fractional heat conduction models and their use for determining thermal diffusivity. A brief historical overview of the authors who have dealt with the heat conduction equation is described in the introduction of the paper. The one-dimensional heat conduction models with using integer- and fractional-order derivatives are listed. Analytical and numerical methods of solution of the heat conduction models with using integer- and fractional-order derivatives are described. Individual methods have been implemented in MATLAB and the examples of simulations are listed. The proposal and experimental verification of the methods for determining thermal diffusivity using half-order derivative of temperature by time are listed at the conclusion of the paper.
Microbially Mediated Kinetic Sulfur Isotope Fractionation: Reactive Transport Modeling Benchmark
Wanner, C.; Druhan, J. L.; Cheng, Y.; Amos, R. T.; Steefel, C. I.; Ajo Franklin, J. B.
2014-12-01
Microbially mediated sulfate reduction is a ubiquitous process in many subsurface systems. Isotopic fractionation is characteristic of this anaerobic process, since sulfate reducing bacteria (SRB) favor the reduction of the lighter sulfate isotopologue (S32O42-) over the heavier isotopologue (S34O42-). Detection of isotopic shifts have been utilized as a proxy for the onset of sulfate reduction in subsurface systems such as oil reservoirs and aquifers undergoing uranium bioremediation. Reactive transport modeling (RTM) of kinetic sulfur isotope fractionation has been applied to field and laboratory studies. These RTM approaches employ different mathematical formulations in the representation of kinetic sulfur isotope fractionation. In order to test the various formulations, we propose a benchmark problem set for the simulation of kinetic sulfur isotope fractionation during microbially mediated sulfate reduction. The benchmark problem set is comprised of four problem levels and is based on a recent laboratory column experimental study of sulfur isotope fractionation. Pertinent processes impacting sulfur isotopic composition such as microbial sulfate reduction and dispersion are included in the problem set. To date, participating RTM codes are: CRUNCHTOPE, TOUGHREACT, MIN3P and THE GEOCHEMIST'S WORKBENCH. Preliminary results from various codes show reasonable agreement for the problem levels simulating sulfur isotope fractionation in 1D.
A fractional diffusion equation model for cancer tumor
Iyiola, Olaniyi Samuel; Zaman, F. D.
2014-10-01
In this article, we consider cancer tumor models and investigate the need for fractional order derivative as compared to the classical first order derivative in time. Three different cases of the net killing rate are taken into account including the case where net killing rate of the cancer cells is dependent on the concentration of the cells. At first, we use a relatively new analytical technique called q-Homotopy Analysis Method on the resulting time-fractional partial differential equations to obtain analytical solution in form of convergent series with easily computable components. Our numerical analysis enables us to give some recommendations on the appropriate order (fractional) of derivative in time to be used in modeling cancer tumor.
A fractional calculus model of anomalous dispersion of acoustic waves.
Wharmby, Andrew W
2016-09-01
An empirical formula based on viscoelastic analysis techniques that employs concepts from the fractional calculus that was used to model the dielectric behavior of materials exposed to oscillating electromagnetic fields in the radiofrequency, terahertz, and infrared bands. This work adapts and applies the formula to model viscoelastic behavior of materials that show an apparent increase of phase velocity of vibration with an increase in frequency, otherwise known as anomalous dispersion. A fractional order wave equation is derived through the application of the classic elastic-viscoelastic correspondence principle whose analytical solution is used to describe absorption and dispersion of acoustic waves in the viscoelastic material displaying anomalous dispersion in a specific frequency range. A brief discussion and comparison of an alternative fractional order wave equation recently formulated is also included.
Modeling Heavy Metal Sorption Kinetics Using Fractional Calculus
Directory of Open Access Journals (Sweden)
V. C. Friesen
2015-01-01
Full Text Available Heavy metals are commonly regarded as environmentally aggressive and hazardous to human health. Among the different metals, lead plays an important economic role due to its large use in the automotive industry, being an essential component of batteries. Different approaches have been reported in the literature aimed at lead removal, and among them a very successful one considers the use of water hyacinths for sorption-based operation. The modeling of the metal sorption kinetics is a fundamental step towards in-depth studies and proper separation equipment design and optimization. Fractional calculus represents a novel approach and a growing research field for process modeling, which is based on the successful use of derivatives of arbitrary order. This paper reports the modeling of the kinetics of lead sorption by water hyacinths (Eichhornia crassipes using a fractional calculus. A general procedure on error analysis is also employed to prove the actual fractional nature of the proposed model by the use of parametric variance analysis, which was carried out using two different approaches (with the complete Hessian matrix and with a simplified Hessian matrix. The joint parameter confidence regions were generated, allowing to successfully show the fractional nature of the model and the sorption process.
Energy Technology Data Exchange (ETDEWEB)
Rodrigues Junior, O
1994-07-01
After an intake of radioactive material, its behaviour in the human body can be described by mathematical models, where organs, tissues or regions of the body are treated as a chain of linked compartments. The mathematical approach for such metabolic models is usually done through a system of differential equations of first order with constant coefficients. The solutions of this system of equations associates the radionuclide intake, with the fraction excreted or retained in the organ of interest. A computer program - called INCORP and for running in PC compatible microcomputers - was developed in order to find the solutions of such system of equations, using an analytical method based on expansion of series of exponential matrices. The metabolic model presented in the ICRP-30 publication was simulated using the INCORP program, in order to find the respective retention and excretion curves for selected radionuclides. (author)
Lithium-ion batteries modeling involving fractional differentiation
Sabatier, Jocelyn; Merveillaut, Mathieu; Francisco, Junior Mbala; Guillemard, Franck; Porcelatto, Denis
2014-09-01
With hybrid and electric vehicles development, automobile battery monitoring systems (BMS) have to meet the new requirements. These systems have to give information on state of health, state of charge, available power. To get this information, BMS often implement battery models. Accuracy of the information manipulated by the BMS thus depends on the model accuracy. This paper is within this framework and addresses lithium-ion battery modeling. The proposed fractional model is based on simplifications of an electrochemical model and on resolution of some partial differential equations used in its description. Such an approach permits to get a simple model in which electrochemical variables and parameters still appear.
Discrete random walk models for space-time fractional diffusion
Energy Technology Data Exchange (ETDEWEB)
Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Pagnini, Gianni; Paradisi, Paolo
2002-11-01
A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. By space-time fractional diffusion equation we mean an evolution equation obtained from the standard linear diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative of order {alpha} is part of (0,2] and skewness {theta} (module{theta}{<=}{l_brace}{alpha},2-{alpha}{r_brace}), and the first-order time derivative with a Caputo derivative of order {beta} is part of (0,1]. Such evolution equation implies for the flux a fractional Fick's law which accounts for spatial and temporal non-locality. The fundamental solution (for the Cauchy problem) of the fractional diffusion equation can be interpreted as a probability density evolving in time of a peculiar self-similar stochastic process that we view as a generalized diffusion process. By adopting appropriate finite-difference schemes of solution, we generate models of random walk discrete in space and time suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation.
Research on Modeling of Hydropneumatic Suspension Based on Fractional Order
Directory of Open Access Journals (Sweden)
Junwei Zhang
2015-01-01
Full Text Available With such excellent performance as nonlinear stiffness, adjustable vehicle height, and good vibration resistance, hydropneumatic suspension (HS has been more and more applied to heavy vehicle and engineering vehicle. Traditional modeling methods are still confined to simple models without taking many factors into consideration. A hydropneumatic suspension model based on fractional order (HSM-FO is built with the advantage of fractional order (FO in viscoelastic material modeling considering the mechanics property of multiphase medium of HS. Then, the detailed calculation method is proposed based on Oustaloup filtering approximation algorithm. The HSM-FO is implemented in Matlab/Simulink, and the results of comparison among the simulation curve of fractional order, integral order, and the curve of real experiment prove the feasibility and validity of HSM-FO. The damping force property of the suspension system under different fractional orders is also studied. In the end of this paper, several conclusions concerning HSM-FO are drawn according to analysis of simulation.
Statistical properties of several models of fractional random point processes
Bendjaballah, C.
2011-08-01
Statistical properties of several models of fractional random point processes have been analyzed from the counting and time interval statistics points of view. Based on the criterion of the reduced variance, it is seen that such processes exhibit nonclassical properties. The conditions for these processes to be treated as conditional Poisson processes are examined. Numerical simulations illustrate part of the theoretical calculations.
Estimating and Forecasting Generalized Fractional Long Memory Stochastic Volatility Models
S. Peiris (Shelton); M. Asai (Manabu); M.J. McAleer (Michael)
2016-01-01
textabstractIn recent years fractionally differenced processes have received a great deal of attention due to its flexibility in financial applications with long memory. This paper considers a class of models generated by Gegenbauer polynomials, incorporating the long memory in stochastic volatility
Fraction Multiplication and Division Models: A Practitioner Reference Paper
Ervin, Heather K.
2017-01-01
It is well documented in literature that rational number is an important area of understanding in mathematics. Therefore, it follows that teachers and students need to have an understanding of rational number and related concepts such as fraction multiplication and division. This practitioner reference paper examines models that are important to…
Spine neck plasticity regulates compartmentalization of synapses.
Tønnesen, Jan; Katona, Gergely; Rózsa, Balázs; Nägerl, U Valentin
2014-05-01
Dendritic spines have been proposed to transform synaptic signals through chemical and electrical compartmentalization. However, the quantitative contribution of spine morphology to synapse compartmentalization and its dynamic regulation are still poorly understood. We used time-lapse super-resolution stimulated emission depletion (STED) imaging in combination with fluorescence recovery after photobleaching (FRAP) measurements, two-photon glutamate uncaging, electrophysiology and simulations to investigate the dynamic link between nanoscale anatomy and compartmentalization in live spines of CA1 neurons in mouse brain slices. We report a diversity of spine morphologies that argues against common categorization schemes and establish a close link between compartmentalization and spine morphology, wherein spine neck width is the most critical morphological parameter. We demonstrate that spine necks are plastic structures that become wider and shorter after long-term potentiation. These morphological changes are predicted to lead to a substantial drop in spine head excitatory postsynaptic potential (EPSP) while preserving overall biochemical compartmentalization.
Atmospheric Turbulence Modeling for Aero Vehicles: Fractional Order Fits
Kopasakis, George
2015-01-01
Atmospheric turbulence models are necessary for the design of both inlet/engine and flight controls, as well as for studying coupling between the propulsion and the vehicle structural dynamics for supersonic vehicles. Models based on the Kolmogorov spectrum have been previously utilized to model atmospheric turbulence. In this paper, a more accurate model is developed in its representative fractional order form, typical of atmospheric disturbances. This is accomplished by first scaling the Kolmogorov spectral to convert them into finite energy von Karman forms and then by deriving an explicit fractional circuit-filter type analog for this model. This circuit model is utilized to develop a generalized formulation in frequency domain to approximate the fractional order with the products of first order transfer functions, which enables accurate time domain simulations. The objective of this work is as follows. Given the parameters describing the conditions of atmospheric disturbances, and utilizing the derived formulations, directly compute the transfer function poles and zeros describing these disturbances for acoustic velocity, temperature, pressure, and density. Time domain simulations of representative atmospheric turbulence can then be developed by utilizing these computed transfer functions together with the disturbance frequencies of interest.
Vimentin compartmentalization in discoid lupus
Directory of Open Access Journals (Sweden)
Ana Maria Abreu-Velez
2010-01-01
Full Text Available Context: Discoid lupus erythematosus (DLE is a chronic skin condition, often presenting inflammatory, scarring lesions predominating on sun exposed areas of the face and scalp. Case Report: A 46-year-old black female was evaluated for possible DLE. Biopsies for hematoxylin and eosin (H&E and immunohistochemistry (IHC examination, as well as for direct immunofluorescence (DIF analysis were performed. The H&E staining demonstrated mild epidermal atrophy with focal follicular plugging. A mild interface infiltrate of lymphocytes and histiocytes and a superficial and deep, perivascular and periadnexal dermal infiltrate of lymphocytes, histiocytes and plasma cells was observed The DIF revealed strong deposits of immunoglobulins IgG, IgM, fibrinogen and Complement/C3, present in a granular pattern at the basement membrane junction (BMZ of the skin as well as in the BMZ of the sebaceous glands. In addition, deposits of IgA surrounding the superficial dermal blood vessels were appreciated. The IHC displayed compartmentalization of vimentin around the BMZ of both the superrficial skin and sebaceous gland BMZs, as well as similar patterns of deposits of the same immunoglobulins, complement, and fibrinogen as visualized by DIF. Conclusions : Minimal attention has been given to the process of compartmentalization of the dermis in inflammatory skin conditions, including DLE. However, it seems that in addition to the classical immunoglobulin and complement "lupus band" deposits at the BMZ, an additional, orchestrated immunologic reorganization of the dermis surrounding the inflammatory process is also present. Such an immunologic reorganization of the dermis could play a significant role in the pathophysiology of this disorder.
Barriers in the brain: resolving dendritic spine morphology and compartmentalization.
Adrian, Max; Kusters, Remy; Wierenga, Corette J; Storm, Cornelis; Hoogenraad, Casper C; Kapitein, Lukas C
2014-01-01
Dendritic spines are micron-sized protrusions that harbor the majority of excitatory synapses in the central nervous system. The head of the spine is connected to the dendritic shaft by a 50-400 nm thin membrane tube, called the spine neck, which has been hypothesized to confine biochemical and electric signals within the spine compartment. Such compartmentalization could minimize interspinal crosstalk and thereby support spine-specific synapse plasticity. However, to what extent compartmentalization is governed by spine morphology, and in particular the diameter of the spine neck, has remained unresolved. Here, we review recent advances in tool development - both experimental and theoretical - that facilitate studying the role of the spine neck in compartmentalization. Special emphasis is given to recent advances in microscopy methods and quantitative modeling applications as we discuss compartmentalization of biochemical signals, membrane receptors and electrical signals in spines. Multidisciplinary approaches should help to answer how dendritic spine architecture affects the cellular and molecular processes required for synapse maintenance and modulation.
Barriers in the Brain: Resolving Dendritic Spine Morphology and Compartmentalization
Directory of Open Access Journals (Sweden)
Max eAdrian
2014-12-01
Full Text Available Dendritic spines are micron-sized protrusions that harbor the majority of excitatory synapses in the central nervous system. The head of the spine is connected to the dendritic shaft by a 50-400 nm thin membrane tube, called the spine neck, which has been hypothesized to confine biochemical and electric signals within the spine compartment. Such compartmentalization could minimize interspinal crosstalk and thereby support spine-specific synapse plasticity. However, to what extent compartmentalization is governed by spine morphology, and in particular the diameter of the spine neck, has remained unresolved. Here, we review recent advances in tool development - both experimental and theoretical - that facilitate studying the role of the spine neck in compartmentalization. Special emphasis is given to recent advances in microscopy methods and quantitative modeling applications as we discuss compartmentalization of biochemical signals, membrane receptors and electrical signals in spines. Multidisciplinary approaches should help to answer how dendritic spine architecture affects the cellular and molecular processes required for synapse maintenance and modulation.
Mathematical modeling of fish burger baking using fractional calculus
Directory of Open Access Journals (Sweden)
Bainy Eduarda M.
2017-01-01
Full Text Available Tilapia (Oreochromis sp. is the most important and abundant fish species in Brazil due to its adaptability to different environments. The development of tilapia-based products could be an alternative in order to aggregate value and increase fish meat consumption. However, there is little information available on fishburger freezing and cooking in the literature. In this work, the mathematical modeling of the fish burger baking was studied. Previously to the baking process, the fishburgers were assembled in cylindrical shape of height equal to 8mm and diameter 100mm and then baked in an electrical oven with forced heat convection at 150ºC. A T-type thermocouple was inserted in the burger to obtain its temperature profile at the central position. In order to describe the temperature of the burger during the baking process, lumped-parameter models of integer and fractional order and also a nonlinear model due to heat capacity temperature dependence were considered. The burger physical properties were obtained from the literature. After proper parameter estimation tasks and statistical validation, the fractional order model could better describe the experimental temperature behavior, a value of 0.91±0.02 was obtained for the fractional order of the system with correlation coefficient of 0.99. Therefore, with the better temperature prediction, process control and economic optimization studies of the baking process can be conducted.
Likelihood inference for a fractionally cointegrated vector autoregressive model
DEFF Research Database (Denmark)
Johansen, Søren; Nielsen, Morten Ørregaard
We consider model based inference in a fractionally cointegrated (or cofractional) vector autoregressive model based on the conditional Gaussian likelihood. The model allows the process X_{t} to be fractional of order d and cofractional of order d-b; that is, there exist vectors β for which β......′X_{t} is fractional of order d-b. The parameters d and b satisfy either d≥b≥1/2, d=b≥1/2, or d=d_{0}≥b≥1/2. Our main technical contribution is the proof of consistency of the maximum likelihood estimators on the set 1/2≤b≤d≤d_{1} for any d_{1}≥d_{0}. To this end, we consider the conditional likelihood as a stochastic...... process in the parameters, and prove that it converges in distribution when errors are i.i.d. with suitable moment conditions and initial values are bounded. We then prove that the estimator of β is asymptotically mixed Gaussian and estimators of the remaining parameters are asymptotically Gaussian. We...
Likelihood Inference for a Fractionally Cointegrated Vector Autoregressive Model
DEFF Research Database (Denmark)
Johansen, Søren; Nielsen, Morten Ørregaard
We consider model based inference in a fractionally cointegrated (or cofractional) vector autoregressive model based on the conditional Gaussian likelihood. The model allows the process X(t) to be fractional of order d and cofractional of order d-b; that is, there exist vectors ß for which ß......'X(t) is fractional of order d-b. The parameters d and b satisfy either d=b=1/2, d=b=1/2, or d=d0=b=1/2. Our main technical contribution is the proof of consistency of the maximum likelihood estimators on the set 1/2=b=d=d1 for any d1=d0. To this end, we consider the conditional likelihood as a stochastic process...... in the parameters, and prove that it converges in distribution when errors are i.i.d. with suitable moment conditions and initial values are bounded. We then prove that the estimator of ß is asymptotically mixed Gaussian and estimators of the remaining parameters are asymptotically Gaussian. We also find...
Time fractional capital-induced labor migration model
Ali Balcı, Mehmet
2017-07-01
In this study we present a new model of neoclassical economic growth by considering that workers move from regions with lower density of capital to regions with higher density of capital. Since the labor migration and capital flow involves self-similarities in long range time, we use the fractional order derivatives for the time variable. To solve this model we proposed Variational Iteration Method, and studied numerically labor migration flow data from Turkey along with other countries throughout the period of 1966-2014.
A Novel Method for Performance Analysis of Compartmentalized Reservoirs
Directory of Open Access Journals (Sweden)
Shahamat Mohammad Sadeq
2016-05-01
Full Text Available This paper presents a simple analytical model for performance analysis of compartmentalized reservoirs producing under Constant Terminal Rate (CTR and Constant Terminal Pressure (CTP. The model is based on the well-known material balance and boundary dominated flow equations and is written in terms of capacitance and resistance of a production and a support compartment. These capacitance and resistance terms account for a combination of reservoir parameters which enable the developed model to be used for characterizing such systems. In addition to considering the properties contrast between the two reservoir compartments, the model takes into account existence of transmissibility barriers with the use of resistance terms. The model is used to analyze production performance of unconventional reservoirs, where the multistage fracturing of horizontal wells effectively creates a Stimulated Reservoir Volume (SRV with an enhanced permeability surrounded by a non-stimulated region. It can also be used for analysis of compartmentalized conventional reservoirs. The analytical solutions provide type curves through which the controlling reservoirs parameters of a compartmentalized system can be estimated. The contribution of the supporting compartment is modeled based on a boundary dominated flow assumption. The transient behaviour of the support compartment is captured by application of “distance of investigation” concept. The model shows that depletion of the production and support compartments exhibit two unit slopes on a log-log plot of pressure versus time for CTR. For CTP, however, the depletions display two exponential declines. The depletion signatures are separated by transition periods, which depend on the contribution of the support compartment (i.e. transient or boundary dominated flow. The developed equations can be implemented easily in a spreadsheet application, and are corroborated with the use of a numerical simulation. The study
A time fractional model to represent rainfall process
Directory of Open Access Journals (Sweden)
Jacques GOLDER
2014-01-01
Full Text Available This paper deals with a stochastic representation of the rainfall process. The analysis of a rainfall time series shows that cumulative representation of a rainfall time series can be modeled as a non-Gaussian random walk with a log-normal jump distribution and a time-waiting distribution following a tempered α-stable probability law. Based on the random walk model, a fractional Fokker-Planck equation (FFPE with tempered α-stable waiting times was obtained. Through the comparison of observed data and simulated results from the random walk model and FFPE model with tempered α-stable waiting times, it can be concluded that the behavior of the rainfall process is globally reproduced, and the FFPE model with tempered α-stable waiting times is more efficient in reproducing the observed behavior.
Deformed Calogero-Sutherland model and fractional quantum Hall effect
Atai, Farrokh; Langmann, Edwin
2017-01-01
The deformed Calogero-Sutherland (CS) model is a quantum integrable system with arbitrary numbers of two types of particles and reducing to the standard CS model in special cases. We show that a known collective field description of the CS model, which is based on conformal field theory (CFT), is actually a collective field description of the deformed CS model. This provides a natural application of the deformed CS model in Wen's effective field theory of the fractional quantum Hall effect (FQHE), with the two kinds of particles corresponding to electrons and quasi-hole excitations. In particular, we use known mathematical results about super-Jack polynomials to obtain simple explicit formulas for the orthonormal CFT basis proposed by van Elburg and Schoutens in the context of the FQHE.
Intrinsic Kinetic Modeling of Thermal Dimerization of C5 Fraction
Institute of Scientific and Technical Information of China (English)
Guo Liang; Wang Tiefeng; Li Dongfeng; Wang Jinfu
2016-01-01
This work aims to investigate the intrinsic kinetics of thermal dimerization of C5 fraction in the reactive distilla-tion process. Experiments are conducted in an 1000-mL stainless steel autoclave under some selected design conditions. By means of the weighted least squares method, the intrinsic kinetics of thermal dimerization of C5 fraction is established, and the corresponding pre-exponential factor as well as the activation energy are determined. For example, the pre-exponential factor A is equal to 4.39×105 and the activation energy Ea is equal to 6.58×104 J/mol for the cyclopentadiene dimerization re-action. The comparison between the experimental and calculated results shows that the kinetics model derived in this work is accurate and reliable, which can be used in the design of reactive distillation columns.
Fractionalized Fermi liquid in a Kondo-Heisenberg model
Tsvelik, A. M.
2016-10-01
The Kondo-Heisenberg model is used as a controllable tool to demonstrate the existence of a peculiar metallic state with unbroken translational symmetry where the Fermi surface volume is not controlled by the total electron density. I use a nonperturbative approach where the strongest interactions are taken into account by means of exact solution, and corrections are controllable. In agreement with the general requirements formulated by T. Senthil et al. [Phys. Rev. Lett. 90, 216403 (2003), 10.1103/PhysRevLett.90.216403], the resulting metallic state represents a fractionalized Fermi liquid where well defined quasiparticles coexist with gapped fractionalized collective excitations. The system undergoes a phase transition to an ordered phase (charge density wave or superconducting), at the transition temperature which is parametrically small in comparison to the quasiparticle Fermi energy.
Generalized elastic model yields a fractional Langevin equation description.
Taloni, Alessandro; Chechkin, Aleksei; Klafter, Joseph
2010-04-23
Starting from a generalized elastic model which accounts for the stochastic motion of several physical systems such as membranes, (semi)flexible polymers, and fluctuating interfaces among others, we derive the fractional Langevin equation (FLE) for a probe particle in such systems, in the case of thermal initial conditions. We show that this FLE is the only one fulfilling the fluctuation-dissipation relation within a new family of fractional Brownian motion equations. The FLE for the time-dependent fluctuations of the donor-acceptor distance in a protein is shown to be recovered. When the system starts from nonthermal conditions, the corresponding FLE, which does not fulfill the fluctuation-dissipation relation, is derived.
Correlations in a generalized elastic model: fractional Langevin equation approach.
Taloni, Alessandro; Chechkin, Aleksei; Klafter, Joseph
2010-12-01
The generalized elastic model (GEM) provides the evolution equation which governs the stochastic motion of several many-body systems in nature, such as polymers, membranes, and growing interfaces. On the other hand a probe (tracer) particle in these systems performs a fractional Brownian motion due to the spatial interactions with the other system's components. The tracer's anomalous dynamics can be described by a fractional Langevin equation (FLE) with a space-time correlated noise. We demonstrate that the description given in terms of GEM coincides with that furnished by the relative FLE, by showing that the correlation functions of the stochastic field obtained within the FLE framework agree with the corresponding quantities calculated from the GEM. Furthermore we show that the Fox H -function formalism appears to be very convenient to describe the correlation properties within the FLE approach.
Transient heat conduction in a pebble fuel applying fractional model
Energy Technology Data Exchange (ETDEWEB)
Gomez A, R.; Espinosa P, G. [Universidad Autonoma Metropolitana, Unidad Iztapalapa, Area de Ingenieria en Recursos Energeticos, Av. San Rafael Atlixco 186, Col. Vicentina, 09340 Mexico D. F. (Mexico)], e-mail: gepe@xanum.uam.mx
2009-10-15
In this paper we presents the equation of thermal diffusion of temporary-fractional order in the one-dimensional space in spherical coordinates, with the objective to analyze the heat transference between the fuel and coolant in a fuel element of a Pebble Bed Modular Reactor. The pebble fuel is the heterogeneous system made by microsphere constitutes by U O, pyrolytic carbon and silicon carbide mixed with graphite. To describe the heat transfer phenomena in the pebble fuel we applied a constitutive law fractional (Non-Fourier) in order to analyze the behaviour transient of the temperature distribution in the pebble fuel with anomalous thermal diffusion effects a numerical model is developed. (Author)
Likelihood Inference for a Fractionally Cointegrated Vector Autoregressive Model
DEFF Research Database (Denmark)
Johansen, Søren; Nielsen, Morten Ørregaard
2012-01-01
We consider model based inference in a fractionally cointegrated (or cofractional) vector autoregressive model with a restricted constant term, ¿, based on the Gaussian likelihood conditional on initial values. The model nests the I(d) VAR model. We give conditions on the parameters......likelihood estimators. To this end we prove weak convergence of the conditional likelihood as a continuous stochastic...... process in the parameters when errors are i.i.d. with suitable moment conditions and initial values are bounded. When the limit is deterministic this implies uniform convergence in probability of the conditional likelihood function. If the true value b0>1/2, we prove that the limit distribution of (ß...
On fractional order composite model reference adaptive control
Wei, Yiheng; Sun, Zhenyuan; Hu, Yangsheng; Wang, Yong
2016-08-01
This paper presents a novel composite model reference adaptive control approach for a class of fractional order linear systems with unknown constant parameters. The method is extended from the model reference adaptive control. The parameter estimation error of our method depends on both the tracking error and the prediction error, whereas the existing method only depends on the tracking error, which makes our method has better transient performance in the sense of generating smooth system output. By the aid of the continuous frequency distributed model, stability of the proposed approach is established in the Lyapunov sense. Furthermore, the convergence property of the model parameters estimation is presented, on the premise that the closed-loop control system is stable. Finally, numerical simulation examples are given to demonstrate the effectiveness of the proposed schemes.
Fractional Langevin model of memory in financial markets.
Picozzi, Sergio; West, Bruce J
2002-10-01
The separation of the microscopic and macroscopic time scales is necessary for the validity of ordinary statistical physics and the dynamical description embodied in the Langevin equation. When the microscopic time scale diverges, the differential equations on the macroscopic level are no longer valid and must be replaced with fractional differential equations of motion; in particular, we obtain a fractional-differential stochastic equation of motion. After decades of statistical analysis of financial time series certain "stylized facts" have emerged, including the statistics of stock price fluctuations having "fat tails" and their linear correlations in time being exceedingly short lived. On the other hand, the magnitude of these fluctuations and other such measures of market volatility possess temporal correlations that decay as an inverse power law. One explanation of this long-term memory is that it is a consequence of the time-scale separation between "microscopic" and "macroscopic" economic variables. We propose a fractional Langevin equation as a dynamical model of the observed memory in financial time series.
Phase noise and jitter modeling for fractional-N PLLs
S. A. Osmany; Herzel, F.; Schmalz, K; Winkler, W.
2007-01-01
We present an analytical phase noise model for fractional-N phase-locked loops (PLL) with emphasis on integrated RF synthesizers in the GHz range. The noise of the crystal reference, the voltage-controlled oscillator (VCO), the loop filter, the charge pump, and the sigma-delta modulator (SDM) is filtered by the PLL operation. We express the rms phase error (jitter) in terms of phase noise of the reference, the VCO phase noise and the third-order loop filter parameters. In addition, we conside...
A mathematical model on fractional Lotka-Volterra equations.
Das, S; Gupta, P K
2011-05-21
The article presents the solutions of Lotka-Volterra equations of fractional-order time derivatives with the help of analytical method of nonlinear problem called the homotopy perturbation method (HPM). By using initial values, the explicit solutions of predator and prey populations for different particular cases have been derived. The numerical solutions show that only a few iterations are needed to obtain accurate approximate solutions. The method performs extremely well in terms of efficiency and simplicity to solve this historical biological model. Copyright © 2011 Elsevier Ltd. All rights reserved.
On the use of fractional order PK-PD models
Ionescu, Clara; Copot, Dana
2017-01-01
Quantifying and controlling depth of anesthesia is a challenging process due to lack of measurement technology for direct effects of drug supply into the body. Efforts are being made to develop new sensor techniques and new horizons are explored for modeling this intricate process. This paper introduces emerging tools available on the ‘engineering market’ imported from the area of fractional calculus. A novel interpretation of the classical drug-effect curve is given, enabling linear control. This enables broadening the horizon of signal processing and control techniques and suggests future research lines.
First-principles models of equilibrium tellurium isotope fractionation
Haghnegahdar, M. A.; Schauble, E. A.; Fornadel, A. P.; Spry, P. G.
2013-12-01
In this study, equilibrium mass-dependent isotopic fractionation among representative Te-bearing species is estimated with first-principles thermodynamic calculations. Tellurium is a group 16 element (along with O, S, and Se) with eight stable isotopes ranging in mass from 120Te to 130Te, and six commonly-occurring oxidation states: -II, -I, 0, +II, +IV, and +VI. In its reduced form, Te(-II), tellurium has a unique crystal-chemical role as a bond partner for gold and silver in epithermal and orogenic gold deposits, which likely form when oxidized Te species (e.g., H2TeO3, TeO32-) or perhaps polytellurides (e.g., Te22-) interact with precious metals in hydrothermal solution. Te(IV) is the most common oxidation state at the Earth's surface, including surface outcrops of telluride ore deposits, where tellurite and tellurate minerals form by oxidation. In the ocean, dissolved tellurium tends to be scavenged by particulate matter. Te(VI) is more abundant than Te(IV) in the ocean water (1), even though it is thought to be less stable thermodynamically. This variety of valence states in natural systems and range of isotopic masses suggest that tellurium could exhibit geochemically useful isotope abundance variations. Tellurium isotope fractionations were determined for representative molecules and crystals of varying complexity and chemistry. Gas-phase calculations are combined with supermolecular cluster models of aqueous and solid species. These in turn are compared with plane-wave density functional theory calculations with periodic boundary conditions. In general, heavyTe/lightTe is predicted to be higher for more oxidized species, and lower for reduced species, with 130Te/125Te fractionations as large as 4‰ at 100οC between coexisting Te(IV) and Te(-II) or Te(0) compounds. This is a much larger fractionation than has been observed in naturally occurring redox pairs (i.e., Te (0) vs. Te(IV) species) so far, suggesting that disequilibrium processes may control
The linear-quadratic model is inappropriate to model high dose per fraction effects in radiosurgery.
Kirkpatrick, John P; Meyer, Jeffrey J; Marks, Lawrence B
2008-10-01
The linear-quadratic (LQ) model is widely used to model the effect of total dose and dose per fraction in conventionally fractionated radiotherapy. Much of the data used to generate the model are obtained in vitro at doses well below those used in radiosurgery. Clinically, the LQ model often underestimates tumor control observed at radiosurgical doses. The underlying mechanisms implied by the LQ model do not reflect the vascular and stromal damage produced at the high doses per fraction encountered in radiosurgery and ignore the impact of radioresistant subpopulations of cells. The appropriate modeling of both tumor control and normal tissue toxicity in radiosurgery requires the application of emerging understanding of molecular-, cellular-, and tissue-level effects of high-dose/fraction-ionizing radiation and the role of cancer stem cells.
Phase noise and jitter modeling for fractional-N PLLs
Directory of Open Access Journals (Sweden)
S. A. Osmany
2007-06-01
Full Text Available We present an analytical phase noise model for fractional-N phase-locked loops (PLL with emphasis on integrated RF synthesizers in the GHz range. The noise of the crystal reference, the voltage-controlled oscillator (VCO, the loop filter, the charge pump, and the sigma-delta modulator (SDM is filtered by the PLL operation. We express the rms phase error (jitter in terms of phase noise of the reference, the VCO phase noise and the third-order loop filter parameters. In addition, we consider OFDM systems, where the PLL phase noise is reduced by digital signal processing after down-conversion of the RF signal to baseband. The rms phase error is discussed as a function of the loop parameters. Our model drastically simplifies the noise optimization of the PLL loop dynamics.
Modelling heat transfer in heterogeneous media using fractional calculus.
Sierociuk, Dominik; Dzielinski, Andrzej; Sarwas, Grzegorz; Petras, Ivo; Podlubny, Igor; Skovranek, Tomas
2013-05-13
This paper presents the results of modelling the heat transfer process in heterogeneous media with the assumption that part of the heat flux is dispersed in the air around the beam. The heat transfer process in a solid material (beam) can be described by an integer order partial differential equation. However, in heterogeneous media, it can be described by a sub- or hyperdiffusion equation which results in a fractional order partial differential equation. Taking into consideration that part of the heat flux is dispersed into the neighbouring environment we additionally modify the main relation between heat flux and the temperature, and we obtain in this case the heat transfer equation in a new form. This leads to the transfer function that describes the dependency between the heat flux at the beginning of the beam and the temperature at a given distance. This article also presents the experimental results of modelling real plant in the frequency domain based on the obtained transfer function.
Phase noise and jitter modeling for fractional-N PLLs
Osmany, S. A.; Herzel, F.; Schmalz, K.; Winkler, W.
2007-06-01
We present an analytical phase noise model for fractional-N phase-locked loops (PLL) with emphasis on integrated RF synthesizers in the GHz range. The noise of the crystal reference, the voltage-controlled oscillator (VCO), the loop filter, the charge pump, and the sigma-delta modulator (SDM) is filtered by the PLL operation. We express the rms phase error (jitter) in terms of phase noise of the reference, the VCO phase noise and the third-order loop filter parameters. In addition, we consider OFDM systems, where the PLL phase noise is reduced by digital signal processing after down-conversion of the RF signal to baseband. The rms phase error is discussed as a function of the loop parameters. Our model drastically simplifies the noise optimization of the PLL loop dynamics.
Modeling the fractional magnetic states of magnetostructural transformations
Energy Technology Data Exchange (ETDEWEB)
Della Torre, Edward [Department of Electrical and Computer Engineering, The George Washington University, Washington, DC 20052 (United States); ElBidweihy, Hatem, E-mail: hatem@gwmail.gwu.edu [Department of Electrical and Computer Engineering, The George Washington University, Washington, DC 20052 (United States); Provenzano, Virgil [National Institute for Standards and Technology, Gaithersburg, MD 20899 (United States); Bennett, Lawrence H. [Department of Electrical and Computer Engineering, The George Washington University, Washington, DC 20052 (United States)
2014-02-15
The large inverse magnetocaloric effect (MCE) in the off-stoichiometric Heusler alloys occurs at a critical temperature near room temperature. At this temperature, the material is in a mixed-state and can have a variable ratio of two stable magnetic crystallographic-states; a high magnetization state (HM) and a low magnetization state (LM). The field-induced thermal hysteresis in the virgin curve of Ni{sub 50}Mn{sub 35}In{sub 15} and the virgin first-order reversal curves (VFORC) are presented. A model is introduced to describe the descending branches of these curves based on the different magnetic fields of conversion (from HM to LM). Using limited measurements, the model is used as a tool to determine the fractions of the two crystallographic-states within the mixed-state region.
When does 1/2 = 1/3?: Modelling with Wet Fractions
Fitzallen, Noleine
2015-01-01
Many fraction activities rely on the use of area models for developing partitioning skills. These models, however, are limited in their ability to assist students to visualise a fraction of an object when the whole changes. This article describes a fraction modelling activity that requires the transfer of water from one container to another. The…
Phosphodiesterase 4 and compartmentalization of cyclic AMP signaling
Institute of Scientific and Technical Information of China (English)
WANG ZhengChao; SHI FangXiong
2007-01-01
Cyclic AMP (cAMP), as a second messenger, plays a critical role in cellular signaling transduction. However, it is not clear how this apparently identical cAMP signal induces divergent physiological responses. The potential explanation that cAMP signaling is compartmentalized was proposed by Buxton and Brunton twenty years ago. Compartmentalization of cAMP signaling allows spatially distinct pools of protein kinase A (PKA) to be differently activated. Research on cAMP signaling has regained impetus in many fields of life sciences due to the progress in understanding cAMP signaling complexity and functional diversity. The cAMP/PKA signaling compartments are maintained by A-kinase anchoring proteins (AKAPs) which bind PKA and other signaling proteins, and by PDEs which hydrolyse cAMP and thus terminate PKA activity. PDE4 enzymes belong to PDE superfamily and stand at a crossroad that allows them to integrate various signaling pathways with that of cAMP in spatially distinct compartments. In the current review, the nomenclature, taxonomy and gene expression of PDE4, and the system and region of its effect are described. In addition, the idiographic molecules, mechanisms, and regulation models of PDE4 are summarized. Furthermore, the important roles PDE4 plays in the maturation of rat granulosa cells and cAMP signaling compartmentalization are discussed.
Dynamical Models to Infer the Core Mass Fraction of Venus
Quintana, Elisa V.; Barclay, Thomas
2016-10-01
The uncompressed density of Venus is just a few percent lower than Earth's, however the nature of the interior core structure of Venus remains unclear. Employing state-of-the-art dynamical formation models that allow both accretion and collisional fragmentation, we perform hundreds of simulations of terrestrial planet growth around the Sun in the presence of the giant planets. For both Earth and Venus analogs, we quantify the iron-silicate ratios, water/volatile abundances and specific impact energies of all collisions that lead to their formation. Preliminary results suggest that the distributions of core mass fraction and water content are comparable among the Earth and Venus analogs, suggesting that Earth and Venus may indeed have formed with similar structures and compositions.
Reservoir compartmentalization assessment by using FTIR spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Permanyer, A. [Dept. Geoquimica, Petrologia i Prospeccio Geologica, Universitat de Barcelona, Marti i Franques, s/n, 08028 - Barcelona, Catalonia (Spain); Rebufa, C.; Kister, J. [Universite d' Aix - Marseille III, Faculte des Sciences et Techniques de St. Jerome, CNRS UMR 6171, Laboratoire de Geochimie Organique Analytique et Environnement (GOAE), Case 561, 13397 Marseille Cedex 20 (France)
2007-09-15
Reservoir geochemistry has traditionally used the gas chromatographic fingerprinting method and star diagrams to provide evidence of petroleum reservoir compartmentalization. Recently alternative techniques such as Fourier Transform Infra Red (FTIR) spectroscopy have been postulated to aid the evaluation of reservoir compartmentalization, and to characterize the geochemical evolution of oils from individual reservoirs. FTIR spectroscopy was applied successfully in the Tarragona Basin, Offshore N.E. Spain, validating the method to identify oils from different reservoirs. Moreover the method was successfully applied to provide evidence of compositional differences in oils from a faulted reservoir (El Furrial field, Venezuela), in which GC fingerprints failed to differentiate the oils. FTIR spectroscopy therefore, proves to be a complementary tool for reservoir compartmentalization studies. (author)
Fractional Calculus in Hydrologic Modeling: A Numerical Perspective
Energy Technology Data Exchange (ETDEWEB)
David A. Benson; Mark M. Meerschaert; Jordan Revielle
2012-01-01
Fractional derivatives can be viewed either as a handy extension of classical calculus or, more deeply, as mathematical operators defined by natural phenomena. This follows the view that the diffusion equation is defined as the governing equation of a Brownian motion. In this paper, we emphasize that fractional derivatives come from the governing equations of stable Levy motion, and that fractional integration is the corresponding inverse operator. Fractional integration, and its multi-dimensional extensions derived in this way, are intimately tied to fractional Brownian (and Levy) motions and noises. By following these general principles, we discuss the Eulerian and Lagrangian numerical solutions to fractional partial differential equations, and Eulerian methods for stochastic integrals. These numerical approximations illuminate the essential nature of the fractional calculus.
Fractional calculus in hydrologic modeling: A numerical perspective.
Benson, David A; Meerschaert, Mark M; Revielle, Jordan
2013-01-01
Fractional derivatives can be viewed either as handy extensions of classical calculus or, more deeply, as mathematical operators defined by natural phenomena. This follows the view that the diffusion equation is defined as the governing equation of a Brownian motion. In this paper, we emphasize that fractional derivatives come from the governing equations of stable Lévy motion, and that fractional integration is the corresponding inverse operator. Fractional integration, and its multi-dimensional extensions derived in this way, are intimately tied to fractional Brownian (and Lévy) motions and noises. By following these general principles, we discuss the Eulerian and Lagrangian numerical solutions to fractional partial differential equations, and Eulerian methods for stochastic integrals. These numerical approximations illuminate the essential nature of the fractional calculus.
Compartmentalized storage tank for electrochemical cell system
Piecuch, Benjamin Michael (Inventor); Dalton, Luke Thomas (Inventor)
2010-01-01
A compartmentalized storage tank is disclosed. The compartmentalized storage tank includes a housing, a first fluid storage section disposed within the housing, a second fluid storage section disposed within the housing, the first and second fluid storage sections being separated by a movable divider, and a constant force spring. The constant force spring is disposed between the housing and the movable divider to exert a constant force on the movable divider to cause a pressure P1 in the first fluid storage section to be greater than a pressure P2 in the second fluid storage section, thereby defining a pressure differential.
Electroviscoelasticity of liquid/liquid interfaces: fractional-order model.
Spasic, Aleksandar M; Lazarevic, Mihailo P
2005-02-01
A number of theories that describe the behavior of liquid-liquid interfaces have been developed and applied to various dispersed systems, e.g., Stokes, Reiner-Rivelin, Ericksen, Einstein, Smoluchowski, and Kinch. A new theory of electroviscoelasticity describes the behavior of electrified liquid-liquid interfaces in fine dispersed systems and is based on a new constitutive model of liquids. According to this model liquid-liquid droplet or droplet-film structure (collective of particles) is considered as a macroscopic system with internal structure determined by the way the molecules (ions) are tuned (structured) into the primary components of a cluster configuration. How the tuning/structuring occurs depends on the physical fields involved, both potential (elastic forces) and nonpotential (resistance forces). All these microelements of the primary structure can be considered as electromechanical oscillators assembled into groups, so that excitation by an external physical field may cause oscillations at the resonant/characteristic frequency of the system itself (coupling at the characteristic frequency). Up to now, three possible mathematical formalisms have been discussed related to the theory of electroviscoelasticity. The first is the tension tensor model, where the normal and tangential forces are considered, only in mathematical formalism, regardless of their origin (mechanical and/or electrical). The second is the Van der Pol derivative model, presented by linear and nonlinear differential equations. Finally, the third model presents an effort to generalize the previous Van der Pol equation: the ordinary time derivative and integral are now replaced with the corresponding fractional-order time derivative and integral of order p<1.
Institute of Scientific and Technical Information of China (English)
Haitao Qi; Hui Jin
2006-01-01
The fractional calculus is used in the constitutive relationship model of viscoelastic fluid.A generalized Maxwell model with fractional calculus is considered.Based on the flow conditions described,two flow cases are solved and the exact solutions are obtained by using the Weber transform and the Laplace transform for fractional calculus.
Mathematical Models Arising in the Fractal Forest Gap via Local Fractional Calculus
Directory of Open Access Journals (Sweden)
Chun-Ying Long
2014-01-01
Full Text Available The forest new gap models via local fractional calculus are investigated. The JABOWA and FORSKA models are extended to deal with the growth of individual trees defined on Cantor sets. The local fractional growth equations with local fractional derivative and difference are discussed. Our results are first attempted to show the key roles for the nondifferentiable growth of individual trees.
Formal modeling and verification of fractional order linear systems.
Zhao, Chunna; Shi, Likun; Guan, Yong; Li, Xiaojuan; Shi, Zhiping
2016-05-01
This paper presents a formalization of a fractional order linear system in a higher-order logic (HOL) theorem proving system. Based on the formalization of the Grünwald-Letnikov (GL) definition, we formally specify and verify the linear and superposition properties of fractional order systems. The proof provides a rigor and solid underpinnings for verifying concrete fractional order linear control systems. Our implementation in HOL demonstrates the effectiveness of our approach in practical applications.
Fractional model for heat conduction in polar bear hairs
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Wang Qing-Li
2012-01-01
Full Text Available Time-fractional differential equations can accurately describe heat conduction in fractal media, such as wool fibers, goose down and polar bear hair. The fractional complex transform is used to convert time-fractional heat conduction equations with the modified Riemann-Liouville derivative into ordinary differential equations, and exact solutions can be easily obtained. The solution process is straightforward and concise.
Modelling in Primary School: Constructing Conceptual Models and Making Sense of Fractions
Shahbari, Juhaina Awawdeh; Peled, Irit
2017-01-01
This article describes sixth-grade students' engagement in two model-eliciting activities offering students the opportunity to construct mathematical models. The findings show that students utilized their knowledge of fractions including conceptual and procedural knowledge in constructing mathematical models for the given situations. Some students…
Fractional Moment Bounds and Disorder Relevance for Pinning Models
Derrida, Bernard; Giacomin, Giambattista; Lacoin, Hubert; Toninelli, Fabio Lucio
2009-05-01
We study the critical point of directed pinning/wetting models with quenched disorder. The distribution K(·) of the location of the first contact of the (free) polymer with the defect line is assumed to be of the form K( n) = n - α-1 L( n), with α ≥ 0 and L(·) slowly varying. The model undergoes a (de)-localization phase transition: the free energy (per unit length) is zero in the delocalized phase and positive in the localized phase. For α 1, then quenched and annealed critical points differ whenever disorder is present, and we give the scaling form of their difference for small disorder. In agreement with the so-called Harris criterion, disorder is therefore relevant in this case. In the marginal case α = 1/2, under the assumption that L(·) vanishes sufficiently fast at infinity, we prove that the difference between quenched and annealed critical points, which is smaller than any power of the disorder strength, is positive: disorder is marginally relevant. Again, the case considered in [12,17] is out of our analysis and remains open. The results are achieved by setting the parameters of the model so that the annealed system is localized, but close to criticality, and by first considering a quenched system of size that does not exceed the correlation length of the annealed model. In such a regime we can show that the expectation of the partition function raised to a suitably chosen power {γ in (0, 1)} is small. We then exploit such an information to prove that the expectation of the same fractional power of the partition function goes to zero with the size of the system, a fact that immediately entails that the quenched system is delocalized.
A note on fractional linear pure birth and pure death processes in epidemic models
Garra, Roberto; 10.1016/j.physa.2011.06.005
2011-01-01
In this note we highlight the role of fractional linear birth and linear death processes recently studied in \\citet{sakhno} and \\citet{pol}, in relation to epidemic models with empirical power law distribution of the events. Taking inspiration from a formal analogy between the equation of self consistency of the epidemic type aftershock sequences (ETAS) model, and the fractional differential equation describing the mean value of fractional linear growth processes, we show some interesting applications of fractional modelling to study \\textit{ab initio} epidemic processes without the assumption of any empirical distribution. We also show that, in the frame of fractional modelling, subcritical regimes can be linked to linear fractional death processes and supercritical regimes to linear fractional birth processes. Moreover we discuss a simple toy model to underline the possible application of these stochastic growth models to more general epidemic phenomena such as tumoral growth.
Compartmentalized Platforms for Neuro-Pharmacological Research.
Jadhav, Amol D; Wei, Li; Shi, Peng
2016-01-01
Dissociated primary neuronal cell culture remains an indispensable approach for neurobiology research in order to investigate basic mechanisms underlying diverse neuronal functions, drug screening and pharmacological investigation. Compartmentalization, a widely adopted technique since its emergence in 1970s enables spatial segregation of neuronal segments and detailed investigation that is otherwise limited with traditional culture methods. Although these compartmental chambers (e.g. Campenot chamber) have been proven valuable for the investigation of Peripheral Nervous System (PNS) neurons and to some extent within Central Nervous System (CNS) neurons, their utility has remained limited given the arduous manufacturing process, incompatibility with high-resolution optical imaging and limited throughput. The development in the area of microfabrication and microfluidics has enabled creation of next generation compartmentalized devices that are cheap, easy to manufacture, require reduced sample volumes, enable precise control over the cellular microenvironment both spatially as well as temporally, and permit highthroughput testing. In this review we briefly evaluate the various compartmentalization tools used for neurobiological research, and highlight application of the emerging microfluidic platforms towards in vitro single cell neurobiology.
Animal models of heart failure with preserved ejection fraction
G. Conceição; I. Heinonen (Ilkka); A.P. Lourenço; D.J.G.M. Duncker (Dirk); I. Falcão-Pires
2016-01-01
textabstractHeart failure with preserved ejection fraction (HFpEF) constitutes a clinical syndrome in which the diagnostic criteria of heart failure are not accompanied by gross disturbances of systolic function, as assessed by ejection fraction. In turn, under most circumstances, diastolic function
Thin stillage fractionation using ultrafiltration: resistance in series model.
Arora, Amit; Dien, Bruce S; Belyea, Ronald L; Wang, Ping; Singh, Vijay; Tumbleson, M E; Rausch, Kent D
2009-02-01
The corn based dry grind process is the most widely used method in the US for fuel ethanol production. Fermentation of corn to ethanol produces whole stillage after ethanol is removed by distillation. It is centrifuged to separate thin stillage from wet grains. Thin stillage contains 5-10% solids. To concentrate solids of thin stillage, it requires evaporation of large amounts of water and maintenance of evaporators. Evaporator maintenance requires excess evaporator capacity at the facility, increasing capital expenses, requiring plant slowdowns or shut downs and results in revenue losses. Membrane filtration is one method that could lead to improved value of thin stillage and may offer an alternative to evaporation. Fractionation of thin stillage using ultrafiltration was conducted to evaluate membranes as an alternative to evaporators in the ethanol industry. Two regenerated cellulose membranes with molecular weight cut offs of 10 and 100 kDa were evaluated. Total solids (suspended and soluble) contents recovered through membrane separation process were similar to those from commercial evaporators. Permeate flux decline of thin stillage using a resistance in series model was determined. Each of the four components of total resistance was evaluated experimentally. Effects of operating variables such as transmembrane pressure and temperature on permeate flux rate and resistances were determined and optimum conditions for maximum flux rates were evaluated. Model equations were developed to evaluate the resistance components that are responsible for fouling and to predict total flux decline with respect to time. Modeling results were in agreement with experimental results (R(2) > 0.98).
A Fractional Fokker-Planck Model for Anomalous Diffusion
anderson, Johan; Moradi, Sara
2014-01-01
In this paper we present a study of anomalous diffusion using a Fokker-Planck description with fractional velocity derivatives. The distribution functions are found using numerical means for varying degree of fractionality observing the transition from a Gaussian distribution to a L\\'evy distribution. The statistical properties of the distribution functions are assessed by a generalized expectation measure and entropy in terms of Tsallis statistical mechanics. We find that the ratio of the generalized entropy and expectation is increasing with decreasing fractionality towards the well known so-called sub-diffusive domain, indicating a self-organising behavior.
Tcp and NTCP radiobiological models: conventional and hypo fractionated treatments in radiotherapy
Energy Technology Data Exchange (ETDEWEB)
Astudillo V, A.; Paredes G, L. [ININ, Carretera Mexico-Toluca s/n, Ocoyoacac 52750, Estado de Mexico (Mexico); Resendiz G, G.; Posadas V, A. [Hospital Angeles Lomas, Av. Vialidad de la Barranca s/n, Col. Valle de las Palmas, 52763 Huixquilucan de Degallado, Estado de Mexico (Mexico); Mitsoura, E. [Universidad Autonoma del Estado de Mexico, Facultad de Medicina, Paseo Tollocan, Esq. Jesus Carranza s/n, Col. Moderna de la Cruz, 50180 Toluca, Estado de Mexico (Mexico); Rodriguez L, A.; Flores C, J. M., E-mail: armando.astudillo@inin.gob.mx [Hospital Medica Sur, Puente de Piedra 150, Col. Toriello Guerra, 14050 Tlalpan, Mexico D. F. (Mexico)
2015-10-15
The hypo and conventional fractionated schedules performance were compared in terms of the tumor control and the normal tissue complications. From the records of ten patients, treated for adenocarcinoma and without mastectomy, the dose-volume histogram was used. Using radiobiological models the probabilities for tumor control and normal tissue complications were calculated. For both schedules the tumor control was approximately the same. However, the damage in the normal tissue was larger in conventional fractionated schedule. This is important because patients assistance time to their fractions (15 fractions/25 fractions) can be optimized. Thus, the hypo fractionated schedule has suitable characteristics to be implemented. (Author)
Numerical simulation for SI model with variable-order fractional
Directory of Open Access Journals (Sweden)
mohamed mohamed
2016-04-01
Full Text Available In this paper numerical studies for the variable-order fractional delay differential equations are presented. Adams-Bashforth-Moulton algorithm has been extended to study this problem, where the derivative is defined in the Caputo variable-order fractional sense. Special attention is given to prove the error estimate of the proposed method. Numerical test examples are presented to demonstrate utility of the method. Chaotic behaviors are observed in variable-order one dimensional delayed systems.
Animal models of heart failure with preserved ejection fraction
Conceição, G.; Heinonen, I.; Lourenço, A. P.; Duncker, D. J.; Falcão-Pires, I.
2016-01-01
Heart failure with preserved ejection fraction (HFpEF) constitutes a clinical syndrome in which the diagnostic criteria of heart failure are not accompanied by gross disturbances of systolic function, as assessed by ejection fraction. In turn, under most circumstances, diastolic function is impaired. Although it now represents over 50 % of all patients with heart failure, the mechanisms of HFpEF remain understood, precluding effective therapy. Understanding the pathophysiology of HFpEF has be...
Fabrice, Delbary
2016-01-01
Compartmental models based on tracer mass balance are extensively used in clinical and pre-clinical nuclear medicine in order to obtain quantitative information on tracer metabolism in the biological tissue. This paper is the second of a series of two that deal with the problem of tracer coefficient estimation via compartmental modelling in an inverse problem framework. While the previous work was devoted to the discussion of identifiability issues for 2, 3 and n-dimension compartmental systems, here we discuss the problem of numerically determining the tracer coefficients by means of a general regularized Multivariate Gauss Newton scheme. In this paper, applications concerning cerebral, hepatic and renal functions are considered, involving experimental measurements on FDG-PET data on different set of murine models.
Regression model for tuning the PID controller with fractional order time delay system
S.P. Agnihotri; Laxman Madhavrao Waghmare
2014-01-01
In this paper a regression model based for tuning proportional integral derivative (PID) controller with fractional order time delay system is proposed. The novelty of this paper is that tuning parameters of the fractional order time delay system are optimally predicted using the regression model. In the proposed method, the output parameters of the fractional order system are used to derive the regression function. Here, the regression model depends on the weights of the exponential function...
2016-01-01
In recent days, fractional calculus (FC) has been accepted as a novel modeling tool that can extend the descriptive power of the traditional calculus. Fractional-order descriptiveness can increase the flexibility and degrees of freedom of the model by means of fractional parameters. Based on the fact that real capacitors and inductors are “intrinsic” fractional order, fractional calculus is introduced into the modeling process to establish a fractional-order state-space averaging model of the...
Chow, Meyrick; Chan, Lawrence
2010-01-01
Information technology (IT) has the potential to improve the clinical learning environment. The extent to which IT enhances or detracts from healthcare professionals' role performance can be expected to affect both student learning and patient outcomes. This study evaluated nursing students' satisfaction with a novel compartmental Picture…
Chow, Meyrick; Chan, Lawrence
2010-01-01
Information technology (IT) has the potential to improve the clinical learning environment. The extent to which IT enhances or detracts from healthcare professionals' role performance can be expected to affect both student learning and patient outcomes. This study evaluated nursing students' satisfaction with a novel compartmental Picture…
Directory of Open Access Journals (Sweden)
Jan Freundlich
2013-01-01
Full Text Available The paper presents vibration analysis of a simply supported beam with a fractional order viscoelastic material model. The Bernoulli-Euler beam model is considered. The beam is excited by the supports movement. The Riemann – Liouville fractional derivative of order 0 α ⩽ 1 is applied. In the first stage, the steady-state vibrations of the beam are analyzed and therefore the Riemann – Liouville fractional derivative with lower terminal at −∞ is assumed. This assumption simplifies solution of the fractional differential equations and enables us to directly obtain amplitude-frequency characteristics of the examined system. The characteristics are obtained for various values of fractional derivative of order α and values of the Voigt material model parameters. The studies show that the selection of appropriate damping coefficients and fractional derivative order of damping model enables us to fit more accurately dynamic characteristic of the beam in comparison with using integer order derivative damping model.
Mittag-Leffler function for discrete fractional modelling
Directory of Open Access Journals (Sweden)
Guo-Cheng Wu
2016-01-01
Full Text Available From the difference equations on discrete time scales, this paper numerically investigates one discrete fractional difference equation in the Caputo delta’s sense which has an explicit solution in form of the discrete Mittag-Leffler function. The exact numerical values of the solutions are given in comparison with the truncated Mittag-Leffler function.
A representation theory for a class of vector autoregressive models for fractional processes
DEFF Research Database (Denmark)
Johansen, Søren
2008-01-01
Based on an idea of Granger (1986), we analyze a new vector autoregressive model defined from the fractional lag operator 1-(1-L)^{d}. We first derive conditions in terms of the coefficients for the model to generate processes which are fractional of order zero. We then show that if there is a unit...... root, the model generates a fractional process X(t) of order d, d>0, for which there are vectors ß so that ß'X(t) is fractional of order d-b, 0...
Human intake fraction of toxic pollutants: a model comparison between caltox and uses-lca
Huijbregts, Mark A J; Geelen, Loes M.J.; Edgar G. Hertwich; McKone, Thomas E.; Meent, Dik van de
2004-01-01
In Life Cycle Assessment and Comparative Risk Assessment potential human exposure to toxic pollutants can be expressed as the human intake fraction (iF), representing the fraction of the quantity emitted that enters the human population. To assess model uncertainty in the human intake fraction, ingestion and inhalation iFs of 367 substances emitted to air and freshwater were calculated with two commonly applied multi-media fate and exposure models, CalTOX and USES-LCA. Comparison of the ...
On a fractal LC-electric circuit modeled by local fractional calculus
Yang, Xiao-Jun; Machado, J. A. Tenreiro; Cattani, Carlo; Gao, Feng
2017-06-01
A non-differentiable model of the LC-electric circuit described by a local fractional differential equation of fractal dimensional order is addressed in this article. From the fractal electrodynamics point of view, the relaxation oscillator, defined on Cantor sets in LC-electric circuit, and its exact solution using the local fractional Laplace transform are obtained. Comparative results among local fractional derivative, Riemann-Liouville fractional derivative and conventional derivative are discussed. Local fractional calculus is proposed as a new tool suitable for the study of a large class of electric circuits.
A proposed fractional-order Gompertz model and its application to tumour growth data.
Bolton, Larisse; Cloot, Alain H J J; Schoombie, Schalk W; Slabbert, Jacobus P
2015-06-01
A fractional-order Gompertz model of orders between 0 and 2 is proposed. The main purpose of this investigation is to determine whether the ordinary or proposed fractional Gompertz model would best fit our experimental dataset. The solutions for the proposed model are obtained using fundamental concepts from fractional calculus. The closed-form equations of both the proposed model and the ordinary Gompertz model are calibrated using an experimental dataset containing tumour growth volumes of a Rhabdomyosarcoma tumour in a mouse. With regard to the proposed model, the order, within the interval mentioned, that resulted in the best fit to the data was used in a further investigation into the prediction capability of the model. This was compared to the prediction capability of the ordinary Gompertz model. The result of the investigation was that a fractional-order Gompertz model of order 0.68 produced a better fit to our experimental dataset than the well-known ordinary Gompertz model.
Compartmental analysis of renal physiology using nuclear medicine data and statistical optimization
Garbarino, Sara; Brignone, Massimo; Massollo, Michela; Sambuceti, Gianmario; Piana, Michele
2012-01-01
This paper describes a general approach to the compartmental modeling of nuclear data based on spectral analysis and statistical optimization. We utilize the renal physiology as test case and validate the method against both synthetic data and real measurements acquired during two micro-PET experiments with murine models.
Cognitive Models: The Missing Link to Learning Fraction Multiplication and Division
de Castro, Belinda V.
2008-01-01
This quasi-experimental study aims to streamline cognitive models on fraction multiplication and division that contain the most worthwhile features of other existing models. Its exploratory nature and its approach to proof elicitation can be used to help establish its effectiveness in building students' understanding of fractions as compared to…
An Investigation of Fraction Models in Early Elementary Grades: A Mixed-Methods Approach
Wilkerson, Trena L.; Cooper, Susan; Gupta, Dittika; Montgomery, Mark; Mechell, Sara; Arterbury, Kristin; Moore, Sherrie; Baker, Betty Ruth; Sharp, Pat T.
2015-01-01
This study examines the effect varying models have on student understanding of fractions. The study addressed the question of what students know and understand about fractional concepts through the use of discrete and continuous models. A sample of 54 students in kindergarten and 3rd grade were given an interview pretest, participated in…
Conceptual Mis(understandings) of Fractions: From Area Models to Multiple Embodiments
Zhang, Xiaofen; Clements, M. A.; Ellerton, Nerida F.
2015-01-01
Area-model representations seem to have been dominant in the teaching and learning of fractions, especially in primary school mathematics curricula. In this study, we investigated 40 fifth grade children's understandings of the unit fractions, 1/2, 1/3, and 1/4, represented through a variety of different models. Analyses of pre-teaching test and…
Li, Hongjie; Qi, Yanyan; Jasper, Heinrich
2016-02-10
Compartmentalization of the gastrointestinal (GI) tract of metazoans is critical for health. GI compartments contain specific microbiota, and microbiota dysbiosis is associated with intestinal dysfunction. Dysbiosis develops in aging intestines, yet how this relates to changes in GI compartmentalization remains unclear. The Drosophila GI tract is an accessible model to address this question. Here we show that the stomach-like copper cell region (CCR) in the middle midgut controls distribution and composition of the microbiota. We find that chronic activation of JAK/Stat signaling in the aging gut induces a metaplasia of the gastric epithelium, CCR decline, and subsequent commensal dysbiosis and epithelial dysplasia along the GI tract. Accordingly, inhibition of JAK/Stat signaling in the CCR specifically prevents age-related metaplasia, commensal dysbiosis and functional decline in old guts, and extends lifespan. Our results establish a mechanism by which age-related chronic inflammation causes the decline of intestinal compartmentalization and microbiota dysbiosis, limiting lifespan.
Deriving pedotransfer functions for soil quartz fraction in southern France from reverse modeling
Calvet, Jean-Christophe; Fritz, Noureddine; Berne, Christine; Piguet, Bruno; Maurel, William; Meurey, Catherine
2016-12-01
The quartz fraction in soils is a key parameter of soil thermal conductivity models. Because it is difficult to measure the quartz fraction in soils, this information is usually unavailable. This source of uncertainty impacts the simulation of sensible heat flux, evapotranspiration and land surface temperature in numerical simulations of the Earth system. Improving the estimation of soil quartz fraction is needed for practical applications in meteorology, hydrology and climate modeling. This paper investigates the use of long time series of routine ground observations made in weather stations to retrieve the soil quartz fraction. Profile soil temperature and water content were monitored at 21 weather stations in southern France. Soil thermal diffusivity was derived from the temperature profiles. Using observations of bulk density, soil texture, and fractions of gravel and soil organic matter, soil heat capacity and thermal conductivity were estimated. The quartz fraction was inversely estimated using an empirical geometric mean thermal conductivity model. Several pedotransfer functions for estimating quartz content from gravimetric or volumetric fractions of soil particles (e.g., sand) were analyzed. The soil volumetric fraction of quartz (fq) was systematically better correlated with soil characteristics than the gravimetric fraction of quartz. More than 60 % of the variance of fq could be explained using indicators based on the sand fraction. It was shown that soil organic matter and/or gravels may have a marked impact on thermal conductivity values depending on which predictor of fq is used. For the grassland soils examined in this study, the ratio of sand-to-soil organic matter fractions was the best predictor of fq, followed by the gravimetric fraction of sand. An error propagation analysis and a comparison with independent data from other tested models showed that the gravimetric fraction of sand is the best predictor of fq when a larger variety of soil types
PLANE SURFACE SUDDENLY SET IN MOTION IN A VISCOELASTIC FLUID WITH FRACTIONAL MAXWELL MODEL
Institute of Scientific and Technical Information of China (English)
谭文长; 徐明瑜
2002-01-01
The fractional calculus approach in the constitutive relationship model of viscoelastic fluid is introduced. The flow near a wall suddenly set in motion is studied for a non-Newtonian viscoelastic fluid with the fractional Maxwell model. Exact solutions of velocity and stress are obtained by using the discrete inverse Laplace transform of the sequential fractional derivatives. It is found that the effect of the fractional orders in the constitutive relationship on the flow field is significant. The results show that for small times there are appreciable viscoelastic effects on the shear stress at the plate, for large times the viscoelastic effects become weak.
Plane surface suddenly set in motion in a viscoelastic fluid with fractional Maxwell model
Wenchang, Tan; Mingyu, Xu
2002-08-01
The fractional calculus approach in the constitutive relationship model of viscoelastic fluid is introduced. The flow near a wall suddenly set in motion is studied for a non-Newtonian viscoelastic fluid with the fractional Maxwell model. Exact solutions of velocity and stress are obtained by using the discrete inverse Laplace transform of the sequential fractional derivatives. It is found that the effect of the fractional orders in the constitutive relationship on the flow field is significant. The results show that for small times there are appreciable viscoelastic effects on the shear stress at the plate, for large times the viscoelastic effects become weak.
SOLVING FRACTIONAL-ORDER COMPETITIVE LOTKA-VOLTERRA MODEL BY NSFD SCHEMES
Directory of Open Access Journals (Sweden)
S.ZIBAEI
2016-12-01
Full Text Available In this paper, we introduce fractional-order into a model competitive Lotka- Volterra prey-predator system. We will discuss the stability analysis of this fractional system. The non-standard nite difference (NSFD scheme is implemented to study the dynamic behaviors in the fractional-order Lotka-Volterra system. Proposed non-standard numerical scheme is compared with the forward Euler and fourth order Runge-Kutta methods. Numerical results show that the NSFD approach is easy and accurate for implementing when applied to fractional-order Lotka-Volterra model.
Modeling of Macroeconomics by a Novel Discrete Nonlinear Fractional Dynamical System
Directory of Open Access Journals (Sweden)
Zhenhua Hu
2013-01-01
Full Text Available We propose a new nonlinear economic system with fractional derivative. According to the Jumarie’s definition of fractional derivative, we obtain a discrete fractional nonlinear economic system. Three variables, the gross domestic production, inflation, and unemployment rate, are considered by this nonlinear system. Based on the concrete macroeconomic data of USA, the coefficients of this nonlinear system are estimated by the method of least squares. The application of discrete fractional economic model with linear and nonlinear structure is shown to illustrate the efficiency of modeling the macroeconomic data with discrete fractional dynamical system. The empirical study suggests that the nonlinear discrete fractional dynamical system can describe the actual economic data accurately and predict the future behavior more reasonably than the linear dynamic system. The method proposed in this paper can be applied to investigate other macroeconomic variables of more states.
The fractional-order modeling and synchronization of electrically coupled neuron systems
Moaddy, K.
2012-11-01
In this paper, we generalize the integer-order cable model of the neuron system into the fractional-order domain, where the long memory dependence of the fractional derivative can be a better fit for the neuron response. Furthermore, the chaotic synchronization with a gap junction of two or multi-coupled-neurons of fractional-order are discussed. The circuit model, fractional-order state equations and the numerical technique are introduced in this paper for individual and multiple coupled neuron systems with different fractional-orders. Various examples are introduced with different fractional orders using the non-standard finite difference scheme together with the Grünwald-Letnikov discretization process which is easily implemented and reliably accurate. © 2011 Elsevier Ltd. All rights reserved.
Modelling viscosity and mass fraction of bitumen - diluent mixtures
Energy Technology Data Exchange (ETDEWEB)
Miadonye, A.; Latour, N.; Puttagunta, V.R. [Lakehead Univ., Thunder Bay, ON (Canada)
1999-07-01
In recovery of bitumen in oil sands extraction, the reduction of the viscosity is important above and below ground. The addition of liquid diluent breaks down or weakens the intermolecular forces that create a high viscosity in bitumen. The addition of even 5% of diluent can cause a viscosity reduction in excess of 8%, thus facilitating the in situ recovery and pipeline transportation of bitumen. Knowledge of bitumen - diluent viscosity is highly important because without it, determination of upgrading processes, in situ recovery, well simulation, heat transfer, fluid flow and a variety of other engineering problems would be difficult or impossible to solve. The development of a simple correlation to predict the viscosity of binary mixtures of bitumen - diluent in any proportion is described. The developed correlation used to estimate the viscosities and mass fractions of bitumen - diluent mixtures was within acceptable limits of error. For the prediction of mixture viscosities, the developed correlation gave the best results with an overall average absolute deviation of 12% compared to those of Chironis (17%) and Cragoe (23%). Predictions of diluent mass fractions yielded a much better result with an overall average absolute deviation of 5%. The unique features of the correlation include its computational simplicity, its applicability to mixtures at temperatures other than 30 degrees C, and the fact that only the bitumen and diluent viscosities are needed to make predictions. It is the only correlation capable of predicting viscosities of mixtures, as well as diluent mass fractions required to reduce bitumen viscosity to pumping viscosities. The prediction of viscosities at 25, 60.3, and 82.6 degrees C produced excellent results, particularly at high temperatures with an average absolute deviation of below 10%. 11 refs., 3 figs., 8 tabs.
Energy Technology Data Exchange (ETDEWEB)
Zheng Yongai, E-mail: zhengyongai@163.co [Department of Computer, Yangzhou University, Yangzhou, 225009 (China); Nian Yibei [School of Energy and Power Engineering, Yangzhou University, Yangzhou, 225009 (China); Wang Dejin [Department of Computer, Yangzhou University, Yangzhou, 225009 (China)
2010-12-01
In this Letter, a kind of novel model, called the generalized Takagi-Sugeno (T-S) fuzzy model, is first developed by extending the conventional T-S fuzzy model. Then, a simple but efficient method to control fractional order chaotic systems is proposed using the generalized T-S fuzzy model and adaptive adjustment mechanism (AAM). Sufficient conditions are derived to guarantee chaos control from the stability criterion of linear fractional order systems. The proposed approach offers a systematic design procedure for stabilizing a large class of fractional order chaotic systems from the literature about chaos research. The effectiveness of the approach is tested on fractional order Roessler system and fractional order Lorenz system.
N'Doye, Ibrahima
2015-05-25
In this paper, a dynamical fractional viscoelastic fluids convection model in porous media is proposed and its chaotic behavior is studied. A preformed equilibrium points analysis indicates the conditions where chaotic dynamics can be observed, and show the existence of chaos. The behavior and stability analysis of the integer-order and the fractional commensurate and non-commensurate orders of a fractional viscoelastic fluids system, which exhibits chaos, are presented as well.
Numerical Solution of Fractional Neutron Point Kinetics Model in Nuclear Reactor
Directory of Open Access Journals (Sweden)
Nowak Tomasz Karol
2014-06-01
Full Text Available This paper presents results concerning solutions of the fractional neutron point kinetics model for a nuclear reactor. Proposed model consists of a bilinear system of fractional and ordinary differential equations. Three methods to solve the model are presented and compared. The first one entails application of discrete Grünwald-Letnikov definition of the fractional derivative in the model. Second involves building an analog scheme in the FOMCON Toolbox in MATLAB environment. Third is the method proposed by Edwards. The impact of selected parameters on the model’s response was examined. The results for typical input were discussed and compared.
Compartmentation prevents a lethal turbo-explosion of glycolysis in trypanosomes
J.R. Haanstra (Jurgen); A. van Tuijl (Arjen); P. Kessler (Peter); W. Reijnders (Willem); P.A.M. Michels (Paul); H.V. Westerhoff (Hans); M. Parsons (Marilyn); B.M. Bakker (Barbara)
2008-01-01
textabstractATP generation by both glycolysis and glycerol catabolism is autocatalytic, because the first kinases of these pathways are fuelled by ATP produced downstream. Previous modeling studies predicted that either feedback inhibition or compartmentation of glycolysis can protect cells from acc
Deliyianni, Eleni; Gagatsis, Athanasios; Elia, Iliada; Panaoura, Areti
2016-01-01
The aim of this study was to propose and validate a structural model in fraction and decimal number addition, which is founded primarily on a synthesis of major theoretical approaches in the field of representations in Mathematics and also on previous research on the learning of fractions and decimals. The study was conducted among 1,701 primary…
The Role of the Mittag-Leffler Function in Fractional Modeling
Directory of Open Access Journals (Sweden)
Sergei Rogosin
2015-05-01
Full Text Available This is a survey paper illuminating the distinguished role of the Mittag-Leffler function and its generalizations in fractional analysis and fractional modeling. The content of the paper is connected to the recently published monograph by Rudolf Gorenflo, Anatoly Kilbas, Francesco Mainardi and Sergei Rogosin.
Deliyianni, Eleni; Gagatsis, Athanasios; Elia, Iliada; Panaoura, Areti
2016-01-01
The aim of this study was to propose and validate a structural model in fraction and decimal number addition, which is founded primarily on a synthesis of major theoretical approaches in the field of representations in Mathematics and also on previous research on the learning of fractions and decimals. The study was conducted among 1,701 primary…
Dividing Fractions Using an Area Model: A Look at In-Service Teachers' Understanding
Lamberg, Teruni; Wiest, Lynda R.
2015-01-01
The paper reports an investigation into how a group of elementary and middle school teachers collectively attempted to solve and understand a fraction division problem using an area model. Solving the word problem required that teachers determine how many two-thirds fit into three-fourths. The teachers struggled to conceptualise fraction division,…
A Verilog-A Based Fractional Frequency Synthesizer Model for Fast and Accurate Noise Assessment
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V. R. Gonzalez-Diaz
2016-04-01
Full Text Available This paper presents a new strategy to simulate fractional frequency synthesizer behavioral models with better performance and reduced simulation time. The models are described in Verilog-A with accurate phase noise predictions and they are based on a time jitter to power spectral density transformation of the principal noise sources in a synthesizer. The results of a fractional frequency synthesizer simulation is compared with state of the art Verilog-A descriptions showing a reduction of nearly 20 times. In addition, experimental results of a fractional frequency synthesizer are compared to the simulation results to validate the proposed model.
A mathematical analysis of second messenger compartmentalization.
Chen, Wen; Levine, Herbert; Rappel, Wouter-Jan
2008-12-10
Intracellular compartmentalization of second messengers can lead to microdomains of elevated concentration that are thought to be involved in ensuring signaling specificity. Most experimental evidence for this compartmentalization involves the second messenger adenosine monophosphate (cAMP), which is degraded by phosphodiesterases (PDEs). One possible way of creating these compartments, supported by recent experiments, is to spatially separate the source of cAMP from regions of elevated PDE concentration. To quantify this possibility, we study here a simplified geometry in two dimensions (2D) and in three dimensions (3D), containing a cAMP point source and regions with different degradation constants. Using the symmetry of our geometry, we are able to derive steady state solutions for the cAMP concentration as a function of the system parameters. Furthermore, we show, using analytics as well as direct numerical simulations, that for physiologically relevant time scales the steady state solution has been reached. Our results indicate that elevating the degradation constant throughout the cell, except for a small microdomain surrounding the source, requires an unphysiologically high cellular PDE concentration. On the other hand, a tight spatial relationship of localized PDEs with the cAMP source can result in functional microdomains while maintaining a physiologically plausible cellular PDE concentration.
Wei, Song; Chen, Wen; Hon, Y. C.
2016-11-01
This paper investigates the temporal effects in the modeling of flows through porous media and particles transport. Studies will be made among the time fractional diffusion model and two classical nonlinear diffusion models. The effects of the parameters upon the mentioned models have been studied. By simulating the sub-diffusion processes and comparing the numerical results of these models under different boundary conditions, we can conclude that the time fractional diffusion model is more suitable for simulating the sub-diffusion with steady diffusion rate; whereas the nonlinear models are more appropriate for depicting the sub-diffusion under changing diffusion rate.
Three-compartmental analysis of effects of D-propranolol on thyroid hormone kinetics
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Van Der Heijden, J.T.M.; Krenning, E.P.; Van Toor, H.; Hennemann, G.; Docter, R. (University Hospital Rotterdam (Netherlands))
1988-07-01
Tracer thyroxine (T{sub 4}), 3,3{prime},5-triiodothyronine (T{sub 3}), and 3,3{prime},5{prime}-triiodothyronine (rT{sub 3}) kinetic studies were performed in normal T{sub 4} substituted subjects before and during oral D-propranolol treatment to determine whether changes in thyroid hormone metabolism in a propranolol-induced low-T{sub 3} syndrome result from inhibition of 5{prime}-deiodination or inhibition of transport of iodothyronines into tissues. Data were analyzed according to a three-compartmental model of distribution and metabolism. No changes were observed in size of the three T{sub 4} compartments or in fractional and mass transfer rates of T{sub 4} from plasma to the rapidly (REP) and slowly (SEP) equilibrating pools. Serum T{sub 3}, free T{sub 3}, T{sub 3} plasma pool, T{sub 3} mass transfer rate to REP and SEP, and the T{sub 3} pool masses were all significantly decreased during propranolol to a similar extent as the T{sub 3} plasma production rate (PR). It is concluded that the D-propranolol-induced changes in thyroid hormone metabolism, resulting in a low-T{sub 3} syndrome, are due to inhibition of thyroid hormone deiodination. This is in contrast to the low-T{sub 3} syndrome during caloric deprivation, which results from inhibition of transport of iodothyronines into the liver.
Aromatization of light naphtha fractions on zeolites 1: Kinetic model
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Rovenskaja Svetlana A.
2003-01-01
Full Text Available On the basis of analyzing kinetic experimental data performed in laboratory integral reactors a lumping kinetic model of the "Zeoforming" process was developed. A reaction scheme of the lumped components was proposed, that was adapted to the technological requirements. The reaction rate constants and activation energies were estimated, that are valid for certain feed compositions. The model is intended for further modeling and optimization of the process.
Mendoza, Carlos I; Santamaría-Holek, I
2009-01-28
We propose a simple and general model accounting for the dependence of the viscosity of a hard sphere suspension at arbitrary volume fractions. The model constitutes a continuum-medium description based on a recursive-differential method where correlations between the spheres are introduced through an effective volume fraction. In contrast to other differential methods, the introduction of the effective volume fraction as the integration variable implicitly considers interactions between the spheres of the same recursive stage. The final expression for the viscosity scales with this effective volume fraction, which allows constructing a master curve that contains all the experimental situations considered. The agreement of our expression for the viscosity with experiments at low- and high-shear rates and in the high-frequency limit is remarkable for all volume fractions.
Numerical Solution of Fractional Diffusion Equation Model for Freezing in Finite Media
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R. S. Damor
2013-01-01
Full Text Available Phase change problems play very important role in engineering sciences including casting of nuclear waste materials, vivo freezing of biological tissues, solar collectors and so forth. In present paper, we propose fractional diffusion equation model for alloy solidification. A transient heat transfer analysis is carried out to study the anomalous diffusion. Finite difference method is used to solve the fractional differential equation model. The temperature profiles, the motion of interface, and interface velocity have been evaluated for space fractional diffusion equation.
A review of inhalability fraction models: discussion and recommendations.
Millage, Kyle K; Bergman, Josh; Asgharian, Bahman; McClellan, Gene
2010-02-01
The first step in mathematically modeling the mechanics of respiratory deposition of particles is to estimate the ability of a particle to enter the head, either through the mouth or nose. Models of the biological effects from inhaled particles are commonly, albeit incorrectly, simplified by making an assumption that the only particles of concern are those that can readily penetrate to the pulmonary region of the lung: typically particles less than 5microm in aerodynamic diameter. Inhalability for particles of this size is effectively 100%, so there is little need to develop a mathematical representation of the phenomenon. However, chemical irritants, biological agents, or radioactive material, in the form of large particles or droplets, can cause adverse biological responses by simply being taken into the head and depositing in the extrathoracic area. As a result, it is important to understand the inhalability of both small and large particles. The concept of particle inhalability received little consideration until the 1970s; since then it has been the subject of many experiments with a fairly wide disparity of results, in part due to the variety of dependent variables and the difficulty in adequate measurement methods. This article describes the currently utilized models of inhalability, recommends specific methods for implementing inhalability into mathematical models of respiratory deposition, and identifies outstanding issues and limitations. In this article, we describe inhalability as it applies to particulate matter and liquid droplets; modeling the inhalability of fibers is a work in progress and is not addressed.
Neuronal spike timing adaptation described with a fractional leaky integrate-and-fire model.
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Wondimu Teka
2014-03-01
Full Text Available The voltage trace of neuronal activities can follow multiple timescale dynamics that arise from correlated membrane conductances. Such processes can result in power-law behavior in which the membrane voltage cannot be characterized with a single time constant. The emergent effect of these membrane correlations is a non-Markovian process that can be modeled with a fractional derivative. A fractional derivative is a non-local process in which the value of the variable is determined by integrating a temporal weighted voltage trace, also called the memory trace. Here we developed and analyzed a fractional leaky integrate-and-fire model in which the exponent of the fractional derivative can vary from 0 to 1, with 1 representing the normal derivative. As the exponent of the fractional derivative decreases, the weights of the voltage trace increase. Thus, the value of the voltage is increasingly correlated with the trajectory of the voltage in the past. By varying only the fractional exponent, our model can reproduce upward and downward spike adaptations found experimentally in neocortical pyramidal cells and tectal neurons in vitro. The model also produces spikes with longer first-spike latency and high inter-spike variability with power-law distribution. We further analyze spike adaptation and the responses to noisy and oscillatory input. The fractional model generates reliable spike patterns in response to noisy input. Overall, the spiking activity of the fractional leaky integrate-and-fire model deviates from the spiking activity of the Markovian model and reflects the temporal accumulated intrinsic membrane dynamics that affect the response of the neuron to external stimulation.
Critical exponents of O(N) models in fractional dimensions
Codello, A; D'Odorico, G
2014-01-01
We compute critical exponents of O(N) models in fractal dimensions between two and four, and for continuos values of the number of field components N, in this way completing the RG classification of universality classes for these models. In d=2 the N-dependence of the correlation length critical exponent gives us the last piece of information needed to establish a RG derivation of the Mermin-Wagner theorem. We also report critical exponents for multi-critical universality classes in the cases N>1 and N=0. Finally, in the large-N limit our critical exponents correctly approach those of the spherical model, allowing us to set N~100 as threshold for the quantitative validity of leading order large-N estimates.
Tian, Li-Ping; Liu, Lizhi; Wu, Fang-Xiang
2010-01-01
Derived from biochemical principles, molecular biological systems can be described by a group of differential equations. Generally these differential equations contain fractional functions plus polynomials (which we call improper fractional model) as reaction rates. As a result, molecular biological systems are nonlinear in both parameters and states. It is well known that it is challenging to estimate parameters nonlinear in a model. However, in fractional functions both the denominator and numerator are linear in the parameters while polynomials are also linear in parameters. Based on this observation, we develop an iterative linear least squares method for estimating parameters in biological systems modeled by improper fractional functions. The basic idea is to transfer optimizing a nonlinear least squares objective function into iteratively solving a sequence of linear least squares problems. The developed method is applied to the estimation of parameters in a metabolism system. The simulation results show the superior performance of the proposed method for estimating parameters in such molecular biological systems.
Magnetization direction in the Heisenberg model exhibiting fractional Brownian motion
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Zhang, Zhengping; Mouritsen, Ole G.; Zuckermann, Martin J.
1993-01-01
The temporal magnetization-direction fluctuations in the three-dimensional classical ferromagnetic Heisenberg model have been generated by Monte Carlo simulation and analyzed by the rescaled-range method to yield the Hurst exponent H. A value of H congruent-to 1 has been found to apply...
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Gianni Pagnini
2012-01-01
inhomogeneity and nonstationarity properties of the medium. For instance, when this superposition is applied to the time-fractional diffusion process, the resulting Master Equation emerges to be the governing equation of the Erdélyi-Kober fractional diffusion, that describes the evolution of the marginal distribution of the so-called generalized grey Brownian motion. This motion is a parametric class of stochastic processes that provides models for both fast and slow anomalous diffusion: it is made up of self-similar processes with stationary increments and depends on two real parameters. The class includes the fractional Brownian motion, the time-fractional diffusion stochastic processes, and the standard Brownian motion. In this framework, the M-Wright function (known also as Mainardi function emerges as a natural generalization of the Gaussian distribution, recovering the same key role of the Gaussian density for the standard and the fractional Brownian motion.
Likelihood inference for a nonstationary fractional autoregressive model
DEFF Research Database (Denmark)
Johansen, Søren; Ørregård Nielsen, Morten
2010-01-01
the conditional Gaussian likelihood and for the probability analysis we also condition on initial values but assume that the errors in the autoregressive model are i.i.d. with suitable moment conditions. We analyze the conditional likelihood and its derivatives as stochastic processes in the parameters, including...... d and b, and prove that they converge in distribution. We use the results to prove consistency of the maximum likelihood estimator for d,b in a large compact subset of {1/2...
A set for relational reasoning: Facilitation of algebraic modeling by a fraction task.
DeWolf, Melissa; Bassok, Miriam; Holyoak, Keith J
2016-12-01
Recent work has identified correlations between early mastery of fractions and later math achievement, especially in algebra. However, causal connections between aspects of reasoning with fractions and improved algebra performance have yet to be established. The current study investigated whether relational reasoning with fractions facilitates subsequent algebraic reasoning using both pre-algebra students and adult college students. Participants were first given either a relational reasoning fractions task or a fraction algebra procedures control task. Then, all participants solved word problems and constructed algebraic equations in either multiplication or division format. The word problems and the equation construction tasks involved simple multiplicative comparison statements such as "There are 4 times as many students as teachers in a classroom." Performance on the algebraic equation construction task was enhanced for participants who had previously completed the relational fractions task compared with those who completed the fraction algebra procedures task. This finding suggests that relational reasoning with fractions can establish a relational set that promotes students' tendency to model relations using algebraic expressions.
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Nicy Sebastian
2015-08-01
Full Text Available The essentials of fractional calculus according to different approaches that can be useful for our applications in the theory of probability and stochastic processes are established. In addition to this, from this fractional integral, one can list out almost all of the extended densities for the pathway parameter q < 1 and q → 1. Here, we bring out the idea of thicker- or thinner-tailed models associated with a gamma-type distribution as a limiting case of the pathway operator. Applications of this extended gamma model in statistical mechanics, input-output models, solar spectral irradiance modeling, etc., are established.
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HASHEM SABERI NAJAFI
2016-07-01
Full Text Available Generalized differential transform method (GDTM is a powerful method to solve the fractional differential equations. In this paper, a new fractional model for systems with single degree of freedom (SDOF is presented, by using the GDTM. The advantage of this method compared with some other numerical methods has been shown. The analysis of new approximations, damping and acceleration of systems are also described. Finally, by reducing damping and analysis of the errors, in one of the fractional cases, we have shown that in addition to having a suitable solution for the displacement close to the exact one, the system enjoys acceleration once crossing the equilibrium point.
Analysis of the Keller–Segel Model with a Fractional Derivative without Singular Kernel
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Abdon Atangana
2015-06-01
Full Text Available Using some investigations based on information theory, the model proposed by Keller and Segel was extended to the concept of fractional derivative using the derivative with fractional order without singular kernel recently proposed by Caputo and Fabrizio. We present in detail the existence of the coupled-solutions using the fixed-point theorem. A detailed analysis of the uniqueness of the coupled-solutions is also presented. Using an iterative approach, we derive special coupled-solutions of the modified system and we present some numerical simulations to see the effect of the fractional order.
Shimabukuro, Yosio Edemir; Smith, James A.
1991-01-01
Constrained-least-squares and weighted-least-squares mixing models for generating fraction images derived from remote sensing multispectral data are presented. An experiment considering three components within the pixels-eucalyptus, soil (understory), and shade-was performed. The generated fraction images for shade (shade image) derived from these two methods were compared by considering the performance and computer time. The derived shade images are related to the observed variation in forest structure, i.e., the fraction of inferred shade in the pixel is related to different eucalyptus ages.
Fractional supersymmetric Liouville theory and the multi-cut matrix models
Irie, Hirotaka
2009-01-01
We argue that the non-critical version of the k-fractional superstring theory can be described with the k-cut critical points of the matrix models. In particular we show that, from the spectrum structure of fractional super-Liouville theory, (p,q) minimal fractional superstrings live in the Z_k-symmetry breaking critical points of the k-cut two-matrix models, and that the operator contents and string susceptibility coincide in both sides. By using this correspondence, we also propose the set of primary operators of the fractional superconformal ghost system which consistently gives the correct gravitational scaling critical exponents of the on-shell vertex operators.
Fractional supersymmetric Liouville theory and the multi-cut matrix models
Irie, Hirotaka
2009-10-01
We point out that the non-critical version of the k-fractional superstring theory can be described by k-cut critical points of the matrix models. In particular, in comparison with the spectrum structure of fractional super-Liouville theory, we show that (p,q) minimal fractional superstring theories appear in the Z-symmetry breaking critical points of the k-cut two-matrix models and the operator contents and string susceptibility coincide on both sides. By using this correspondence, we also propose a set of primary operators of the fractional superconformal ghost system which consistently produces the correct gravitational scaling critical exponents of the on-shell vertex operators.
A New Empirical Model for Estimation of sp3 Fraction in Diamond-Like Carbon Films
Institute of Scientific and Technical Information of China (English)
DAI Hai-Yang; WANG Li-Wu; JIANG Hui; HUANG Ning-Kang
2007-01-01
A new empirical model to estimate the content of sp3 in diamond-like carbon (DLC) films is presented, based on the conventional Raman spectra excited by 488nm or 514nm visible light for different carbons. It is found that bandwidth of the G peak is related to the sp3 fraction. A wider bandwidth of the G peak shows a higher sp3 fraction in DLC films.
Exact Solution of Unsteady Flow of Viscoelastic Fluid in a Pipe with Fractional Maxwell Model
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The unsteady flow of viscoelastic fluid in a cylindrical pipe was investigated using the fractional Maxwell model. Two special cases of unsteady pipe flow were expressed. The first is start-up flow, and the second is oscillating flow. The exact solution of start-up flow under a constant pressure gradient was obtained by using the theories of Laplace transform and Fourier-Bessel series for fractional derivatives. The exact solution of oscillating flow was obtained by utilizing the separation of variables.
Cure fraction estimation from the mixture cure models for grouped survival data.
Yu, Binbing; Tiwari, Ram C; Cronin, Kathleen A; Feuer, Eric J
2004-06-15
Mixture cure models are usually used to model failure time data with long-term survivors. These models have been applied to grouped survival data. The models provide simultaneous estimates of the proportion of the patients cured from disease and the distribution of the survival times for uncured patients (latency distribution). However, a crucial issue with mixture cure models is the identifiability of the cure fraction and parameters of kernel distribution. Cure fraction estimates can be quite sensitive to the choice of latency distributions and length of follow-up time. In this paper, sensitivity of parameter estimates under semi-parametric model and several most commonly used parametric models, namely lognormal, loglogistic, Weibull and generalized Gamma distributions, is explored. The cure fraction estimates from the model with generalized Gamma distribution is found to be quite robust. A simulation study was carried out to examine the effect of follow-up time and latency distribution specification on cure fraction estimation. The cure models with generalized Gamma latency distribution are applied to the population-based survival data for several cancer sites from the Surveillance, Epidemiology and End Results (SEER) Program. Several cautions on the general use of cure model are advised.
Fractional modeling of viscoelasticity in 3D cerebral arteries and aneurysms
Yu, Yue; Perdikaris, Paris; Karniadakis, George Em
2016-10-01
We develop efficient numerical methods for fractional order PDEs, and employ them to investigate viscoelastic constitutive laws for arterial wall mechanics. Recent simulations using one-dimensional models [1] have indicated that fractional order models may offer a more powerful alternative for modeling the arterial wall response, exhibiting reduced sensitivity to parametric uncertainties compared with the integer-calculus-based models. Here, we study three-dimensional (3D) fractional PDEs that naturally model the continuous relaxation properties of soft tissue, and for the first time employ them to simulate flow structure interactions for patient-specific brain aneurysms. To deal with the high memory requirements and in order to accelerate the numerical evaluation of hereditary integrals, we employ a fast convolution method [2] that reduces the memory cost to O (log (N)) and the computational complexity to O (Nlog (N)). Furthermore, we combine the fast convolution with high-order backward differentiation to achieve third-order time integration accuracy. We confirm that in 3D viscoelastic simulations, the integer order models strongly depends on the relaxation parameters, while the fractional order models are less sensitive. As an application to long-time simulations in complex geometries, we also apply the method to modeling fluid-structure interaction of a 3D patient-specific compliant cerebral artery with an aneurysm. Taken together, our findings demonstrate that fractional calculus can be employed effectively in modeling complex behavior of materials in realistic 3D time-dependent problems if properly designed efficient algorithms are employed to overcome the extra memory requirements and computational complexity associated with the non-local character of fractional derivatives.
Field Testing of Compartmentalization Methods for Multifamily Construction
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Ueno, K. [Building Science Corporation, Westford, MA (United States); Lstiburek, J. W. [Building Science Corporation, Westford, MA (United States)
2015-03-01
The 2012 International Energy Conservation Code (IECC) has an airtightness requirement of 3 air changes per hour at 50 Pascals test pressure (3 ACH50) for single-family and multifamily construction (in climate zones 3–8). The Leadership in Energy & Environmental Design certification program and ASHRAE Standard 189 have comparable compartmentalization requirements. ASHRAE Standard 62.2 will soon be responsible for all multifamily ventilation requirements (low rise and high rise); it has an exceptionally stringent compartmentalization requirement. These code and program requirements are driving the need for easier and more effective methods of compartmentalization in multifamily buildings.
Tsai, C.; Yeh, G.
2011-12-01
In this investigation, newly proposed constitutive retentions are implemented to a fractional-flow based compressible multiphase-phase flow model. With the new model, a compressible three-phase (water, non-aqueous phase liquid (NAPL) and air) flow problem is simulated. In fractional-flow approaches, the three mass balance equations written in terms of three phase pressures are transformed to those in terms of the total pressure, saturation of water, and saturation of total liquid. These three governing equations are discretized with the Galerkin finite element method (FEM). The resulted matrix equation is solved with Bi-CGSTAB. Several numerical experiments are presented to examine the accuracy and robustness of the proposed model. The results show the presented fractional-flow based multiphase flow model is feasible and yields physically realistic solutions for compressible three-phase flow problems in porous media.
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J. E. Macías-Díaz
2017-01-01
Full Text Available We depart from the well-known one-dimensional Fisher’s equation from population dynamics and consider an extension of this model using Riesz fractional derivatives in space. Positive and bounded initial-boundary data are imposed on a closed and bounded domain, and a fully discrete form of this fractional initial-boundary-value problem is provided next using fractional centered differences. The fully discrete population model is implicit and linear, so a convenient vector representation is readily derived. Under suitable conditions, the matrix representing the implicit problem is an inverse-positive matrix. Using this fact, we establish that the discrete population model is capable of preserving the positivity and the boundedness of the discrete initial-boundary conditions. Moreover, the computational solubility of the discrete model is tackled in the closing remarks.
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Bin Wang
2016-01-01
Full Text Available This paper studies the application of frequency distributed model for finite time control of a fractional order nonlinear hydroturbine governing system (HGS. Firstly, the mathematical model of HGS with external random disturbances is introduced. Secondly, a novel terminal sliding surface is proposed and its stability to origin is proved based on the frequency distributed model and Lyapunov stability theory. Furthermore, based on finite time stability and sliding mode control theory, a robust control law to ensure the occurrence of the sliding motion in a finite time is designed for stabilization of the fractional order HGS. Finally, simulation results show the effectiveness and robustness of the proposed scheme.
A fractional model for time-variant non-Newtonian flow
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Yang Xu
2017-01-01
Full Text Available This work applies a fractional flow model to describe a time-variant behavior of non-Newtonian substances. Specifically, we model the physical mechanism underlying the thixotropic and anti-thixotropic phenomena of non-Newtonian flow. This study investigates the behaviors of cellulose suspensions and SMS pastes under constant shear rate. The results imply that the presented model with only two parameters is adequate to fit experimental data. Moreover, the parameter of fractional order is an appropriate index to characterize the state of given substances. Its value indicates the extent of thixotropy and anti-thixotropy with positive and negative order respectively.
Institute of Scientific and Technical Information of China (English)
叶昆; 李黎; 唐家祥
2003-01-01
Viscoelastic dampers, as supplementary energy dissipation devices, have been used in building structures under seismic excitation or wind loads. Different analytical models have been proposed to describe their dynamic force deformation characteristics. Among these analytical models, the fractional derivative models have attracted more attention as they can capture the frequency dependence of the material stiffness and damping properties observed from tests very well. In this paper, a Fourier-transform-based technique is presented to obtain the fractional unit impulse function and the response of structures with added viscoelastic dampers whose force-deformation relationship is described by a fractional derivative model. Then, a Duhamel integral-type expression is suggested for the response analysis of a fractional damped dynamic system subjected to deterministic or random excitation. Through numerical verification, it is shown that viscoelastic dampers are effective in reducing structural responses over a wide frequency range, and the proposed schemes can be used to accurately predict the stochastic seismic response of structures with added viscoelastic dampers described by a Kelvin model with fractional derivative.
Human intake fraction of toxic pollutants: a model comparison between caltox and uses-lca
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Huijbregts, Mark A.J.; Geelen, Loes M.J.; Hertwich, Edgar G.; McKone, Thomas E.; van de Meent, Dik
2004-01-06
In Life Cycle Assessment and Comparative Risk Assessment potential human exposure to toxic pollutants can be expressed as the human intake fraction (iF), representing the fraction of the quantity emitted that enters the human population. To assess model uncertainty in the human intake fraction, ingestion and inhalation iFs of 367 substances emitted to air and freshwater were calculated with two commonly applied multi-media fate and exposure models, CalTOX and USES-LCA. Comparison of the model outcomes reveal that uncertainty in the ingestion iFs was up to a factor of 70. The uncertainty in the inhalation iFs was up to a factor of 865,000. The comparison showed that relatively few model differences account for the uncertainties found. An optimal model structure in the calculation of human intake fractions can be achieved by including (1) rain and no-rain scenarios, (2) a continental sea water compartment, (3) drinking water purification, (4) pH-correction of chemical properties, and (5) aerosol-associated deposition on plants. Finally, vertical stratification of the soil compartment combined with a chemical-dependent soil depth may be considered in future intake fraction calculations.
Tapiero, Charles S.; Vallois, Pierre
2016-11-01
The premise of this paper is that a fractional probability distribution is based on fractional operators and the fractional (Hurst) index used that alters the classical setting of random variables. For example, a random variable defined by its density function might not have a fractional density function defined in its conventional sense. Practically, it implies that a distribution's granularity defined by a fractional kernel may have properties that differ due to the fractional index used and the fractional calculus applied to define it. The purpose of this paper is to consider an application of fractional calculus to define the fractional density function of a random variable. In addition, we provide and prove a number of results, defining the functional forms of these distributions as well as their existence. In particular, we define fractional probability distributions for increasing and decreasing functions that are right continuous. Examples are used to motivate the usefulness of a statistical approach to fractional calculus and its application to economic and financial problems. In conclusion, this paper is a preliminary attempt to construct statistical fractional models. Due to the breadth and the extent of such problems, this paper may be considered as an initial attempt to do so.
Forecasting daily political opinion polls using the fractionally cointegrated VAR model
DEFF Research Database (Denmark)
Nielsen, Morten Ørregaard; Shibaev, Sergei S.
trend from the model follows the vote share of the UKIP very closely, and we thus interpret it as a measure of Euro-skepticism in public opinion rather than an indicator of the more traditional left-right political spectrum. In terms of prediction of vote shares in the election, forecasts generated......We examine forecasting performance of the recent fractionally cointegrated vector autoregressive (FCVAR) model. We use daily polling data of political support in the United Kingdom for 2010-2015 and compare with popular competing models at several forecast horizons. Our findings show that the four...... variants of the FCVAR model considered are generally ranked as the top four models in terms of forecast accuracy, and the FCVAR model significantly outperforms both univariate fractional models and the standard cointegrated VAR (CVAR) model at all forecast horizons. The relative forecast improvement...
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Shiqian Nie
2017-01-01
Full Text Available The fractional advection-diffusion equation (fADE model is a new approach to describe the vertical distribution of suspended sediment concentration in steady turbulent flow. However, the advantages and parameter definition of the fADE model in describing the sediment suspension distribution are still unclear. To address this knowledge gap, this study first reviews seven models, including the fADE model, for the vertical distribution of suspended sediment concentration in steady turbulent flow. The fADE model, among others, describes both Fickian and non-Fickian diffusive characteristics of suspended sediment, while the other six models assume that the vertical diffusion of suspended sediment follows Fick’s first law. Second, this study explores the sensitivity of the fractional index of the fADE model to the variation of particle sizes and sediment settling velocities, based on experimental data collected from the literatures. Finally, empirical formulas are developed to relate the fractional derivative order to particle size and sediment settling velocity. These formulas offer river engineers a substitutive way to estimate the fractional derivative order in the fADE model.
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Ørregård Nielsen, Morten
2015-01-01
This article proves consistency and asymptotic normality for the conditional-sum-of-squares estimator, which is equivalent to the conditional maximum likelihood estimator, in multivariate fractional time-series models. The model is parametric and quite general and, in particular, encompasses...
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Ørregård Nielsen, Morten
This paper proves consistency and asymptotic normality for the conditional-sum-of-squares estimator, which is equivalent to the conditional maximum likelihood estimator, in multivariate fractional time series models. The model is parametric and quite general, and, in particular, encompasses...
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Atangana Abdon
2016-01-01
Full Text Available In this manuscript we proposed a new fractional derivative with non-local and no-singular kernel. We presented some useful properties of the new derivative and applied it to solve the fractional heat transfer model.
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Mavroidis, Panayiotis, E-mail: mavroidis@uthscsa.edu [Department of Radiation Oncology, University of Texas Health Sciences Center, San Antonio, Texas (United States); Department of Medical Radiation Physics, Karolinska Institutet and Stockholm University, Stockholm (Sweden); Milickovic, Natasa [Department of Medical Physics and Engineering, Strahlenklinik, Klinikum Offenbach GmbH, Offenbach (Germany); Cruz, Wilbert F. [Department of Radiation Oncology, University of Texas Health Sciences Center, San Antonio, Texas (United States); Tselis, Nikolaos [Strahlenklinik, Klinikum Offenbach GmbH, Offenbach (Germany); Karabis, Andreas [Pi-Medical Ltd., Athens (Greece); Stathakis, Sotirios; Papanikolaou, Nikos [Department of Radiation Oncology, University of Texas Health Sciences Center, San Antonio, Texas (United States); Zamboglou, Nikolaos [Strahlenklinik, Klinikum Offenbach GmbH, Offenbach (Germany); Baltas, Dimos [Department of Medical Physics and Engineering, Strahlenklinik, Klinikum Offenbach GmbH, Offenbach (Germany); Nuclear and Particle Physics Section, Physics Department, University of Athens, Athens (Greece)
2014-01-01
Purpose: The aim of the present study was the investigation of different fractionation schemes to estimate their clinical impact. For this purpose, widely applied radiobiological models and dosimetric measures were used to associate their results with clinical findings. Methods and Materials: The dose distributions of 12 clinical high-dose-rate brachytherapy implants for prostate were evaluated in relation to different fractionation schemes. The fractionation schemes compared were: (1) 1 fraction of 20 Gy; (2) 2 fractions of 14 Gy; (3) 3 fractions of 11 Gy; and (4) 4 fractions of 9.5 Gy. The clinical effectiveness of the different fractionation schemes was estimated through the complication-free tumor control probability (P{sub +}), the biologically effective uniform dose, and the generalized equivalent uniform dose index. Results: For the different fractionation schemes, the tumor control probabilities were 98.5% in 1 × 20 Gy, 98.6% in 2 × 14 Gy, 97.5% in 3 × 11 Gy, and 97.8% in 4 × 9.5 Gy. The corresponding P{sub +} values were 88.8% in 1 × 20 Gy, 83.9% in 2 × 14 Gy, 86.0% in 3 × 11 Gy, and 82.3% in 4 × 9.5 Gy. With use of the fractionation scheme 4 × 9.5 Gy as reference, the isoeffective schemes regarding tumor control for 1, 2, and 3 fractions were 1 × 19.68 Gy, 2 × 13.75 Gy, and 3 × 11.05 Gy. The optimum fractionation schemes for 1, 2, 3, and 4 fractions were 1 × 19.16 Gy with a P{sub +} of 91.8%, 2 × 13.2 Gy with a P{sub +} of 89.6%, 3 × 10.6 Gy with a P{sub +} of 88.4%, and 4 × 9.02 Gy with a P{sub +} of 86.9%. Conclusions: Among the fractionation schemes 1 × 20 Gy, 2 × 14 Gy, 3 × 11 Gy, and 4 × 9.5 Gy, the first scheme was more effective in terms of P{sub +}. After performance of a radiobiological optimization, it was shown that a single fraction of 19.2 to 19.7 Gy (average 19.5 Gy) should produce at least the same benefit as that given by the 4 × 9.5 Gy scheme, and it should reduce the expected total complication probability by
Tuning algorithms for fractional order internal model controllers for time delay processes
Muresan, Cristina I.; Dutta, Abhishek; Dulf, Eva H.; Pinar, Zehra; Maxim, Anca; Ionescu, Clara M.
2016-03-01
This paper presents two tuning algorithms for fractional-order internal model control (IMC) controllers for time delay processes. The two tuning algorithms are based on two specific closed-loop control configurations: the IMC control structure and the Smith predictor structure. In the latter, the equivalency between IMC and Smith predictor control structures is used to tune a fractional-order IMC controller as the primary controller of the Smith predictor structure. Fractional-order IMC controllers are designed in both cases in order to enhance the closed-loop performance and robustness of classical integer order IMC controllers. The tuning procedures are exemplified for both single-input-single-output as well as multivariable processes, described by first-order and second-order transfer functions with time delays. Different numerical examples are provided, including a general multivariable time delay process. Integer order IMC controllers are designed in each case, as well as fractional-order IMC controllers. The simulation results show that the proposed fractional-order IMC controller ensures an increased robustness to modelling uncertainties. Experimental results are also provided, for the design of a multivariable fractional-order IMC controller in a Smith predictor structure for a quadruple-tank system.
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Sarah Malec
2015-09-01
Full Text Available Soil erosion can be linked to relative fractional cover of photosynthetic-active vegetation (PV, non-photosynthetic-active vegetation (NPV and bare soil (BS, which can be integrated into erosion models as the cover-management C-factor. This study investigates the capability of EnMAP imagery to map fractional cover in a region near San Jose, Costa Rica, characterized by spatially extensive coffee plantations and grazing in a mountainous terrain. Simulated EnMAP imagery is based on airborne hyperspectral HyMap data. Fractional cover estimates are derived in an automated fashion by extracting image endmembers to be used with a Multiple End-member Spectral Mixture Analysis approach. The C-factor is calculated based on the fractional cover estimates determined independently for EnMAP and HyMap. Results demonstrate that with EnMAP imagery it is possible to extract quality endmember classes with important spectral features related to PV, NPV and soil, and be able to estimate relative cover fractions. This spectral information is critical to separate BS and NPV which greatly can impact the C-factor derivation. From a regional perspective, we can use EnMAP to provide good fractional cover estimates that can be integrated into soil erosion modeling.
Isotropic model of fractional transport in two-dimensional bounded domains.
Kullberg, A; del-Castillo-Negrete, D; Morales, G J; Maggs, J E
2013-05-01
A two-dimensional fractional Laplacian operator is derived and used to model nonlocal, nondiffusive transport. This integro-differential operator appears in the long-wavelength, fluid description of quantities undergoing non-Brownian random walks without characteristic length scale. To study bounded domains, a mask function is introduced that modifies the kernel in the fractional Laplacian and removes singularities at the boundary. Green's function solutions to the fractional diffusion equation are presented for the unbounded domain and compared to the one-dimensional Cartesian approximations. A time-implicit numerical integration scheme is presented to study fractional diffusion in a circular disk with azimuthal symmetry. Numerical studies of steady-state reveal temperature profiles in which the heat flux and temperature gradient are in the same direction, i.e., uphill transport. The response to off-axis heating, scaling of confinement time with system size, and propagation of cold pulses are investigated.
Fractionations of rare earth elements in plants and their conceptive model
Institute of Scientific and Technical Information of China (English)
2007-01-01
Fractionations of rare earth elements (REEs) and their mechanisms in soybean were studied through application of exogenous mixed REEs under hydroponic conditions. Significant enrichment of middle REEs (MREEs) and heavy REEs (HREEs) was observed in plant roots and leaves respectively, with slight fractionation between light REEs (LREEs) and HREEs in stems. Moreover, the tetrad effect was observed in these organs. Investigations into REE speciation in roots and in the xylem sap using X-ray absorption spectroscopy (XAS) and nanometer-sized TiO2 adsorption techniques, associated with other controlled experiments, demonstrated that REE fractionations should be dominated by fixation mechanism in roots caused by cell wall absorption and phosphate precipitation, and by the combined effects of fixation mechanism and transport mechanism in aboveground parts caused by solution complexation by intrinsic organic ligands. A conceptive model was established for REE fractionations in plants based on the above studies.
Sudden spreading of infections in an epidemic model with a finite seed fraction
Hasegawa, Takehisa
2016-01-01
We study a simple case of the susceptible-weakened-infected-removed model in regular random graphs in a situation where an epidemic starts from a finite fraction of initially infected nodes (seeds). Previous studies have shown that, assuming a single seed, this model exhibits a kind of discontinuous transition at a certain value of infection rate. Performing Monte Carlo simulations and evaluating approximate master equations, we find that the present model has two critical infection rates with a finite seed fraction. At the first critical rate the system shows a percolation transition of clusters composed of removed nodes, and at the second critical rate, which is larger than the first one, a giant cluster suddenly grows and the order parameter jumps even though it has been already rising. Numerical evaluation of the master equations shows that such sudden epidemic spreading does occur if the degree of the underlying network is large and the seed fraction is small.
Directory of Open Access Journals (Sweden)
José Francisco Gómez Aguilar
2012-07-01
Full Text Available Using the fractional calculus approach, we present the Laplace analysis of an equivalent electrical circuit for a multilayered system, which includes distributed elements of the Cole model type. The Bode graphs are obtained from the numerical simulation of the corresponding transfer functions using arbitrary electrical parameters in order to illustrate the methodology. A numerical Laplace transform is used with respect to the simulation of the fractional differential equations. From the results shown in the analysis, we obtain the formula for the equivalent electrical circuit of a simple spectrum, such as that generated by a real sample of blood tissue, and the corresponding Nyquist diagrams. In addition to maintaining consistency in adjusted electrical parameters, the advantage of using fractional differential equations in the study of the impedance spectra is made clear in the analysis used to determine a compact formula for the equivalent electrical circuit, which includes the Cole model and a simple RC model as special cases.
A fractional order model for lead-acid battery crankability estimation
Sabatier, J.; Cugnet, M.; Laruelle, S.; Grugeon, S.; Sahut, B.; Oustaloup, A.; Tarascon, J. M.
2010-05-01
With EV and HEV developments, battery monitoring systems have to meet the new requirements of car industry. This paper deals with one of them, the battery ability to start a vehicle, also called battery crankability. A fractional order model obtained by system identification is used to estimate the crankability of lead-acid batteries. Fractional order modelling permits an accurate simulation of the battery electrical behaviour with a low number of parameters. It is demonstrated that battery available power is correlated to the battery crankability and its resistance. Moreover, the high-frequency gain of the fractional model can be used to evaluate the battery resistance. Then, a battery crankability estimator using the battery resistance is proposed. Finally, this technique is validated with various battery experimental data measured on test rigs and vehicles.
Model for computation of solar fraction in a single-slope solar still
Energy Technology Data Exchange (ETDEWEB)
Madhlopa, A.; Johnstone, C. [Energy Systems Research Unit, Department of Mechanical Engineering, University of Strathclyde, 75 Montrose Street, Glasgow G1 1XJ (United Kingdom)
2009-06-15
A new model that calculates the distribution of solar radiation inside a single-slope solar still has been proposed. In this model, the solar fraction on a vertical surface is divided into beam and diffuse parts and the optical view factors of surfaces inside the still are taken into account. To validate the model, outdoor tests of a conventional solar still were conducted under different weather conditions at the University of Strathclyde. The proposed model is compared with the previous one. It is found that the beam solar fraction is affected by both the geometry of the solar still and position of the sun in the sky. In contrast, the diffuse solar fraction is only dependent on the geometry of the solar distiller. The present model exhibited a lower root mean square error than that of the previous model. It appears that splitting the solar fraction into beam and diffuse parts improves the accuracy of modelling the performance of a single-slope solar still. (author)
Kaur, A; Takhar, P S; Smith, D M; Mann, J E; Brashears, M M
2008-10-01
A fractional differential equations (FDEs)-based theory involving 1- and 2-term equations was developed to predict the nonlinear survival and growth curves of foodborne pathogens. It is interesting to note that the solution of 1-term FDE leads to the Weibull model. Nonlinear regression (Gauss-Newton method) was performed to calculate the parameters of the 1-term and 2-term FDEs. The experimental inactivation data of Salmonella cocktail in ground turkey breast, ground turkey thigh, and pork shoulder; and cocktail of Salmonella, E. coli, and Listeria monocytogenes in ground beef exposed at isothermal cooking conditions of 50 to 66 degrees C were used for validation. To evaluate the performance of 2-term FDE in predicting the growth curves-growth of Salmonella typhimurium, Salmonella Enteritidis, and background flora in ground pork and boneless pork chops; and E. coli O157:H7 in ground beef in the temperature range of 22.2 to 4.4 degrees C were chosen. A program was written in Matlab to predict the model parameters and survival and growth curves. Two-term FDE was more successful in describing the complex shapes of microbial survival and growth curves as compared to the linear and Weibull models. Predicted curves of 2-term FDE had higher magnitudes of R(2) (0.89 to 0.99) and lower magnitudes of root mean square error (0.0182 to 0.5461) for all experimental cases in comparison to the linear and Weibull models. This model was capable of predicting the tails in survival curves, which was not possible using Weibull and linear models. The developed model can be used for other foodborne pathogens in a variety of food products to study the destruction and growth behavior.
Subcellular compartmentation of ascorbate and its variation in disease states.
Bánhegyi, Gábor; Benedetti, Angelo; Margittai, Eva; Marcolongo, Paola; Fulceri, Rosella; Németh, Csilla E; Szarka, András
2014-09-01
Beyond its general role as antioxidant, specific functions of ascorbate are compartmentalized within the eukaryotic cell. The list of organelle-specific functions of ascorbate has been recently expanded with the epigenetic role exerted as a cofactor for DNA and histone demethylases in the nucleus. Compartmentation necessitates the transport through intracellular membranes; members of the GLUT family and sodium-vitamin C cotransporters mediate the permeation of dehydroascorbic acid and ascorbate, respectively. Recent observations show that increased consumption and/or hindered entrance of ascorbate in/to a compartment results in pathological alterations partially resembling to scurvy, thus diseases of ascorbate compartmentation can exist. The review focuses on the reactions and transporters that can modulate ascorbate concentration and redox state in three compartments: endoplasmic reticulum, mitochondria and nucleus. By introducing the relevant experimental and clinical findings we make an attempt to coin the term of ascorbate compartmentation disease.
Compartmentalization and Transport in Synthetic Vesicles
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Christine eSchmitt
2016-02-01
Full Text Available Nano-scale vesicles have become a popular tool in life sciences. Besides liposomes that are generated from phospholipids of natural origin, polymersomes fabricated of synthetic block copolymers enjoy increasing popularity, as they represent more versatile membrane building blocks that can be selected based on their specific physicochemical properties, like permeability, stability or chemical reactivity.In this review, we focus on the application of simple and nested artificial vesicles in synthetic biology. First, we provide an introduction into the utilization of multi-compartmented vesosomes as compartmentalized nano-scale bioreactors. In the bottom-up development of protocells from vesicular nano-reactors, the specific exchange of pathway intermediates across compartment boundaries represents a bottleneck for future studies. To date, most compartmented bioreactors rely on unspecific exchange of substrates and products. This is either based on changes in permeability of the coblock polymer shell by physicochemical triggers or by the incorporation of unspecific porin proteins into the vesicle membrane. Since the incorporation of membrane transport proteins into simple and nested artificial vesicles offers the potential for specific exchange of substances between subcompartments, it opens new vistas in the design of protocells. Therefore we devote the main part of the review to summarize the technical advances in the use of phospholipids and block copolymers for the reconstitution of membrane proteins.
Compartmentalized Cytokine Responses in Hidradenitis Suppurativa.
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Theodora Kanni
Full Text Available Favorable treatment outcomes with TNF blockade led us to explore cytokine responses in hidradenitis suppurativa (HS.Blood monocytes of 120 patients and 24 healthy volunteers were subtyped by flow cytometry. Isolated blood mononuclear cells (PBMCs were stimulated for cytokine production; this was repeated in 13 severe patients during treatment with etanercept. Cytokines in pus were measured.CD14brightCD16dim inflammatory monocytes and patrolling monocytes were increased in Hurley III patients. Cytokine production by stimulated PBMCs was low compared to controls but the cytokine gene copies did not differ, indicating post-translational inhibition. The low production of IL-17 was restored, when cells were incubated with adalimumab. In pus, high concentrations of pro-inflammatory cytokines were detected. Based on the patterns, six different cytokine profiles were discerned, which are potentially relevant for the choice of treatment. Clinical improvement with etanercept was predicted by increased production of IL-1β and IL-17 by PBMCs at week 8.Findings indicate compartmentalized cytokine expression in HS; high in pus but suppressed in PBMCs. This is modulated through blockade of TNF.
HYGROSCOPIC MOISTURE SORPTION KINETICS MODELING OF CORN STOVER AND ITS FRACTIONS
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Igathinathane, C. [Mississippi State University (MSU); Pordesimo, L. O. [Mississippi State University (MSU); Womac, A.R. [University of Tennessee; Sokhansanj, Shahabaddine [ORNL
2009-01-01
Corn stover, a major crop-based lignocellulosic biomass feedstock, is required to be at an optimum moisture content for efficient bioconversion processes. Environmental conditions surrounding corn stover, as in storage facilities, affect its moisture due to hygroscopic sorption or desorption. The measurement and modeling of sorption characteristics of corn stover and its leaf, husk, and stalk fractions are useful from utilization and storage standpoints, hence investigated in this article. A benchtop low-temperature humidity chamber provided the test environments of 20 C, 30 C, and 40 C at a constant 95% relative humidity. Measured sorption characteristics with three replications for each fraction were obtained from instantaneous sample masses and initial moisture contents. Observed sorption characteristics were fitted using exponential, Page, and Peleg models. Corn stover fractions displayed a rapid initial moisture uptake followed by a slower sorption rates and eventually becoming almost asymptotic after 25 h. Sorption characteristics of all corn stover fractions were significantly different (P < 0.0001) but not the effect of temperature (P > 0.05) on these fractions. The initial 30 min of sorption was found to be critical due to peak rates of sorption from storage, handling, and processing standpoints. The Page and Peleg models had comparable performance fitting the sorption curves (R2 = 0.995), however the exponential model (R2 = 0.91) was not found suitable because of patterned residuals. The Arrhenius type relationship (P < 0.05; R2 = 0.80) explained the temperature variation of the fitted sorption model parameters. The Peleg model fitted constants, among the sorption models studied, had the best fit (R2 = 0.93) with the Arrhenius relationship. A developed method of mass proportion, involving individual corn stover fraction dry matter ratios, predicted the whole corn stover sorption characteristics from that of its individual fractions. Sorption
Ali, Farhad; Sheikh, Nadeem Ahmad; Khan, Ilyas; Saqib, Muhammad
2017-02-01
The effects of magnetohydrodynamics on the blood flow when blood is represented as a Casson fluid, along with magnetic particles in a horizontal cylinder is studied. The flow is due to an oscillating pressure gradient. The Laplace and finite Hankel transforms are used to obtain the closed form solutions of the fractional partial differential equations. Effects of various parameters on the flow of both blood and magnetic particles are shown graphically. The analysis shows that, the model with fractional order derivatives bring a remarkable changes as compared to the ordinary model. The study highlights that applied magnetic field reduces the velocities of both the blood and magnetic particles.
Functional Compartmentalization of the Human Superficial Masseter Muscle
Guzmán-Venegas, Rodrigo A.; Biotti Picand, Jorge L.; Francisco J Berral de la Rosa
2015-01-01
Some muscles have demonstrated a differential recruitment of their motor units in relation to their location and the nature of the motor task performed; this involves functional compartmentalization. There is little evidence that demonstrates the presence of a compartmentalization of the superficial masseter muscle during biting. The aim of this study was to describe the topographic distribution of the activity of the superficial masseter (SM) muscle's motor units using high-density surface e...
Comlekoglu, T.; Weinberg, S. H.
2017-09-01
Cardiac memory is the dependence of electrical activity on the prior history of one or more system state variables, including transmembrane potential (Vm), ionic current gating, and ion concentrations. While prior work has represented memory either phenomenologically or with biophysical detail, in this study, we consider an intermediate approach of a minimal three-variable cardiomyocyte model, modified with fractional-order dynamics, i.e., a differential equation of order between 0 and 1, to account for history-dependence. Memory is represented via both capacitive memory, due to fractional-order Vm dynamics, that arises due to non-ideal behavior of membrane capacitance; and ionic current gating memory, due to fractional-order gating variable dynamics, that arises due to gating history-dependence. We perform simulations for varying Vm and gating variable fractional-orders and pacing cycle length and measure action potential duration (APD) and incidence of alternans, loss of capture, and spontaneous activity. In the absence of ionic current gating memory, we find that capacitive memory, i.e., decreased Vm fractional-order, typically shortens APD, suppresses alternans, and decreases the minimum cycle length (MCL) for loss of capture. However, in the presence of ionic current gating memory, capacitive memory can prolong APD, promote alternans, and increase MCL. Further, we find that reduced Vm fractional order (typically less than 0.75) can drive phase 4 depolarizations that promote spontaneous activity. Collectively, our results demonstrate that memory reproduced by a fractional-order model can play a role in alternans formation and pacemaking, and in general, can greatly increase the range of electrophysiological characteristics exhibited by a minimal model.
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Emile Franc Doungmo Goufo
2014-01-01
Full Text Available Until now, classical models of clusters’ fission remain unable to fully explain strange phenomena like the phenomenon of shattering (Ziff and McGrady, 1987 and the sudden appearance of infinitely many particles in some systems having initial finite number of particles. That is why there is a need to extend classical models to models with fractional derivative order and use new and various techniques to analyze them. In this paper, we prove the existence of strongly continuous solution operators for nonlocal fragmentation models with Michaud time derivative of fractional order (Samko et al., 1993. We focus on the case where the splitting rate is dependent on size and position and where new particles generating from fragmentation are distributed in space randomly according to some probability density. In the analysis, we make use of the substochastic semigroup theory, the subordination principle for differential equations of fractional order (Prüss, 1993, Bazhlekova, 2000, the analogy of Hille-Yosida theorem for fractional model (Prüss, 1993, and useful properties of Mittag-Leffler relaxation function (Berberan-Santos, 2005. We are then able to show that the solution operator to the full model is positive and contractive.
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Bo Yu
2013-01-01
Full Text Available The authors present a fractional anomalous diffusion model to describe the uptake of sodium ions across the epithelium of gastrointestinal mucosa and their subsequent diffusion in the underlying blood capillaries using fractional Fick’s law. A heterogeneous two-phase model of the gastrointestinal mucosa is considered, consisting of a continuous extracellular phase and a dispersed cellular phase. The main mode of uptake is considered to be a fractional anomalous diffusion under concentration gradient and potential gradient. Appropriate partial differential equations describing the variation with time of concentrations of sodium ions in both the two phases across the intestinal wall are obtained using Riemann-Liouville space-fractional derivative and are solved by finite difference methods. The concentrations of sodium ions in the interstitial space and in the cells have been studied as a function of time, and the mean concentration of sodium ions available for absorption by the blood capillaries has also been studied. Finally, numerical results are presented graphically for various values of different parameters. This study demonstrates that fractional anomalous diffusion model is appropriate for describing the uptake of sodium ions across the epithelium of gastrointestinal mucosa.
A comparative analysis of radiobiological models for cell surviving fractions at high doses.
Andisheh, B; Edgren, M; Belkić, Dž; Mavroidis, P; Brahme, A; Lind, B K
2013-04-01
For many years the linear-quadratic (LQ) model has been widely used to describe the effects of total dose and dose per fraction at low-to-intermediate doses in conventional fractionated radiotherapy. Recent advances in stereotactic radiosurgery (SRS) and stereotactic radiotherapy (SRT) have increased the interest in finding a reliable cell survival model, which will be accurate at high doses, as well. Different models have been proposed for improving descriptions of high dose survival responses, such as the Universal Survival Curve (USC), the Kavanagh-Newman (KN) and several generalizations of the LQ model, e.g. the Linear-Quadratic-Linear (LQL) model and the Pade Linear Quadratic (PLQ) model. The purpose of the present study is to compare a number of models in order to find the best option(s) which could successfully be used as a fractionation correction method in SRT. In this work, six independent experimental data sets were used: CHOAA8 (Chinese hamster fibroblast), H460 (non-small cell lung cancer, NSLC), NCI-H841 (small cell lung cancer, SCLC), CP3 and DU145 (human prostate carcinoma cell lines) and U1690 (SCLC). By detailed comparisons with these measurements, the performance of nine different radiobiological models was examined for the entire dose range, including high doses beyond the shoulder of the survival curves. Using the computed and measured cell surviving fractions, comparison of the goodness-of-fit for all the models was performed by means of the reduced χ (2)-test with a 95% confidence interval. The obtained results indicate that models with dose-independent final slopes and extrapolation numbers generally represent better choices for SRT. This is especially important at high doses where the final slope and extrapolation numbers are presently found to play a major role. The PLQ, USC and LQL models have the least number of shortcomings at all doses. The extrapolation numbers and final slopes of these models do not depend on dose. Their asymptotes
Coil fraction-dependent phase behaviour of a model globular protein–polymer diblock copolymer
Energy Technology Data Exchange (ETDEWEB)
Thomas, Carla S. [MIT (Massachusetts Inst. of Technology), Cambridge, MA (United States); Olsen, Bradley D. [MIT (Massachusetts Inst. of Technology), Cambridge, MA (United States)
2014-01-01
The self-assembly of the model globular protein–polymer block copolymer mCherry-b-poly(N-isopropyl acrylamide) is explored across a range of polymer coil fractions from 0.21 to 0.82 to produce a phase diagram for these materials as a function of molecular composition. Overall, four types of morphologies were observed: hexagonally packed cylinders, perforated lamellae, lamellae, and disordered nanostructures. Across all coil fractions and morphologies, a lyotropic re-entrant order–disorder transition in water was observed, with disordered structures below 30 wt% and above 70 wt% and well-ordered morphologies at intermediate concentrations. Solid state samples prepared by solvent evaporation show moderately ordered structures similar to those observed in 60 wt% solutions, suggesting that bulk structures result from kinetic trapping of morphologies which appear at lower concentrations. While highly ordered cylindrical nanostructures are observed around a bioconjugate polymer volume fraction of 0.3 and well-ordered lamellae are seen near a volume fraction of 0.6, materials at lower or higher coil fractions become increasingly disordered. Notable differences between the phase behaviour of globular protein–polymer block copolymers and coil–coil diblock copolymers include the lack of spherical nanostructures at either high or low polymer coil fractions as well as shifted phase boundaries between morphologies which result in an asymmetric phase diagram.
Juraske, R; Antón, A; Castells, F; Huijbregts, M A J
2007-04-01
Human intake due to pesticide residues in food commodities can be much higher than those related to water consumption and air inhalation, stressing the importance to correctly estimate pesticide uptake into plants and predict subsequent intake by humans. We calculated the human intake fraction of captan via tomato consumption taking into account the time between pesticide application and harvest, the time between harvest and consumption, the absorption of spray deposit on plant surfaces, transfer properties through the cuticle, degradation inside the plant and loss due to food processing. Human population intake fractions due to ingestion were calculated for complete, washed and peeled tomatoes. The calculated intake fractions were compared with measurements derived from an experimental setup in a Mediterranean greenhouse. The fraction of captan applied in the greenhouse as plant treatment that eventually is ingested by the human population is on average 10(-2)-10(-5), depending on the time between pesticide application and ingestion of tomatoes and the processing step considered. Model and experimentally derived intake fractions deviated less than a factor of 2 for complete and washed tomatoes and a factor of 3 for peeled tomatoes. Intake fractions due to air inhalation and consumption of drinking water are expected to be significantly lower (5-9 orders of magnitude) than those induced by the intake of tomatoes in this case study.
Directory of Open Access Journals (Sweden)
Andrew McAloon
2011-12-01
Full Text Available An economical and environmentally friendly whey protein fractionation process was developed using supercritical carbon dioxide (sCO2 as an acid to produce enriched fractions of α-lactalbumin (α-LA and β-lactoglobulin (β-LG from a commercial whey protein isolate (WPI containing 20% α-LA and 55% β-LG, through selective precipitation of α-LA. Pilot-scale experiments were performed around the optimal parameter range (T = 60 to 65 °C, P = 8 to 31 MPa, C = 5 to 15% (w/w WPI to quantify the recovery rates of the individual proteins and the compositions of both fractions as a function of processing conditions. Mass balances were calculated in a process flow-sheet to design a large-scale, semi-continuous process model using SuperproDesigner® software. Total startup and production costs were estimated as a function of processing parameters, product yield and purity. Temperature, T, pressure, P, and concentration, C, showed conflicting effects on equipment costs and the individual precipitation rates of the two proteins, affecting the quantity, quality, and production cost of the fractions considerably. The highest α-LA purity, 61%, with 80% α-LA recovery in the solid fraction, was obtained at T = 60 °C, C = 5% WPI, P = 8.3 MPa, with a production cost of $8.65 per kilogram of WPI treated. The most profitable conditions resulted in 57%-pure α-LA, with 71% α-LA recovery in the solid fraction and 89% β-LG recovery in the soluble fraction, and production cost of $5.43 per kilogram of WPI treated at T = 62 °C, C = 10% WPI and P = 5.5 MPa. The two fractions are ready-to-use, new food ingredients with a pH of 6.7 and contain no residual acid or chemical contaminants.
Effective-field-theory model for the fractional quantum Hall effect
Zhang, S. C.; Hansson, T. H.; Kivelson, S.
1989-01-01
Starting directly from the microscopic Hamiltonian, a field-theory model is derived for the fractional quantum Hall effect. By considering an approximate coarse-grained version of the same model, a Landau-Ginzburg theory similar to that of Girvin (1986) is constructed. The partition function of the model exhibits cusps as a function of density. It is shown that the collective density fluctuations are massive.
Numerical Fractional-Calculus Model for Two-Phase Flow in Fractured Media
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Wenwen Zhong
2013-01-01
Full Text Available Numerical simulation of two-phase flow in fractured porous media is an important topic in the subsurface flow, environmental problems, and petroleum reservoir engineering. The conventional model does not work well in many cases since it lacks the memory property of fracture media. In this paper, we develop a new numerical formulation with fractional time derivative for two-phase flow in fractured porous media. In the proposed formulation, the different fractional time derivatives are applied to fracture and matrix regions since they have different memory properties. We further develop a two-level time discrete method, which uses a large time step for the pressure and a small time step size for the saturation. The pressure equation is solved implicitly in each large time step, while the saturation is updated by an explicit fractional time scheme in each time substep. Finally, the numerical tests are carried out to demonstrate the effectiveness of the proposed numerical model.
Fractional-order mathematical model of an irrigation main canal pool
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Shlomi N. Calderon-Valdez
2015-09-01
Full Text Available In this paper a fractional order model for an irrigation main canal is proposed. It is based on the experiments developed in a laboratory prototype of a hydraulic canal and the application of a direct system identification methodology. The hydraulic processes that take place in this canal are equivalent to those that occur in real main irrigation canals and the results obtained here can therefore be easily extended to real canals. The accuracy of the proposed fractional order model is compared by deriving two other integer-order models of the canal of a complexity similar to that proposed here. The parameters of these three mathematical models have been identified by minimizing the Integral Square Error (ISE performance index existing between the models and the real-time experimental data obtained from the canal prototype. A comparison of the performances of these three models shows that the fractional-order model has the lowest error and therefore the higher accuracy. Experiments showed that our model outperformed the accuracy of the integer-order models by about 25%, which is a significant improvement as regards to capturing the canal dynamics.
Development of a three dimensional circulation model based on fractional step method
Abualtayef, Mazen; Kuroiwa, Masamitsu; Seif, Ahmed Khaled; Matsubara, Yuhei; Aly, Ahmed M.; Sayed, Ahmed A.; Sambe, Alioune Nar
2010-03-01
A numerical model was developed for simulating a three-dimensional multilayer hydrodynamic and thermodynamic model in domains with irregular bottom topography. The model was designed for examining the interactions between flow and topography. The model was based on the three-dimensional Navier-Stokes equations and was solved using the fractional step method, which combines the finite difference method in the horizontal plane and the finite element method in the vertical plane. The numerical techniques were described and the model test and application were presented. For the model application to the northern part of Ariake Sea, the hydrodynamic.
Fractional Modeling of the AC Large-Signal Frequency Response in Magnetoresistive Current Sensors
Directory of Open Access Journals (Sweden)
Sergio Iván Ravelo Arias
2013-12-01
Full Text Available Fractional calculus is considered when derivatives and integrals of non-integer order are applied over a specific function. In the electrical and electronic domain, the transfer function dependence of a fractional filter not only by the filter order n, but additionally, of the fractional order α is an example of a great number of systems where its input-output behavior could be more exactly modeled by a fractional behavior. Following this aim, the present work shows the experimental ac large-signal frequency response of a family of electrical current sensors based in different spintronic conduction mechanisms. Using an ac characterization set-up the sensor transimpedance function is obtained considering it as the relationship between sensor output voltage and input sensing current,[PLEASE CHECK FORMULA IN THE PDF]. The study has been extended to various magnetoresistance sensors based in different technologies like anisotropic magnetoresistance (AMR, giant magnetoresistance (GMR, spin-valve (GMR-SV and tunnel magnetoresistance (TMR. The resulting modeling shows two predominant behaviors, the low-pass and the inverse low-pass with fractional index different from the classical integer response. The TMR technology with internal magnetization offers the best dynamic and sensitivity properties opening the way to develop actual industrial applications.
Bayesian bivariate generalized Lindley model for survival data with a cure fraction.
Martinez, Edson Z; Achcar, Jorge A
2014-11-01
The cure fraction models have been widely used to analyze survival data in which a proportion of the individuals is not susceptible to the event of interest. In this article, we introduce a bivariate model for survival data with a cure fraction based on the three-parameter generalized Lindley distribution. The joint distribution of the survival times is obtained by using copula functions. We consider three types of copula function models, the Farlie-Gumbel-Morgenstern (FGM), Clayton and Gumbel-Barnett copulas. The model is implemented under a Bayesian framework, where the parameter estimation is based on Markov Chain Monte Carlo (MCMC) techniques. To illustrate the utility of the model, we consider an application to a real data set related to an invasive cervical cancer study.
Jazia, Abderrahmin Ben; Bellis, Cédric
2013-01-01
This study focuses on the numerical modeling of wave propagation in fractionally-dissipative media. These viscoelastic models are such that the attenuation is frequency dependent and follows a power law with non-integer exponent. As a prototypical example, the Andrade model is chosen for its simplicity and its satisfactory fits of experimental flow laws in rocks and metals. The corresponding constitutive equation features a fractional derivative in time, a non-local term that can be expressed as a convolution product which direct implementation bears substantial memory cost. To circumvent this limitation, a diffusive representation approach is deployed, replacing the convolution product by an integral of a function satisfying a local time-domain ordinary differential equation. An associated quadrature formula yields a local-in-time system of partial differential equations, which is then proven to be well-posed. The properties of the resulting model are also compared to those of the original Andrade model. The...
Su, Qian; Tan, Chao; Dong, Feng
2017-03-01
When measuring the phase fraction of oil–water two-phase flow with the ultrasound attenuation, the phase distribution and fraction have direct influence on the attenuation coefficient. Therefore, the ultrasound propagation at various phase fractions and distributions were investigated. Mechanism models describing phase fraction with the ultrasound attenuation coefficient were established by analyzing the interaction between ultrasound and two-phase flow by considering the scattering, absorption and diffusion effect. Experiments were performed to verify the theoretical analysis, and the test results gave good agreement with the theoretical analysis. When the dispersed phase fraction is low, the relationship between ultrasound attenuation coefficient and phase fraction is of monotonic linearity; at higher dispersed phase fraction, ultrasound attenuation coefficient presents an irregular response to the dispersed phase fraction. The presented mechanism models give reasonable explanations about the trend of ultrasound attenuation.
DEVELOPMENT OF A POPULATION BALANCE MODEL TO SIMULATE FRACTIONATION OF GROUND SWITCHGRASS
Energy Technology Data Exchange (ETDEWEB)
Naimi, L.J. [University of British Columbia, Vancouver; Bi, X.T. [University of British Columbia, Vancouver; Lau, A.K. [University of British Columbia, Vancouver; Sokhansanj, Shahabaddine [ORNL; Womac, A.R. [University of Tennessee, Knoxville (UTK); Igathinathane, C. [North Dakota State University; Sowlati, T. [University of British Columbia, Vancouver; Melin, Staffan [Delta Research Corporation; Emami, M. [University of British Columbia, Vancouver; Afzal, M [University of New Brunswick
2011-01-01
The population balance model represents a time-dependent formulation of mass conservation for a ground biomass that flows through a set of sieves. The model is suitable for predicting the change in size and distribution of ground biomass while taking into account the flow rate processes of particles through a grinder. This article describes the development and application of this model to a switchgrass grinding operation. The mass conservation formulation of the model contains two parameters: breakage rate and breakage ratio. A laboratory knife mill was modified to act as a batch or flow-through grinder. The ground switchgrass was analyzed over a set of six Tyler sieves with apertures ranging from 5.66 mm (top sieve) to 1 mm (bottom sieve). The breakage rate was estimated from the sieving tests. For estimating the breakage ratio, each of the six fractions was further ground and sieved to 11 fractions on a set of sieves with apertures ranging from 5.66 to 0.25 mm (and pan). These data formed a matrix of values for determining the breakage ratio. Using the two estimated parameters, the transient population balance model was solved numerically. Results indicated that the population balance model generally underpredicted the fractions remaining on sieves with 5.66, 4.00, and 2.83 mm apertures and overpredicted fractions remaining on sieves with 2.00, 1.41, and 1.00 mm apertures. These trends were similar for both the batch and flow-through grinder configurations. The root mean square of residuals (RSE), representing the difference between experimental and simulated mass of fractions, was 0.32 g for batch grinding and 0.1 g for flow-through grinding. The breakage rate exhibited a linear function of the logarithm of particle size, with a regression coefficient of 0.99.
Freed, Alan D.; Diethelm, Kai; Gray, Hugh R. (Technical Monitor)
2002-01-01
Fraction-order viscoelastic (FOV) material models have been proposed and studied in 1D since the 1930's, and were extended into three dimensions in the 1970's under the assumption of infinitesimal straining. It was not until 1997 that Drozdov introduced the first finite-strain FOV constitutive equations. In our presentation, we shall continue in this tradition by extending the standard, FOV, fluid and solid, material models introduced in 1971 by Caputo and Mainardi into 3D constitutive formula applicable for finite-strain analyses. To achieve this, we generalize both the convected and co-rotational derivatives of tensor fields to fractional order. This is accomplished by defining them first as body tensor fields and then mapping them into space as objective Cartesian tensor fields. Constitutive equations are constructed using both variants for fractional rate, and their responses are contrasted in simple shear. After five years of research and development, we now possess a basic suite of numerical tools necessary to study finite-strain FOV constitutive equations and their iterative refinement into a mature collection of material models. Numerical methods still need to be developed for efficiently solving fraction al-order integrals, derivatives, and differential equations in a finite element setting where such constitutive formulae would need to be solved at each Gauss point in each element of a finite model, which can number into the millions in today's analysis.
Using Semiotic Resources to Build Images When Teaching the Part-Whole Model of Fractions
Mildenhall, Paula
2013-01-01
This paper reports an exploration into the use of a combination of semiotic resources when teaching the part-whole model of fractions. The study involved a single case study of one class teacher and six students in an Australian primary classroom. Using video as the predominate research tool it was possible to describe how gesture and language…
The role of initial values in nonstationary fractional time series models
DEFF Research Database (Denmark)
Johansen, Søren; Nielsen, Morten Ørregaard
We consider the nonstationary fractional model $\\Delta^{d}X_{t}=\\varepsilon _{t}$ with $\\varepsilon_{t}$ i.i.d.$(0,\\sigma^{2})$ and $d>1/2$. We derive an analytical expression for the main term of the asymptotic bias of the maximum likelihood estimator of $d$ conditional on initial values, and we...
The Solution of Modified Fractional Bergman’s Minimal Blood Glucose-Insulin Model
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Badr S. Alkahtani
2017-05-01
Full Text Available In the present paper, we use analytical techniques to solve fractional nonlinear differential equations systems that arise in Bergman’s minimal model, used to describe blood glucose and insulin metabolism, after intravenous tolerance testing. We also discuss the stability and uniqueness of the solution.
Longère, Patrice; Dragon, A. André
2008-01-01
Evaluation of the inelastic heat fraction in the context of microstructure supported dynamic plasticity modelling correspondence: Corresponding author. (Longere, Patrice) (Longere, Patrice) (Dragon, A. Andre) Laboratoire de Genie Mecanique et Materiaux ? Universite de Bretagne Sud ? Rue de Saint-Maude - BP 92116--> , 56321 LORIENT Cedex--> - FRANCE (Longere, Patrice)...
Sharp, Emily; Shih Dennis, Minyi
2017-01-01
This study used a multiple probe across participants design to examine the effects of a model drawing strategy (MDS) intervention package on fraction comparing and ordering word problem-solving performance of three Grade 4 students. MDS is a form of cognitive strategy instruction for teaching word problem solving that includes explicit instruction…
Momentum Fractions carried by quarks and gluons in models of proton structure functions at small $x$
Choudhury, D K; Kalita, K
2016-01-01
The paper reports analysis of momentum fractions carried by quarks and gluons in models of Proton structure functions at small $x$. First, we analyze the model proposed by Lastovicka based on self-similarity sometime back. We then make a similar analysis for a second model based on the same notion which is also free from singularity in $x$ : $0
Directory of Open Access Journals (Sweden)
Petráš Ivo
2011-01-01
Full Text Available This paper deals with the fractional-order linear and nonlinear models used in bioengineering applications and an effective method for their numerical solution. The proposed method is based on the power series expansion of a generating function. Numerical solution is in the form of the difference equation, which can be simply applied in the Matlab/Simulink to simulate the dynamics of system. Several illustrative examples are presented, which can be widely used in bioengineering as well as in the other disciplines, where the fractional calculus is often used.
Mao, Haidan; Du, Xinyue; Chen, Linfei; Zhao, Daomu
2011-06-01
On the basis of the fact that a hard-edged aperture function can be expressed as finite matrices with different weighting coefficients, we obtain the analytical formula for the propagation of the broadband gaussian Schell-model (BGSM) beam through the apertured fractional Fourier transformation (AFrFT) system. It is shown by numerical examples that the intensity distribution in the plane of a small fractional order is obviously influenced by the bandwidth when the BGSM beams propagate through the AFrFT system. Further extensions are also pointed out.
Impact of Model and Observation Error on Assimilating Snow Cover Fraction Observations
Arsenault, Kristi R.
Accurately modeling or observing snow cover fraction (SCF) estimates, which represent fractional snow cover area within a gridcell, can help with better understanding earth system dynamics, improving weather and climate prediction, and providing end-use water solutions. Seeking to obtain more accurate snowpack estimates, high resolution snow cover fraction observations are assimilated with different data assimilation (DA) methods within a land surface model (LSM). The LSM simulates snowpack states, snow water equivalent and snow depth, to obtain improved snowpack estimates known as the analysis. Data assimilation experiments are conducted for two mountainous areas where high spatial snow variability occurs, which can impact realistic snowpack representation for different hydrological and meteorological applications. Consequently, the experiments are conducted at higher model resolutions to better capture this variability. This study focuses on four key aspects of how assimilating SCF observations may improve snowpack estimates and impact the LSM overall. These include investigating the role of data assimilation method complexity, evaluating the impact of model and observational errors on snow state analysis estimates, improving the model's SCF representation for assimilation using observation operators, and examining subsequent model state and flux impacts when SCF observations are assimilated. A simpler direct insertion (DI) and a more complex ensemble Kalman filter (EnKF) data assimilation method were applied. The more complex method proved to be superior to the simpler one; however, this method required accounting for more realistic observational and model errors. Also, the EnKF method required an ensemble of model forecasts, in which bias in the ensemble generation was found and removed. Reducing this bias improved the model snowpack estimates. Detection and geolocation errors in the satellite-based snow cover fraction observations also contributed to degrading
Energy Technology Data Exchange (ETDEWEB)
Decker, A.D.; Kuuskraa, V.A.; Klawitter, A.L.
1995-10-01
Recurrent basement faulting is the primary controlling mechanism for aligning and compartmentalizing upper Cretaceous aged tight gas reservoirs of the San Juan and Piceance Basins. Northwest trending structural lineaments that formed in conjunction with the Uncompahgre Highlands have profoundly influenced sedimentation trends and created boundaries for gas migration; sealing and compartmentalizing sedimentary packages in both basins. Fractures which formed over the structural lineaments provide permeability pathways which allowing gas recovery from otherwise tight gas reservoirs. Structural alignments and associated reservoir compartments have been accurately targeted by integrating advanced remote sensing imagery, high resolution aeromagnetics, seismic interpretation, stratigraphic mapping and dynamic structural modelling. This unifying methodology is a powerful tool for exploration geologists and is also a systematic approach to tight gas resource assessment in frontier basins.
Fractional order Buck-Boost converter in CCM: modelling, analysis and simulations
Wang, Faqiang; Ma, Xikui
2014-12-01
In this paper, the modelling, analysis and the power electronics simulator (PSIM) simulations of the fractional order Buck-Boost converter operating in continuous conduction mode (CCM) operation are investigated. Based on the three-terminal switch device method, the average circuit model of the fractional order Buck-Boost converter is established, and the corresponding DC equivalent circuit model and AC small signal equivalent circuit model are presented. And then, the equilibrium point and the transfer functions are derived. It is found that the equilibrium point is not influenced by the inductor's or the capacitor's order, but both these orders are included in the derived transfer functions. Finally, the comparisons between the theoretical analysis and the PSIM simulations are given for confirmation.
Bouchard, D; Höhener, P; Hunkeler, D; 10.1016/j.jconhyd.2010.09.006
2011-01-01
Analytical models were developed that simulate stable isotope ratios of volatile organic compounds (VOCs) near a point source contamination in the unsaturated zone. The models describe diffusive transport of VOCs, biodegradation and source ageing. The mass transport is governed by Fick's law for diffusion, and the equation for reactive transport of VOCs in the soil gas phase was solved for different source geometries and for different boundary conditions. Model results were compared to experimental data from a one-dimensional laboratory column and a radial-symmetric field experiment, and the comparison yielded a satisfying agreement. The model results clearly illustrate the significant isotope fractionation by gas-phase diffusion under transient state conditions. This leads to an initial depletion of heavy isotopes with increasing distance from the source. The isotope evolution of the source is governed by the combined effects of isotope fractionation due to vaporization, diffusion and biodegradation. The net...
DEFF Research Database (Denmark)
Zhou, H. W.; Yi, H. Y.; Mishnaevsky, Leon
2016-01-01
A modeling approach to time-dependent property of Glass Fiber Reinforced Polymers (GFRP) composites is of special interest for quantitative description of long-term behavior. An electronic creep machine is employed to investigate the time-dependent deformation of four specimens of dog......-bond-shaped GFRP composites at various stress level. A negative exponent function based on structural changes is introduced to describe the damage evolution of material properties in the process of creep test. Accordingly, a new creep constitutive equation, referred to fractional derivative Maxwell model...... by the fractional derivative Maxwell model proposed in the paper are in a good agreement with the experimental data. It is shown that the new creep constitutive model proposed in the paper needs few parameters to represent various time-dependent behaviors....
POLYNOMIAL MODEL BASED FAST FRACTIONAL PIXEL SEARCH ALGORITHM FOR H.264/AVC
Institute of Scientific and Technical Information of China (English)
Xi Yinglai; Hao Chongyang; Lai Changcai
2006-01-01
This paper proposed a novel fast fractional pixel search algorithm based on polynomial model.With the analysis of distribution characteristics of motion compensation error surface inside fractional pixel searching window, the matching error is fitted with parabola along horizontal and vertical direction respectively. The proposed searching strategy needs to check only 6 points rather than 16 or 24 points, which are used in the Hierarchical Fractional Pel Search algorithm (HFPS) for 1/4-pel and 1/8-pel Motion Estimation (ME). The experimental results show that the proposed algorithm shows very good capability in keeping the rate distortion performance while reduces computation load to a large extent compared with HFPS algorithm.
Treeby, Bradley E; Cox, B T
2010-05-01
The efficient simulation of wave propagation through lossy media in which the absorption follows a frequency power law has many important applications in biomedical ultrasonics. Previous wave equations which use time-domain fractional operators require the storage of the complete pressure field at previous time steps (such operators are convolution based). This makes them unsuitable for many three-dimensional problems of interest. Here, a wave equation that utilizes two lossy derivative operators based on the fractional Laplacian is derived. These operators account separately for the required power law absorption and dispersion and can be efficiently incorporated into Fourier based pseudospectral and k-space methods without the increase in memory required by their time-domain fractional counterparts. A framework for encoding the developed wave equation using three coupled first-order constitutive equations is discussed, and the model is demonstrated through several one-, two-, and three-dimensional simulations.
Modular Data and Verlinde Formulae for Fractional Level WZW Models I
Creutzig, Thomas
2012-01-01
The modular properties of fractional level affine sl(2)-theories and, in particular, the application of the Verlinde formula, have a long and checkered history in conformal field theory. Recent advances in logarithmic conformal field theory have led to the realisation that problems with fractional level models stem from trying to build the theory with an insufficiently rich category of representations. In particular, the appearance of negative fusion coefficients for admissible highest weight representations is now completely understood. Here, the modular story for certain fractional level theories is completed. Modular transformations are derived for the complete set of admissible irreducible representations when the level is k=-1/2 or k=-4/3. The S-matrix data and Verlinde formula are then checked against the known fusion rules with complete agreement. Finally, an infinite set of modular invariant partition functions is constructed in each case.
Directory of Open Access Journals (Sweden)
Maneesha Gupta
2013-01-01
Full Text Available Second and third order digital integrators (DIs have been optimized first using Particle Swarm Optimization (PSO with minimized error fitness function obtained by registering mean, median, and standard deviation values in different random iterations. Later indirect discretization using Continued Fraction Expansion (CFE has been used to ascertain a better fitting of proposed integer order optimized DIs into their corresponding fractional counterparts by utilizing their refined properties, now restored in them due to PSO algorithm. Simulation results for the comparisons of the frequency responses of proposed 2nd and 3rd order optimized DIs and proposed discretized mathematical models of half integrators based on them, with their respective existing operators, have been presented. Proposed integer order PSO optimized integrators as well as fractional order integrators (FOIs have been observed to outperform the existing recently published operators in their respective domains reasonably well in complete range of Nyquist frequency.
Global Existence of Weak Solutions to a Fractional Model in Magnetoelastic Interactions
Directory of Open Access Journals (Sweden)
Idriss Ellahiani
2016-01-01
Full Text Available The paper deals with global existence of weak solutions to a one-dimensional mathematical model describing magnetoelastic interactions. The model is described by a fractional Landau-Lifshitz-Gilbert equation for the magnetization field coupled to an evolution equation for the displacement. We prove global existence by using Faedo-Galerkin/penalty method. Some commutator estimates are used to prove the convergence of nonlinear terms.
Directory of Open Access Journals (Sweden)
Ningning Yang
2016-01-01
Full Text Available In recent days, fractional calculus (FC has been accepted as a novel modeling tool that can extend the descriptive power of the traditional calculus. Fractional-order descriptiveness can increase the flexibility and degrees of freedom of the model by means of fractional parameters. Based on the fact that real capacitors and inductors are “intrinsic” fractional order, fractional calculus is introduced into the modeling process to establish a fractional-order state-space averaging model of the Buck-Boost converter in pseudo-continuous conduction mode (PCCM. Orders of the model are considered as extra parameters, and these parameters have significant influences on the performance of the model. The inductor current, the inductor current ripple, the amplitude of the output voltage, and the transfer functions of the fractional-order model are all related to orders. The contrast simulation experiments are conducted to investigate the performance of integer-order and fractional-order Buck-Boost converters in PCCM. Results of numerical and circuit simulations demonstrate that the proposed theoretical analysis is effective; the fractional-order model of the Buck-Boost converter in PCCM has certain theoretical and practical significance for modeling and performance analysis of other electrical or electronic equipment.
Zhou, H. W.; Yi, H. Y.; Mishnaevsky, L.; Wang, R.; Duan, Z. Q.; Chen, Q.
2016-08-01
A modeling approach to time-dependent property of Glass Fiber Reinforced Polymers (GFRP) composites is of special interest for quantitative description of long-term behavior. An electronic creep machine is employed to investigate the time-dependent deformation of four specimens of dog-bond-shaped GFRP composites at various stress level. A negative exponent function based on structural changes is introduced to describe the damage evolution of material properties in the process of creep test. Accordingly, a new creep constitutive equation, referred to fractional derivative Maxwell model, is suggested to characterize the time-dependent behavior of GFRP composites by replacing Newtonian dashpot with the Abel dashpot in the classical Maxwell model. The analytic solution for the fractional derivative Maxwell model is given and the relative parameters are determined. The results estimated by the fractional derivative Maxwell model proposed in the paper are in a good agreement with the experimental data. It is shown that the new creep constitutive model proposed in the paper needs few parameters to represent various time-dependent behaviors.
Gabor-based kernel PCA with fractional power polynomial models for face recognition.
Liu, Chengjun
2004-05-01
This paper presents a novel Gabor-based kernel Principal Component Analysis (PCA) method by integrating the Gabor wavelet representation of face images and the kernel PCA method for face recognition. Gabor wavelets first derive desirable facial features characterized by spatial frequency, spatial locality, and orientation selectivity to cope with the variations due to illumination and facial expression changes. The kernel PCA method is then extended to include fractional power polynomial models for enhanced face recognition performance. A fractional power polynomial, however, does not necessarily define a kernel function, as it might not define a positive semidefinite Gram matrix. Note that the sigmoid kernels, one of the three classes of widely used kernel functions (polynomial kernels, Gaussian kernels, and sigmoid kernels), do not actually define a positive semidefinite Gram matrix either. Nevertheless, the sigmoid kernels have been successfully used in practice, such as in building support vector machines. In order to derive real kernel PCA features, we apply only those kernel PCA eigenvectors that are associated with positive eigenvalues. The feasibility of the Gabor-based kernel PCA method with fractional power polynomial models has been successfully tested on both frontal and pose-angled face recognition, using two data sets from the FERET database and the CMU PIE database, respectively. The FERET data set contains 600 frontal face images of 200 subjects, while the PIE data set consists of 680 images across five poses (left and right profiles, left and right half profiles, and frontal view) with two different facial expressions (neutral and smiling) of 68 subjects. The effectiveness of the Gabor-based kernel PCA method with fractional power polynomial models is shown in terms of both absolute performance indices and comparative performance against the PCA method, the kernel PCA method with polynomial kernels, the kernel PCA method with fractional power
Compartmentalization of prostaglandins in the canine kidney
Energy Technology Data Exchange (ETDEWEB)
Morgan-Boyd, R.L.
1986-01-01
The kidney has been shown to synthesize all of the naturally occurring major prostaglandins which may be restricted to a discrete part of the kidney where their actions are physiologically important, such as the vascular compartment and the tubular compartment. In order to examine this concept of compartmentalization, the authors conducted a series of experiments to determine whether PGl/sub 2/, measured as 6-keto-pGF/sub 1..cap alpha../, produced in the kidney is restricted to the renal vascular compartment or whether it also has access to the tubular compartment. Experiments were performed in the pentobarbital-anesthetized dog. Increasing pre-glomerular levels of 6-keto-PFG/sub 1..cap alpha../ caused marked increases in both the urinary excretion and the renal venous outflow to 6-keto-PGF/sub 1..cap alpha../. When /sup 3/H-6-keto-PGF/sub 1..cap alpha../ was co-infused with inulin into the renal artery, 33% of the radioactivity and 23% of the inulin was recovered on first pass. With infusion of /sup 3/H-PGl/sub 2/ and inulin, 20% of the radioactivity and 28% of the inulin reached the urine on first pass. Radioactive PGl/sub 2/ appeared to be less filterable at the glomeruli than either /sup 3/H-6-keto-PGF/sub 1..cap alpha../ or inulin. In the final set of experiments, in which dogs were prepared for a ureteral stopped-flow study, the PGE/sub 2//U/P/sub In/ ratio a peak was observed proximal to the Na/sup +/ plateau but distal to the Na+ nadir. In light of the results from the stopped-flow study and the intrarenal infusion studies, they conclude that PGE/sub 2/ synthesized in the kidney enters both the renal and tubular compartments. In contrast, they find that 6-keto-PGF/sub 1..cap alpha../ of renal origin enters only the renal origin enters only the renal vascular compartment and not the tubular compartment.
Frequency dependence of complex moduli of brain tissue using a fractional Zener model
Energy Technology Data Exchange (ETDEWEB)
Kohandel, M [Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada); Sivaloganathan, S [Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada); Tenti, G [Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada); Darvish, K [Center for Applied Biomechanics, University of Virginia, Charlottesville, VA (United States)
2005-06-21
Brain tissue exhibits viscoelastic behaviour. If loading times are substantially short, static tests are not sufficient to determine the complete viscoelastic behaviour of the material, and dynamic test methods are more appropriate. The concept of complex modulus of elasticity is a powerful tool for characterizing the frequency domain behaviour of viscoelastic materials. On the other hand, it is well known that classical viscoelastic models can be generalized by means of fractional calculus to describe more complex viscoelastic behaviour of materials. In this paper, the fractional Zener model is investigated in order to describe the dynamic behaviour of brain tissue. The model is fitted to experimental data of oscillatory shear tests of bovine brain tissue to verify its behaviour and to obtain the material parameters.
Linear Regression Model of the Ash Mass Fraction and Electrical Conductivity for Slovenian Honey
Directory of Open Access Journals (Sweden)
Mojca Jamnik
2008-01-01
Full Text Available Mass fraction of ash is a quality criterion for determining the botanical origin of honey. At present, this parameter is generally being replaced by the measurement of electrical conductivity (κ. The value κ depends on the ash and acid content of honey; the higher their content, the higher the resulting conductivity. A linear regression model for the relationship between ash and electrical conductivity has been established for Slovenian honey by analysing 290 samples of Slovenian honey (including acacia, lime, chestnut, spruce, fir, multifloral and mixed forest honeydew honey. The obtained model differs from the one proposed by the International Honey Commission (IHC in the slope, but not in the section part of the relation formula. Therefore, the Slovenian model is recommended when calculating the ash mass fraction from the results of electrical conductivity in samples of Slovenian honey.
A model to determine the petroleum pressure in a well using fractional differential equations
Brito Martinez, Beatriz; Brambila Paz, Fernando; Fuentes Ruiz, Carlos
2016-11-01
A noninvasive method was used to determine the pressure of petroleum leaving a well. The mathematical model is based on nonlinear fractional differential equations. This model comes from the fractal dimension of the porous medium. The problem is solved in three stages. In the first stage the fractal dimension of the porous medium is determined. We show that microwaves reflected and transmitted through soil have a fractal dimension which is correlated with the fractal dimension of the porous medium. The fractal signature of microwave scattering correlates with certain physical and mechanical properties of soils (porosity, permeability, conductivity, etc.). In the second stage we use three partial fractional equations as a mathematical model to study the diffusion inside the porous medium. In this model sub-diffusive phenomenon occurs if fractal derivative is between zero and one and supra-diffusive occurs if the derivative is greater than 1 and less than 2. Finally in the third stage the mathematical model is used to determinate the petroleum pressure output in a Mexican oil field, which contains three partial fractional equations with triple porosity and permeability.
Energy Technology Data Exchange (ETDEWEB)
Eliazar, Iddo I., E-mail: eliazar@post.tau.ac.il [Holon Institute of Technology, P.O. Box 305, Holon 58102 (Israel); Shlesinger, Michael F., E-mail: mike.shlesinger@navy.mil [Office of Naval Research, Code 30, 875 N. Randolph St., Arlington, VA 22203 (United States)
2013-06-10
Brownian motion is the archetypal model for random transport processes in science and engineering. Brownian motion displays neither wild fluctuations (the “Noah effect”), nor long-range correlations (the “Joseph effect”). The quintessential model for processes displaying the Noah effect is Lévy motion, the quintessential model for processes displaying the Joseph effect is fractional Brownian motion, and the prototypical model for processes displaying both the Noah and Joseph effects is fractional Lévy motion. In this paper we review these four random-motion models–henceforth termed “fractional motions” –via a unified physical setting that is based on Langevin’s equation, the Einstein–Smoluchowski paradigm, and stochastic scaling limits. The unified setting explains the universal macroscopic emergence of fractional motions, and predicts–according to microscopic-level details–which of the four fractional motions will emerge on the macroscopic level. The statistical properties of fractional motions are classified and parametrized by two exponents—a “Noah exponent” governing their fluctuations, and a “Joseph exponent” governing their dispersions and correlations. This self-contained review provides a concise and cohesive introduction to fractional motions.
Cheong, Chin Wen
2008-02-01
This article investigated the influences of structural breaks on the fractionally integrated time-varying volatility model in the Malaysian stock markets which included the Kuala Lumpur composite index and four major sectoral indices. A fractionally integrated time-varying volatility model combined with sudden changes is developed to study the possibility of structural change in the empirical data sets. Our empirical results showed substantial reduction in fractional differencing parameters after the inclusion of structural change during the Asian financial and currency crises. Moreover, the fractionally integrated model with sudden change in volatility performed better in the estimation and specification evaluations.
Fernández-Manso, O.; Fernández-Manso, A.; Quintano, C.
2014-09-01
Aboveground biomass (AGB) estimation from optical satellite data is usually based on regression models of original or synthetic bands. To overcome the poor relation between AGB and spectral bands due to mixed-pixels when a medium spatial resolution sensor is considered, we propose to base the AGB estimation on fraction images from Linear Spectral Mixture Analysis (LSMA). Our study area is a managed Mediterranean pine woodland (Pinus pinaster Ait.) in central Spain. A total of 1033 circular field plots were used to estimate AGB from Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) optical data. We applied Pearson correlation statistics and stepwise multiple regression to identify suitable predictors from the set of variables of original bands, fraction imagery, Normalized Difference Vegetation Index and Tasselled Cap components. Four linear models and one nonlinear model were tested. A linear combination of ASTER band 2 (red, 0.630-0.690 μm), band 8 (short wave infrared 5, 2.295-2.365 μm) and green vegetation fraction (from LSMA) was the best AGB predictor (Radj2=0.632, the root-mean-squared error of estimated AGB was 13.3 Mg ha-1 (or 37.7%), resulting from cross-validation), rather than other combinations of the above cited independent variables. Results indicated that using ASTER fraction images in regression models improves the AGB estimation in Mediterranean pine forests. The spatial distribution of the estimated AGB, based on a multiple linear regression model, may be used as baseline information for forest managers in future studies, such as quantifying the regional carbon budget, fuel accumulation or monitoring of management practices.
Fractional Brownian motion, the Matérn process, and stochastic modeling of turbulent dispersion
Lilly, Jonathan M.; Sykulski, Adam M.; Early, Jeffrey J.; Olhede, Sofia C.
2017-08-01
Stochastic processes exhibiting power-law slopes in the frequency domain are frequently well modeled by fractional Brownian motion (fBm), with the spectral slope at high frequencies being associated with the degree of small-scale roughness or fractal dimension. However, a broad class of real-world signals have a high-frequency slope, like fBm, but a plateau in the vicinity of zero frequency. This low-frequency plateau, it is shown, implies that the temporal integral of the process exhibits diffusive behavior, dispersing from its initial location at a constant rate. Such processes are not well modeled by fBm, which has a singularity at zero frequency corresponding to an unbounded rate of dispersion. A more appropriate stochastic model is a much lesser-known random process called the Matérn process, which is shown herein to be a damped version of fractional Brownian motion. This article first provides a thorough introduction to fractional Brownian motion, then examines the details of the Matérn process and its relationship to fBm. An algorithm for the simulation of the Matérn process in O(NlogN) operations is given. Unlike fBm, the Matérn process is found to provide an excellent match to modeling velocities from particle trajectories in an application to two-dimensional fluid turbulence.
A New Model of the Fractional Order Dynamics of the Planetary Gears
Directory of Open Access Journals (Sweden)
Vera Nikolic-Stanojevic
2013-01-01
Full Text Available A theoretical model of planetary gears dynamics is presented. Planetary gears are parametrically excited by the time-varying mesh stiffness that fluctuates as the number of gear tooth pairs in contact changes during gear rotation. In the paper, it has been indicated that even the small disturbance in design realizations of this gear cause nonlinear properties of dynamics which are the source of vibrations and noise in the gear transmission. Dynamic model of the planetary gears with four degrees of freedom is used. Applying the basic principles of analytical mechanics and taking the initial and boundary conditions into consideration, it is possible to obtain the system of equations representing physical meshing process between the two or more gears. This investigation was focused to a new model of the fractional order dynamics of the planetary gear. For this model analytical expressions for the corresponding fractional order modes like one frequency eigen vibrational modes are obtained. For one planetary gear, eigen fractional modes are obtained, and a visualization is presented. By using MathCAD the solution is obtained.
Upper extremity compartmental anatomy: clinical relevance to radiologists
Energy Technology Data Exchange (ETDEWEB)
Toomayan, Glen A.; Robertson, Fabienne; Major, Nancy M. [Duke University Medical Center, Department of Radiology, P.O. Box 3808, Durham, NC (United States); Duke University Medical Center, Division of Orthopaedic Surgery, Department of Surgery, P.O. Box 3808, Durham, NC (United States); Brigman, Brian E. [Duke University Medical Center, Division of Orthopaedic Surgery, Department of Surgery, P.O. Box 3808, Durham, NC (United States)
2006-04-15
Malignant tumors of the upper extremity are uncommon, and their care should be referred to specialized facilities with experience treating these lesions. The Musculoskeletal Tumor Society (MSTS) staging system is used by the surgeon to determine appropriate surgical management, assess prognosis, and communicate with other healthcare providers. Magnetic resonance imaging (MRI) is employed pre-operatively to identify a lesion's compartment of origin, determine extent of spread, and plan biopsy and resection approaches. Involvement of neurovascular structures may result in devastating loss of upper extremity function, requiring amputation. Violation of high-resistance compartmental barriers necessitates more extensive surgical resection. Biopsy may be performed by the radiologist using imaging guidance. Knowledge of compartmental anatomy allows the radiologist or surgeon to use an easily excisable biopsy approach and prevent iatrogenic spread to unaffected compartments. Case examples are presented to illustrate the importance of compartmental anatomy in the management of benign and malignant upper extremity tumors. (orig.)
STELLAR LOCI II. A MODEL-FREE ESTIMATE OF THE BINARY FRACTION FOR FIELD FGK STARS
Energy Technology Data Exchange (ETDEWEB)
Yuan, Haibo; Liu, Xiaowei [Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing 100871 (China); Xiang, Maosheng; Huang, Yang; Chen, Bingqiu [Department of Astronomy, Peking University, Beijing 100871 (China); Wu, Yue [Key Laboratory of Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012 (China); Hou, Yonghui; Zhang, Yong, E-mail: yuanhb4861@pku.edu.cn, E-mail: x.liu@pku.edu.cn [Nanjing Institute of Astronomical Optics and Technology, National Astronomical Observatories, Chinese Academy of Sciences, Nanjing 210042 (China)
2015-02-01
We propose a stellar locus outlier (SLOT) method to determine the binary fraction of main-sequence stars statistically. The method is sensitive to neither the period nor mass ratio distributions of binaries and is able to provide model-free estimates of binary fraction for large numbers of stars of different populations in large survey volumes. We have applied the SLOT method to two samples of stars from the Sloan Digital Sky Survey (SDSS) Stripe 82, constructed by combining the recalibrated SDSS photometric data with the spectroscopic information from the SDSS and LAMOST surveys. For the SDSS spectroscopic sample, we find an average binary fraction for field FGK stars of 41% ± 2%. The fractions decrease toward late spectral types and are 44% ± 5%, 43% ± 3%, 35% ± 5%, and 28% ± 6% for stars with g – i colors in the range 0.3-0.6 mag, 0.6-0.9 mag, 0.9-1.2 mag, and 1.2-1.6 mag, respectively. A modest metallicity dependence is also found. The fraction decreases with increasing metallicity. For stars with [Fe/H] between –0.5 and 0.0 dex, –1.0 and –0.5 dex, –1.5 and –1.0 dex, and –2.0 and –1.5 dex, the inferred binary fractions are 37% ± 3%, 39% ± 3%, 50% ± 9%, and 53% ± 20%, respectively. We have further divided the sample into stars from the thin disk, the thick disk, the transition zone between them, and the halo. The results suggest that the Galactic thin and thick disks have comparable binary fractions, whereas the Galactic halo contains a significantly larger fraction of binaries. Applying the method to the LAMOST spectroscopic sample yields consistent results. Finally, other potential applications and future work with the method are discussed.
Institute of Scientific and Technical Information of China (English)
Xiao-Kang Zheng; Long-Hua Chen; Xiao Yan; Hong-Mei Wang
2005-01-01
AIM: To explore the impact of prolonged fraction dosedelivery time modeling intensity-modulated radiation therapy (IMRT) on cell killing of human hepatocellular carcinoma (HCC) HepG2 and Hep3B cell lines.METHODS: The radiobiological characteristics of human HCC HepG2 and Hep3b cell lines were studied with standard clonogenic assays, using standard linear-quadratic model and incomplete repair model to fit the dose-survival curves. The identical methods were also employed to investigate the biological effectiveness of irradiation protocols modeling clinical conventional fractionated external beam radiotherapy (EBRT, fraction delivery time 3 min) and IMRT with different prolonged fraction delivery time (15, 30, and 45 min). The differences of cell surviving fraction irradiated with different fraction delivery time were tested with paired t-test. Factors determining the impact of prolonged fraction delivery time on cell killing were analyzed.RESULTS: The α/β and repair half-time (T1/2) of HepG2and Hep3b were 3.1 and 7.4 Gy, and 22 and 19 min respectively. The surviving fraction of HepG2 irradiated modeling IMRT with different fraction delivery time was significantly higher than irradiated modeling EBRT and the cell survival increased more pronouncedly with the fraction delivery time prolonged from 15 to 45 min,while no significant differences of cell survival in Hep3b were found between different fraction delivery time protocols.CONCLUSION: The prolonged fraction delivery time modeling IMRT significantly decreased the cell killing in HepG2 but not in Hep3b. The capability of sub-lethal damage repair was the predominant factor determining the cell killing decrease. These effects, if confirmed by clinical studies, should be considered in designing IMRT treatments for HCC.
Diagnosing ΛHDE model with statefinder hierarchy and fractional growth parameter
Zhou, LanJun; Wang, Shuang
2016-07-01
Recently, a new dark energy model called ΛHDE was proposed. In this model, dark energy consists of two parts: cosmological constant Λ and holographic dark energy (HDE). Two key parameters of this model are the fractional density of cosmological constant ΩΛ0, and the dimensionless HDE parameter c. Since these two parameters determine the dynamical properties of DE and the destiny of universe, it is important to study the impacts of different values of ΩΛ0 and c on the ΛHDE model. In this paper, we apply various DE diagnostic tools to diagnose ΛHDE models with different values of ΩΛ0 and c; these tools include statefinder hierarchy {S 3 (1) , S 4 (1) }, fractional growth parameter ɛ, and composite null diagnostic (CND), which is a combination of {S 3 (1) , S 4 (1) } and ɛ. We find that: (1) adopting different values of ΩΛ0 only has quantitative impacts on the evolution of the ΛHDE model, while adopting different c has qualitative impacts; (2) compared with S 3 (1) , S 4 (1) can give larger differences among the cosmic evolutions of the ΛHDE model associated with different ΩΛ0 or different c; (3) compared with the case of using a single diagnostic, adopting a CND pair has much stronger ability to diagnose the ΛHDE model.
Modelling the fine and coarse fraction of Pb, Cd, As and Ni air concentration in Spain
Energy Technology Data Exchange (ETDEWEB)
Gonzalez, M. A.; Vivanco, M. G.
2015-07-01
Lead, cadmium, arsenic and nickel are present in the air due to natural and anthropogenic emissions, normally joined to particles. Human health and ecosystems can be damaged by high atmospheric levels of these metals, since they can be introduced in organisms via inhalation or ingestion. Small particles are inhaled and embebed in lungs and alveolus more easily than coarse particles. The CHIMERE model is a eulerian air quality model extensively used in air quality modelling. Metals have been recently included in this model in a special version developed in the CIEMAT modelling group (Madrid, Spain). Vivanco et al. (2011) and Gonzalez et al. (2012) showed an evaluation of the model performance for some metals in Spain and Europe. In these studies, metals were considered as fine particles. Nevertheless there is some observational evidence of the presence of some metals also in the coarse fraction. For this reason, a new attempt of modelling metals considering a fine (<2.5 μm) and coarse (2.5-10 μm) fraction has been done. Measurements of metal concentration in PM10, PM2.5 and PM1 recorded in Spain were used to obtain the new metal particle distribution size. On the other hand, natural emissions, not considered in the above mentioned studies, were implemented in the model, by considering metal emissions associated to dust resuspensiont. An evaluation of the new version is presented and discussed for two domains in Spain, centered on Barcelona and Huelva respectively. (Author)
Modelling the fine and coarse fraction of Pb, Cd, As and Ni air concentration in Spain
Energy Technology Data Exchange (ETDEWEB)
Gonzalez, M.A.; Vivanco, M.
2015-07-01
Lead, cadmium, arsenic and nickel are present in the air due to natural and anthropogenic emissions, normally joined to particles. Human health and ecosystems can be damaged by high atmospheric levels of these metals, since they can be introduced in organisms via inhalation or ingestion. Small particles are inhaled and embebed in lungs and alveolus more easily than coarse particles. The CHIMERE model is a eulerian air quality model extensively used in air quality modelling. Metals have been recently included in this model in a special version developed in the CIEMAT modelling group (Madrid, Spain). Vivanco et al. (2011) and González et al. (2012) showed an evaluation of the model performance for some metals in Spain and Europe. In these studies, metals were considered as fine particles. Nevertheless there is some observational evidence of the presence of some metals also in the coarse fraction. For this reason, a new attempt of modelling metals considering a fine (<2.5 μm) and coarse (2.5-10 μm) fraction has been done. Measurements of metal concentration in PM10, PM2.5 and PM1 recorded in Spain were used to obtain the new metal particle distribution size. On the other hand, natural emissions, not considered in the above mentioned studies, were implemented in the model, by considering metal emissions associated to dust resuspensiont. An evaluation of the new version is presented and discussed for two domains in Spain, centered on Barcelona and Huelva respectively. (Author)
Structural analysis of gluten-free doughs by fractional rheological model
Orczykowska, Magdalena; Dziubiński, Marek; Owczarz, Piotr
2015-02-01
This study examines the effects of various components of tested gluten-free doughs, such as corn starch, amaranth flour, pea protein isolate, and cellulose in the form of plantain fibers on rheological properties of such doughs. The rheological properties of gluten-free doughs were assessed by using the rheological fractional standard linear solid model (FSLSM). Parameter analysis of the Maxwell-Wiechert fractional derivative rheological model allows to state that gluten-free doughs present a typical behavior of viscoelastic quasi-solid bodies. We obtained the contribution dependence of each component used in preparations of gluten-free doughs (either hard-gel or soft-gel structure). The complicate analysis of the mechanical structure of gluten-free dough was done by applying the FSLSM to explain quite precisely the effects of individual ingredients of the dough on its rheological properties.
Richard MT Webb; David L. Parkhurst
2016-01-01
The U.S. Geological Surveyâs (USGS) Water, Energy, and Biogeochemical ModelÂ (WEBMOD) was used to simulate hydrology, weathering, and isotopic fractionation in theÂ Andrews Creek watershed in Rocky Mountain National Park, Colorado and the Icacos RiverÂ watershed in the Luquillo Experimental Forest, Puerto Rico. WEBMOD includes hydrologicÂ modules derived from the USGS...
Gencoglu, Muharrem Tuncay; Baskonus, Haci Mehmet; Bulut, Hasan
2017-01-01
The main aim of this manuscript is to obtain numerical solutions for the nonlinear model of interpersonal relationships with time fractional derivative. The variational iteration method is theoretically implemented and numerically conducted only to yield the desired solutions. Numerical simulations of desired solutions are plotted by using Wolfram Mathematica 9. The authors would like to thank the reviewers for their comments that help improve the manuscript.
Watkins, N. W.; Rosenberg, S.; Sanchez, R.; Chapman, S. C.; Credgington, D.
2008-12-01
Since the 1960s Mandelbrot has advocated the use of fractals for the description of the non-Euclidean geometry of many aspects of nature. In particular he proposed two kinds of model to capture persistence in time (his Joseph effect, common in hydrology and with fractional Brownian motion as the prototype) and/or prone to heavy tailed jumps (the Noah effect, typical of economic indices, for which he proposed Lévy flights as an exemplar). Both effects are now well demonstrated in space plasmas, notably in the turbulent solar wind. Models have, however, typically emphasised one of the Noah and Joseph parameters (the Lévy exponent μ and the temporal exponent β) at the other's expense. I will describe recent work in which we studied a simple self-affine stable model-linear fractional stable motion, LFSM, which unifies both effects and present a recently-derived diffusion equation for LFSM. This replaces the second order spatial derivative in the equation of fBm with a fractional derivative of order μ, but retains a diffusion coefficient with a power law time dependence rather than a fractional derivative in time. I will also show work in progress using an LFSM model and simple analytic scaling arguments to study the problem of the area between an LFSM curve and a threshold. This problem relates to the burst size measure introduced by Takalo and Consolini into solar-terrestrial physics and further studied by Freeman et al [PRE, 2000] on solar wind Poynting flux near L1. We test how expressions derived by other authors generalise to the non-Gaussian, constant threshold problem. Ongoing work on extension of these LFSM results to multifractals will also be discussed.
Synchronous Generator Model with Fractional Order Voltage Regulator PIbDa
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Dariusz Spałek
2015-06-01
Full Text Available Synchronous generator together with excitation circuit, voltage controller and system stabilizer constitute nonlinear ordinary differential equations set. The nonlinearity of differential equations set results from magnetic circuits saturation. One of the most important, from the electric energy distribution point of view, is the influence of voltage control applied on the generator voltage. There could be applied regulator either classical PID or fractional of type PIbDa which bases on the so-called fractional derivative idea. Numerical solutions of nonlinear differential equations set, that takes into account both magnetic circuits saturation and fractional regulator PIbDa, lead to decisions either to accept or to reject the chosen parameters. The sensibility of generator work on chosen fractional regulator parameters is the main aim of this paper. With the help of C++ program provided the most important states of work (short–circuit, setting voltage change, reactive power rejection can be analyzed basing on the accepted model of synchronous generator such as (1,1, (2,2 or (3,3.
Fractional brownian functions as mathematical models of natural rhythm in architecture.
Cirovic, Ivana M
2014-10-01
Carl Bovill suggested and described a method of generating rhythm in architecture with the help of fractional Brownian functions, as they are mathematical models of natural rhythm. A relationship established in the stated procedure between fractional Brownian functions as models of rhythm, and the observed group of architectural elements, is recognized as an analogical relationship, and the procedure of generating rhythm as a process of analogical transfer from the natural domain to the architectural domain. Since analogical transfer implies relational similarity of two domains, and the establishment of one-to-one correspondence, this paper is trying to determine under which conditions such correspondence could be established. For example, if the values of the observed visual feature of architectural elements are not similar to each other in a way in which they can form a monotonically increasing, or a monotonically decreasing bounded sequence, then the structural alignment and the one-to-one correspondence with a single fractional Brownian function cannot be established, hence, this function is deemed inappropriate as a model for the architectural rhythm. In this case we propose overlapping of two or more functions, so that each of them is an analog for one subset of mutually similar values of the visual feature of architectural elements.
Fractional Brownian motion, the Matern process, and stochastic modeling of turbulent dispersion
Lilly, J M; Early, J J; Olhede, S C
2016-01-01
Stochastic process exhibiting power-law slopes in the frequency domain are frequently well modeled by fractional Brownian motion (fBm). In particular, the spectral slope at high frequencies is associated with the degree of small-scale roughness or fractal dimension. However, a broad class of real-world signals have a high-frequency slope, like fBm, but a plateau in the vicinity of zero frequency. This low-frequency plateau, it is shown, implies that the temporal integral of the process exhibits diffusive behavior, dispersing from its initial location at a constant rate. Such processes are not well modeled by fBm, which has a singularity at zero frequency corresponding to an unbounded rate of dispersion. A more appropriate stochastic model is a much lesser-known random process called the Matern process, which is shown herein to be a damped version of fractional Brownian motion. This article first provides a thorough introduction to fractional Brownian motion, then examines the details of the Matern process and...
Robertson, Andy; Schipanski, Meagan; Sherrod, Lucretia; Ma, Liwang; Ahuja, Lajpat; McNamara, Niall; Smith, Pete; Davies, Christian
2016-04-01
Agriculture, covering more than 30% of global land area, has an exciting opportunity to help combat climate change by effectively managing its soil to promote increased C sequestration. Further, newly sequestered soil carbon (C) through agriculture needs to be stored in more stable forms in order to have a lasting impact on reducing atmospheric CO2 concentrations. While land uses in different climates and soils require different management strategies, the fundamental mechanisms that regulate C sequestration and stabilisation remain the same. These mechanisms are used by a number of different systems models to simulate C dynamics, and thus assess the impacts of change in management or climate. To evaluate the accuracy of these model simulations, our research uses a multidirectional approach to compare C stocks of physicochemical soil fractions collected at two long-term agricultural sites. Carbon stocks for a number of soil fractions were measured at two sites (Lincoln, UK; Colorado, USA) over 8 and 12 years, respectively. Both sites represent managed agricultural land but have notably different climates and levels of disturbance. The measured soil fractions act as proxies for varying degrees of stability, with C contained within these fractions relatable to the C simulated within the soil pools of mechanistic systems models1. Using stable isotope techniques at the UK site, specific turnover times of C within the different fractions were determined and compared with those simulated in the pools of 3 different models of varying complexity (RothC, DayCent and RZWQM2). Further, C dynamics and N-mineralisation rates of the measured fractions at the US site were assessed and compared to results of the same three models. The UK site saw a significant increase in C stocks within the most stable fractions, with topsoil (0-30cm) sequestration rates of just over 0.3 tC ha-1 yr-1 after only 8 years. Further, the sum of all fractions reported C sequestration rates of nearly 1
Li, Zheng; Wang, Hong; Yang, Danping
2017-10-01
We present a space-time fractional Allen-Cahn phase-field model that describes the transport of the fluid mixture of two immiscible fluid phases. The space and time fractional order parameters control the sharpness and the decay behavior of the interface via a seamless transition of the parameters. Although they are shown to provide more accurate description of anomalous diffusion processes and sharper interfaces than traditional integer-order phase-field models do, fractional models yield numerical methods with dense stiffness matrices. Consequently, the resulting numerical schemes have significantly increased computational work and memory requirement. We develop a lossless fast numerical method for the accurate and efficient numerical simulation of the space-time fractional phase-field model. Numerical experiments shows the utility of the fractional phase-field model and the corresponding fast numerical method.
DEFF Research Database (Denmark)
Nielsen, Kræn Vodder; Blanke, Mogens; Eriksson, Lars
2016-01-01
therefore focus on deriving and validating a mean-value model of a large two-stroke crosshead diesel engines with EGR. The model introduces a number of amendments and extensions to previous, complex models and shows in theory and practice that a simplified nonlinear model captures all essential dynamics...... the behavior of the scavenge oxygen fraction well over the entire envelope of load and blower speed range that are relevant for EGR. The simplicity of the new model makes it suitable for observer and control design, which are essential steps to meet the emission requirements for marine diesel engines that take......Exhaust gas recirculation (EGR) systems have been introduced to large marine engines in order to reduce NOx formation. Adequate modelling for control design is one of the bottlenecks to design EGR control that also meets emission requirements during transient loading conditions. This paper...
Hamiltonian analysis of gauged $CP^1$ model, with or without Hopf term, and fractional spin
Chakraborty, B
1997-01-01
Recently it has been shown by Cho and Kimm that the gauged $CP^1$ model, obtained by gauging the global SU(2) group of $CP^1$ model and adding a corresponding Chern-Simons term, has got its own soliton. These solitons are somewhat distinct from those of pure $CP^1$ model, as they cannot always be characterised by $\\pi_2(CP^1)=Z$. In this paper, we first carry out the Hamiltonian analysis of this gauged $CP^1$ model. Then we couple the Hopf term, associated to these solitons and again carry out its Hamiltonian analysis. The symplectic structures, along with the structures of the constraints, of these two models (with or without Hopf term) are found to be essentially the same. The model with Hopf term, is then shown to have fractional spin, which however depends not only on the soliton number $N$ but also on the nonabelian charge.
Development of a three dimensional circulation model based on fractional step method
Directory of Open Access Journals (Sweden)
Mazen Abualtayef
2010-03-01
Full Text Available A numerical model was developed for simulating a three-dimensional multilayer hydrodynamic and thermodynamic model in domains with irregular bottom topography. The model was designed for examining the interactions between flow and topography. The model was based on the three-dimensional Navier-Stokes equations and was solved using the fractional step method, which combines the finite difference method in the horizontal plane and the finite element method in the vertical plane. The numerical techniques were described and the model test and application were presented. For the model application to the northern part of Ariake Sea, the hydrodynamic and thermodynamic results were predicted. The numerically predicted amplitudes and phase angles were well consistent with the field observations.
Yang, Ning-Ning; Liu, Chong-Xin; Wu, Chao-Jun
2012-08-01
In this paper, the fractional-order mathematical model and the fractional-order state-space averaging model of the Buck—Boost converter in continuous conduction mode (CCM) are established based on the fractional calculus and the Adomian decomposition method. Some dynamical properties of the current-mode controlled fractional-order Buck—Boost converter are analysed. The simulation is accomplished by using SIMULINK. Numerical simulations are presented to verify the analytical results and we find that bifurcation points will be moved backward as α and β vary. At the same time, the simulation results show that the converter goes through different routes to chaos.
Xuefang, L.; Liu, Y.
2015-12-01
Huang et al (2010) found that Fe, Ca and Mg isotope fractionations of high-temperature silicate melts are only associated with the temperature gradients in thermal diffusion processes and are independent of compositions and mean temperatures [1]. Richter et al (2010) doubted that the existing data are sufficient to obtain such conclusion [2]. A few theoretical models have been proposed for explaining isotopic fractionations in these processes under high temperatures [3, 4]. However, molecular-level mechanisms and theoretical treatments of these processes are still under debating. Here we provide a unified theory based on the local thermodynamic equilibrium treatment (LTE) of statistical mechanics for evaluating thermal isotopic fractionations under a wide range of temperatures. Under high temperatures, our theory however can be reasonably approximated to this equation: where A and B are constants which are related to specific isotope systems and chemical compositions of silicate melts. If the thermal gradient is not very large and the mean temperature is high, the second part of the above equation can be safely neglected and obtain an extremely simple equation which is linearly depended on temperatures, agreeing with what Huang et al (2010) concluded. Based on this terse equation, we can not only easily provide isotope fractionation data for almost all kinds of isotope systems, but also can provide the mechanisms of isotope fractionation in thermal diffusion processes. [1] Huang et al (2010) Nature 464, 396-400. [2] Richter et al (2010) Nature 472, E1-E1. [3] Dominguez et al (2011) Nature 473, 70-73.
Directory of Open Access Journals (Sweden)
J.-P. Lhomme
1999-01-01
Full Text Available In many experimental conditions, the evaporative fraction, defined as the ratio between evaporation and available energy, has been found stable during daylight hours. This constancy is investigated over fully covering vegetation by means of a land surface scheme coupled with a mixed-layer model, which accounts for entrainment of overlying air. The evaporation rate follows the Penman-Monteith equation and the surface resistance is given by a Jarvis type parameterization involving solar radiation, saturation deficit and leaf water potential. The diurnal course of the evaporative fraction is examined, together with the influence of environmental factors (soil water availability, solar radiation input, wind velocity, saturation deficit above the well-mixed layer. In conditions of fair weather, the curves representing the diurnal course of the evaporative fraction have a typical concave-up shape. Around midday (solar time these curves appear as relatively constant, but always lower that the daytime mean value. Evaporative fraction decreases when soil water decreases or when solar energy increases. An increment of saturation deficit above the mixed-layer provokes only a slight increase of evaporative fraction, and wind velocity has almost no effect. The possibility of estimation daytime evaporation from daytime available energy multiplied by the evaporative fraction at a single time of the day is also investigated. It appears that it is possible to obtain fairly good estimates of daytime evaporation by choosing adequately the time of the measurement of the evaporative fraction. The central hours of the day, and preferably about 3 hr before or after noon, are the most appropriate to provide good estimates. The estimation appears also to be much better when soil water availability (or evaporation is high than when it is low.
Fractional Generalizations of Maxwell and Kelvin-Voigt Models for Biopolymer Characterization.
Directory of Open Access Journals (Sweden)
Bertrand Jóźwiak
Full Text Available The paper proposes a fractional generalization of the Maxwell and Kelvin-Voigt rheological models for a description of dynamic behavior of biopolymer materials. It was found that the rheological models of Maxwell-type do not work in the case of modeling of viscoelastic solids, and the model which significantly better describes the nature of changes in rheological properties of such media is the modified fractional Kelvin-Voigt model with two built-in springpots (MFKVM2. The proposed model was used to describe the experimental data from the oscillatory and creep tests of 3% (w/v kuzu starch pastes, and to determine the values of their rheological parameters as a function of pasting time. These parameters provide a lot of additional information about structure and viscoelastic properties of the medium in comparison to the classical analysis of dynamic curves G' and G" and shear creep compliance J(t. It allowed for a comprehensive description of a wide range of properties of kuzu starch pastes, depending on the conditions of pasting process.
A Stochastic Fractional Dynamics Model of Space-time Variability of Rain
Kundu, Prasun K.; Travis, James E.
2013-01-01
Rainfall varies in space and time in a highly irregular manner and is described naturally in terms of a stochastic process. A characteristic feature of rainfall statistics is that they depend strongly on the space-time scales over which rain data are averaged. A spectral model of precipitation has been developed based on a stochastic differential equation of fractional order for the point rain rate, that allows a concise description of the second moment statistics of rain at any prescribed space-time averaging scale. The model is thus capable of providing a unified description of the statistics of both radar and rain gauge data. The underlying dynamical equation can be expressed in terms of space-time derivatives of fractional orders that are adjusted together with other model parameters to fit the data. The form of the resulting spectrum gives the model adequate flexibility to capture the subtle interplay between the spatial and temporal scales of variability of rain but strongly constrains the predicted statistical behavior as a function of the averaging length and times scales. We test the model with radar and gauge data collected contemporaneously at the NASA TRMM ground validation sites located near Melbourne, Florida and in Kwajalein Atoll, Marshall Islands in the tropical Pacific. We estimate the parameters by tuning them to the second moment statistics of radar data. The model predictions are then found to fit the second moment statistics of the gauge data reasonably well without any further adjustment.
Recoilless fractions calculated with the nearest-neighbour interaction model by Kagan and Maslow
Kemerink, G. J.; Pleiter, F.
1986-08-01
The recoilless fraction is calculated for a number of Mössbauer atoms that are natural constituents of HfC, TaC, NdSb, FeO, NiO, EuO, EuS, EuSe, EuTe, SnTe, PbTe and CsF. The calculations are based on a model developed by Kagan and Maslow for binary compounds with rocksalt structure. With the exception of SnTe and, to a lesser extent, PbTe, the results are in reasonable agreement with the available experimental data and values derived from other models.
Application of fractional calculus to modeling transient combustion of solid propellants
Kulish, Vladimir; Horák, Vladimír; Duc, Linh Do; Lukáč, Tomáš
2017-01-01
It was Zel'dovich, who first considered the transient combustion problem of solid propellants. Some more detailed models of that process have been developed afterwards. However, until today, numerical methods remain the prevailing tool for modeling unsteady combustion processes. In this work, it has been demonstrated that at least one of the problems of the unsteady combustion theory, which previously investigated numerically, can be treated analytically by means of fractional calculus. The solution for the unsteady speed of combustion thus derived is then compared with the solution obtained by numerical means in previous studies. The comparison shows a good agreement between those results, especially for small values of time.
Fractional snow cover mapping from MODIS data using wavelet-artificial intelligence hybrid models
Moosavi, Vahid; Malekinezhad, Hossein; Shirmohammadi, Bagher
2014-04-01
This study was carried out to evaluate the wavelet-artificial intelligence hybrid models to produce fractional snow cover maps. At first, cloud cover was removed from MODIS data and cloud free images were produced. SVM-based binary classified ETM+ imagery were then used as reference maps in order to obtain train and test data for sub-pixel classification models. ANN and ANFIS-based modeling were performed using raw data (without wavelet-based preprocessing). In the next step, several mother wavelets and levels were used in order to decompose the original data to obtain wavelet coefficients. Then, the decomposed data were used for further modeling processes. ANN, ANFIS, wavelet-ANN and wavelet-ANFIS models were compared to evaluate the effect of wavelet transformation on the ability of artificial intelligence models. It was demonstrated that wavelet transformation as a preprocessing approach can significantly enhance the performance of ANN and ANFIS models. This study indicated an overall accuracy of 92.45% for wavelet-ANFIS model, 86.13% for wavelet-ANN, 72.23% for ANFIS model and 66.78% for ANN model. In fact, hybrid wavelet-artificial intelligence models can extract the characteristics of the original signals (i.e. model inputs) accurately through decomposing the non-stationary and complex signals into several stationary and simpler signals. The positive effect of fuzzification as well as wavelet transformation in the wavelet-ANFIS model was also confirmed.
Directory of Open Access Journals (Sweden)
Abdon Atangana
2014-01-01
Full Text Available The notion of uncertainty in groundwater hydrology is of great importance as it is known to result in misleading output when neglected or not properly accounted for. In this paper we examine this effect in groundwater flow models. To achieve this, we first introduce the uncertainties functions u as function of time and space. The function u accounts for the lack of knowledge or variability of the geological formations in which flow occur (aquifer in time and space. We next make use of Riemann-Liouville fractional derivatives that were introduced by Kobelev and Romano in 2000 and its approximation to modify the standard version of groundwater flow equation. Some properties of the modified Riemann-Liouville fractional derivative approximation are presented. The classical model for groundwater flow, in the case of density-independent flow in a uniform homogeneous aquifer is reformulated by replacing the classical derivative by the Riemann-Liouville fractional derivatives approximations. The modified equation is solved via the technique of green function and the variational iteration method.
Fractional Diffusion Based Modelling and Prediction of Human Brain Response to External Stimuli
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Hamidreza Namazi
2015-01-01
Full Text Available Human brain response is the result of the overall ability of the brain in analyzing different internal and external stimuli and thus making the proper decisions. During the last decades scientists have discovered more about this phenomenon and proposed some models based on computational, biological, or neuropsychological methods. Despite some advances in studies related to this area of the brain research, there were fewer efforts which have been done on the mathematical modeling of the human brain response to external stimuli. This research is devoted to the modeling and prediction of the human EEG signal, as an alert state of overall human brain activity monitoring, upon receiving external stimuli, based on fractional diffusion equations. The results of this modeling show very good agreement with the real human EEG signal and thus this model can be used for many types of applications such as prediction of seizure onset in patient with epilepsy.
A model-independent determination of the inclusive semileptonic decay fraction of B mesons
Albrecht, H.; Ehrlichmann, H.; Hamacher, T.; Hofmann, R. P.; Kirchhoff, T.; Nau, A.; Nowak, S.; Schröder, H.; Schulz, H. D.; Walter, M.; Wurth, R.; Hast, C.; Kolanoski, H.; Kosche, A.; Lange, A.; Lindner, A.; Mankel, R.; Schieber, M.; Siegmund, T.; Spaan, B.; Thurn, H.; Töpfer, D.; Wegener, D.; Bittner, M.; Eckstein, P.; Paulini, M.; Reim, K.; Wegener, H.; Eckmann, R.; Mundt, R.; Oest, T.; Reiner, R.; Schmidt-Parzefall, W.; Funk, W.; Stiewe, J.; Werner, S.; Ehret, K.; Hofmann, W.; Hüpper, A.; Khan, S.; Knöpfle, K. T.; Seeger, M.; Spengler, J.; Britton, D. I.; Charlesworth, C. E. K.; Edwards, K. W.; Hyatt, E. R. F.; Kapitza, H.; Krieger, P.; Macfarlane, D. B.; Patel, P. M.; Prentice, J. D.; Saull, P. R. B.; Tzamariudaki, K.; van de Water, R. G.; Yoon, T.-S.; Reßing, D.; Schmidtler, M.; Schneider, M.; Schubert, K. R.; Strahl, K.; Waldi, R.; Weseler, S.; Kernel, G.; Križnič, P.; Podobnik, T.; Živko, T.; Balagura, V.; Belyaev, I.; Chechelnitsky, S.; Danilov, M.; Droutskoy, A.; Gershtein, Yu.; Golutvin, A.; Kostina, G.; Litvintsev, D.; Lubimov, V.; Pakhlov, P.; Ratnikov, F.; Semenov, S.; Snizhko, A.; Soloshenko, V.; Tichomirov, I.; Zaitsev, Yu.; Argus Collaboration
1993-12-01
With the ARGUS detector at the e +e - storage ring DORIS II, we have determined decay fraction and electron momentum spectrum of the inclusive decay mode B → eνX. Usinng lepton tags from the second B meson. in 209 000 γ(4 S) → BoverlineB decays, we could determine the spectrum for all electron momenta pe > 0.6 GeV/ c. Including the small extrapolation to pe > 0, we find the model-independent decay fraction B(B → eνX) = (9.6 ± 0.5 ± 0.4)%. Adding D meson tags, our result is (9.7 ± 0.5 ± 0.4)%.
Nonlethal Fraction of Virus Population in Evolution Models with Lethal Mutations
Yakushkina, Tatiana; Saakian, David B.
2017-03-01
Lethal mutations are very common in asexual evolution, both in RNA viruses and in the clonal evolution of cancer cells. In a special case of lethal mutations (truncated selection), after a critical total number of mutations the replicator (the virus or the cell) has no offspring. We consider the Eigen and Crow-Kimura models with truncated fitness landscapes, and calculate the fraction of viable replicators (that do have offspring) in the population. We derive a formula for the fraction of the population with nonlethal replicators for the case of a uniform distribution of lethal sequences in the sequence space. We assume that our results can be applied to the origin of life and cancer biology.
Pastro, Lucía; Smircich, Pablo; Di Paolo, Andrés; Becco, Lorena; Duhagon, María A.; Sotelo-Silveira, José; Garat, Beatriz
2017-01-01
In the protozoan parasite Trypanosoma cruzi, as in other trypanosomatids, transcription of protein coding genes occurs in a constitutive fashion, producing large polycistronic transcription units. These units are composed of non-functionally related genes which are pervasively processed to yield each mRNA. Therefore, post-transcriptional processes are crucial to regulate gene expression. Considering that nuclear compartmentalization could contribute to gene expression regulation, we comparatively studied the nuclear, cytoplasmic and whole cell transcriptomes of the non-infective epimastigote stage of T. cruzi, using RNA-Seq. We found that the cytoplasmic transcriptome tightly correlates with the whole cell transcriptome and both equally correlate with the proteome. Nonetheless, 1,200 transcripts showed differential abundance between the nuclear and cytoplasmic fractions. For the genes with transcript content augmented in the nucleus, significant structural and compositional differences were found. The analysis of the reported epimastigote translatome and proteome, revealed scarce ribosome footprints and encoded proteins for them. Ontology analyses unveiled that many of these genes are distinctive of other parasite life-cycle stages. Finally, the relocalization of transcript abundance in the metacyclic trypomastigote infective stage was confirmed for specific genes. While gene expression is strongly dependent on transcript steady-state level, we here highlight the importance of the distribution of transcripts abundance between compartments in T. cruzi. Particularly, we show that nuclear compartmentation is playing an active role in the developmental stage determination preventing off-stage expression. PMID:28243589
Directory of Open Access Journals (Sweden)
Yong Zhang
2013-01-01
Full Text Available Heterogeneous media consisting of segregated flow regions are fractional-order systems, where the regional-scale anomalous diffusion can be described by the fractional derivative model (FDM. The standard FDM, however, first, cannot characterize the Darcy-scale dispersion through repacked sand columns, and second, the link between medium properties and model parameters remains unknown. To fill these two knowledge gaps, this study applies a tempered fractional derivative model (TFDM to capture bromide transport through laboratory repacked sand. Column transport experiments are conducted first, where glass beads and silica sand with different diameters are repacked individually. Late-time tails are observed in the breakthrough curves (BTC of bromide even in relatively homogeneous glass beads. The TFDM can capture the observed subdiffusion, especially the late-time BTC with a transient declining rate. Results also show that both the size distribution of repacked sand and the magnitude of fluid velocity can affect subdiffusion. In particular, a wider sand size distribution or a smaller flow rate can enhance the subdiffusion, leading to a smaller time index and a higher truncation parameter in the TFDM. Therefore, the Darcy-scale dispersion follows the tempered stable law, and the model parameters might be related to the soil size and flow conditions.
Differential gating of dendritic spikes by compartmentalized inhibition
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Katharina Anna Wilmes
2014-03-01
Full Text Available Different types of local inhibitory interneurons innervate different dendritic sites of pyramidal neurons in cortex and hippocampus (Klausberger 2009. What could be the functional role of compartmentalized inhibition? Pyramidal cell dendrites support different forms of active signal propagation, which are important not only for dendritic and neuronal signal processing (Smith et al. 2013, but also for synaptic plasticity. While back-propagating action potentials signal post-synaptic activity to synapses in apical oblique and basal dendrites (Markram et al. 1997, Cho et al. 2006, calcium spikes cause plasticity of distal apical tuft synapses (Golding et al. 2002. Suspiciously, the associated regions of the dendrite are targeted by different interneuron populations. Parvalbumin-positive interneurons typically target the proximal dendritic and somatic parts of the neuron, while somatostatin-positive interneurons target the apical dendrite. The matching compartmentalization in terms of dendritic spikes and inhibitory control suggests that inhibition could differentially regulate different dendritic spikes and thereby introduce a compartment-specific modulation of synaptic plasticity. We evaluate this hypothesis in a biophysical multi-compartment model of a pyramidal neuron, receiving shunting inhibition at different locations on the dendrite. The model shows that, first, inhibition can gate dendritic spikes in an all-or-none manner. Second, spatially selective inhibition can individually suppress back-propagating action potentials and calcium spikes, thereby allowing a compartment-specific switch for synaptic plasticity. In our model, proximal inhibition on the apical dendrite eliminated both the back-propagating action potential and the calcium spike, thus influencing plasticity in the whole apical dendrite. Distal apical inhibition could selectively affect calcium spikes and thus distal plasticity, without suppressing backpropagation of action
Zhang, Hongmei; Wang, Yue; Fatemi, Mostafa; Insana, Michael F.
2017-03-01
Kelvin-Voigt fractional derivative (KVFD) model parameters have been used to describe viscoelastic properties of soft tissues. However, translating model parameters into a concise set of intrinsic mechanical properties related to tissue composition and structure remains challenging. This paper begins by exploring these relationships using a biphasic emulsion materials with known composition. Mechanical properties are measured by analyzing data from two indentation techniques—ramp-stress relaxation and load-unload hysteresis tests. Material composition is predictably correlated with viscoelastic model parameters. Model parameters estimated from the tests reveal that elastic modulus E 0 closely approximates the shear modulus for pure gelatin. Fractional-order parameter α and time constant τ vary monotonically with the volume fraction of the material’s fluid component. α characterizes medium fluidity and the rate of energy dissipation, and τ is a viscous time constant. Numerical simulations suggest that the viscous coefficient η is proportional to the energy lost during quasi-static force-displacement cycles, E A . The slope of E A versus η is determined by α and the applied indentation ramp time T r. Experimental measurements from phantom and ex vivo liver data show close agreement with theoretical predictions of the η -{{E}A} relation. The relative error is less than 20% for emulsions 22% for liver. We find that KVFD model parameters form a concise features space for biphasic medium characterization that described time-varying mechanical properties. The experimental work was carried out at the Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA. Methodological development, including numerical simulation and all data analysis, were carried out at the school of Life Science and Technology, Xi’an JiaoTong University, 710049, China.
Dörr, Aaron; Mehdizadeh, Amirfarhang
2012-01-01
Based on the notion of a construction process consisting of the stepwise addition of particles to the pure fluid, a discrete model for the apparent viscosity as well as for the maximum packing fraction of polydisperse suspensions of spherical, non-colloidal particles is derived. The model connects the approaches by Bruggeman and Farris and is valid for large size ratios of consecutive particle classes during the construction process. Furthermore, a new general form of the well-known Krieger equation allowing for the choice of a second-order Taylor coefficient for the volume fraction is proposed and then applied as a monodisperse reference equation in the course of polydisperse modeling. By applying the polydisperse viscosity model to two different particle size distributions (Rosin-Rammler and uniform distribution), the influence of polydispersity on the apparent viscosity is examined. The extension of the model to the case of small size ratios as well as to the inclusion of shear rate effects is left for fut...
Diagnosing $\\Lambda$HDE model with statefinder hierarchy and fractional growth parameter
Zhou, Lanjun
2016-01-01
Recently, a new dark energy model called $\\Lambda$HDE was proposed. In this model, dark energy consists of two parts: cosmological constant $\\Lambda$ and holographic dark energy (HDE). Two key parameters of this model are the fractional density of cosmological constant $\\Omega_{\\Lambda0}$, and the dimensionless HDE parameter $c$. Since these two parameters determine the dynamical properties of DE and the destiny of universe, it is important to study the impacts of different values of $\\Omega_{\\Lambda0}$ and $c$ on the $\\Lambda$HDE model. In this paper, we apply various DE diagnostic tools to diagnose $\\Lambda$HDE models with different values of $\\Omega_{\\Lambda0}$ and $c$; these tools include statefinder hierarchy \\{$S_3^{(1)}, S_4^{(1)}$\\}, fractional growth parameter $\\epsilon$, and composite null diagnostic (CND), which is a combination of \\{$S_3^{(1)}, S_4^{(1)}$\\} and $\\epsilon$. We find that: (1) adopting different values of $\\Omega_{\\Lambda0}$ only has quantitative impacts on the evolution of the $\\Lam...
Shared and Distinct Mechanisms of Compartmentalized and Cytosolic Ciliogenesis.
Avidor-Reiss, Tomer; Leroux, Michel R
2015-12-07
Most motile and all non-motile (also known as primary) eukaryotic cilia possess microtubule-based axonemes that are assembled at the cell surface to form hair-like or more elaborate compartments endowed with motility and/or signaling functions. Such compartmentalized ciliogenesis depends on the core intraflagellar transport (IFT) machinery and the associated Bardet-Biedl syndrome complex (BBSome) for dynamic delivery of ciliary components. The transition zone (TZ), an ultrastructurally complex barrier or 'gate' at the base of cilia, also contributes to the formation of compartmentalized cilia. Yet, some ciliated protists do not have IFT components and, like some metazoan spermatozoa, use IFT-independent mechanisms to build axonemes exposed to the cytosol. Moreover, various ciliated protists lack TZ components, whereas Drosophila sperm surprisingly requires the activity of dynamically localized TZ proteins for cytosolic ciliogenesis. Here, we discuss the various ways eukaryotes use IFT and/or TZ proteins to generate the wide assortment of compartmentalized and cytosolic cilia observed in nature. Consideration of the different ciliogenesis pathways allows us to propose how three types of cytosol-exposed cilia (primary, secondary and tertiary), including cilia found in the human sperm proximal segment, are likely generated by evolutionary derivations of compartmentalized ciliogenesis.
Tenreiro Machado, J. A.
2015-08-01
This paper addresses the matrix representation of dynamical systems in the perspective of fractional calculus. Fractional elements and fractional systems are interpreted under the light of the classical Cole-Cole, Davidson-Cole, and Havriliak-Negami heuristic models. Numerical simulations for an electrical circuit enlighten the results for matrix based models and high fractional orders. The conclusions clarify the distinction between fractional elements and fractional systems.
Blockhuys, S; Vanhoecke, B; Paelinck, L; Bracke, M; DeWagter, C
2009-03-01
We present different in vitro experimental models which allow us to evaluate the effect of spatially fractionated dose distributions on metabolic activity. We irradiated a monolayer of MCF-7/6 human breast cancer cells with a steep and a smooth 6 MV x-ray dose gradient. In the steep gradient model, we irradiated the cells with three separate small fields. We also developed two smooth gradient models. In the first model, the cells are cultured in a T25 flask and irradiated with a smooth dose gradient over the length of the flask, while in the second one, the cells are cultured in a 96-well plate and also irradiated over the length of the plate. In an attempt to correlate the spatially fractionated dose distributions with metabolic activity, the effect of irradiation was evaluated by means of the MTT assay. This assay is used to determine the metabolic activity by measuring the amount of formazan formed after the conversion of MTT (3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide) by cellular dehydrogenases. The results obtained with our different models suggest a dose-specific effect on metabolic activity, characterized by an increased formazan optical density occurring in the dose range 1.0-4.0 Gy in the steep dose gradient model and in the dose ranges 4.2-6.5 Gy and 2.3-5.1 Gy in the two smooth dose gradient models. The corresponding times for maximal formazan accumulation were 5-7 days in the steep dose gradient model and day 9-13 and day 9-11 in the smooth dose gradient models. Altogether, our results suggest that the MTT assay may be used as a biological dose-response meter to monitor the radiotherapeutic effectiveness.
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Blockhuys, S; Vanhoecke, B; Bracke, M [Laboratory Experimental Cancer Research, Ghent University Hospital, De Pintelaan 185, B-9000 Gent (Belgium); Paelinck, L; De Wagter, C [Department of Radiotherapy, Ghent University Hospital, De Pintelaan 185, B-9000 Gent (Belgium)], E-mail: Stephanie.Blockhuys@ugent.be
2009-03-21
We present different in vitro experimental models which allow us to evaluate the effect of spatially fractionated dose distributions on metabolic activity. We irradiated a monolayer of MCF-7/6 human breast cancer cells with a steep and a smooth 6 MV x-ray dose gradient. In the steep gradient model, we irradiated the cells with three separate small fields. We also developed two smooth gradient models. In the first model, the cells are cultured in a T25 flask and irradiated with a smooth dose gradient over the length of the flask, while in the second one, the cells are cultured in a 96-well plate and also irradiated over the length of the plate. In an attempt to correlate the spatially fractionated dose distributions with metabolic activity, the effect of irradiation was evaluated by means of the MTT assay. This assay is used to determine the metabolic activity by measuring the amount of formazan formed after the conversion of MTT (3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide) by cellular dehydrogenases. The results obtained with our different models suggest a dose-specific effect on metabolic activity, characterized by an increased formazan optical density occurring in the dose range 1.0-4.0 Gy in the steep dose gradient model and in the dose ranges 4.2-6.5 Gy and 2.3-5.1 Gy in the two smooth dose gradient models. The corresponding times for maximal formazan accumulation were 5-7 days in the steep dose gradient model and day 9-13 and day 9-11 in the smooth dose gradient models. Altogether, our results suggest that the MTT assay may be used as a biological dose-response meter to monitor the radiotherapeutic effectiveness.
Directory of Open Access Journals (Sweden)
Ying Li
Full Text Available Vegetation is an important part of ecosystem and estimation of fractional vegetation cover is of significant meaning to monitoring of vegetation growth in a certain region. With Landsat TM images and HJ-1B images as data source, an improved selective endmember linear spectral mixture model (SELSMM was put forward in this research to estimate the fractional vegetation cover in Huangfuchuan watershed in China. We compared the result with the vegetation coverage estimated with linear spectral mixture model (LSMM and conducted accuracy test on the two results with field survey data to study the effectiveness of different models in estimation of vegetation coverage. Results indicated that: (1 the RMSE of the estimation result of SELSMM based on TM images is the lowest, which is 0.044. The RMSEs of the estimation results of LSMM based on TM images, SELSMM based on HJ-1B images and LSMM based on HJ-1B images are respectively 0.052, 0.077 and 0.082, which are all higher than that of SELSMM based on TM images; (2 the R2 of SELSMM based on TM images, LSMM based on TM images, SELSMM based on HJ-1B images and LSMM based on HJ-1B images are respectively 0.668, 0.531, 0.342 and 0.336. Among these models, SELSMM based on TM images has the highest estimation accuracy and also the highest correlation with measured vegetation coverage. Of the two methods tested, SELSMM is superior to LSMM in estimation of vegetation coverage and it is also better at unmixing mixed pixels of TM images than pixels of HJ-1B images. So, the SELSMM based on TM images is comparatively accurate and reliable in the research of regional fractional vegetation cover estimation.
Li, Ying; Wang, Hong; Li, Xiao Bing
2015-01-01
Vegetation is an important part of ecosystem and estimation of fractional vegetation cover is of significant meaning to monitoring of vegetation growth in a certain region. With Landsat TM images and HJ-1B images as data source, an improved selective endmember linear spectral mixture model (SELSMM) was put forward in this research to estimate the fractional vegetation cover in Huangfuchuan watershed in China. We compared the result with the vegetation coverage estimated with linear spectral mixture model (LSMM) and conducted accuracy test on the two results with field survey data to study the effectiveness of different models in estimation of vegetation coverage. Results indicated that: (1) the RMSE of the estimation result of SELSMM based on TM images is the lowest, which is 0.044. The RMSEs of the estimation results of LSMM based on TM images, SELSMM based on HJ-1B images and LSMM based on HJ-1B images are respectively 0.052, 0.077 and 0.082, which are all higher than that of SELSMM based on TM images; (2) the R2 of SELSMM based on TM images, LSMM based on TM images, SELSMM based on HJ-1B images and LSMM based on HJ-1B images are respectively 0.668, 0.531, 0.342 and 0.336. Among these models, SELSMM based on TM images has the highest estimation accuracy and also the highest correlation with measured vegetation coverage. Of the two methods tested, SELSMM is superior to LSMM in estimation of vegetation coverage and it is also better at unmixing mixed pixels of TM images than pixels of HJ-1B images. So, the SELSMM based on TM images is comparatively accurate and reliable in the research of regional fractional vegetation cover estimation.
A predictor-corrector algorithm to estimate the fractional flow in oil-water models
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Savioli, Gabriela B [Laboratorio de IngenierIa de Reservorios, IGPUBA and Departamento de IngenierIa Quimica, Facultad de IngenierIa, Universidad de Buenos Aires, Av. Las Heras 2214 Piso 3 C1127AAR Buenos Aires (Argentina); Berdaguer, Elena M Fernandez [Instituto de Calculo, Facultad de Ciencias Exactas y Naturales, UBA-CONICET and Departamento de Matematica, Facultad de IngenierIa, Universidad de Buenos Aires, 1428 Buenos Aires (Argentina)], E-mail: gsavioli@di.fcen.uba.ar, E-mail: efernan@ic.fcen.uba.ar
2008-11-01
We introduce a predictor-corrector algorithm to estimate parameters in a nonlinear hyperbolic problem. It can be used to estimate the oil-fractional flow function from the Buckley-Leverett equation. The forward model is non-linear: the sought- for parameter is a function of the solution of the equation. Traditionally, the estimation of functions requires the selection of a fitting parametric model. The algorithm that we develop does not require a predetermined parameter model. Therefore, the estimation problem is carried out over a set of parameters which are functions. The algorithm is based on the linearization of the parameter-to-output mapping. This technique is new in the field of nonlinear estimation. It has the advantage of laying aside parametric models. The algorithm is iterative and is of predictor-corrector type. We present theoretical results on the inverse problem. We use synthetic data to test the new algorithm.
Fractional Black-Scholes Model and Technical Analysis of Stock Price
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Song Xu
2013-01-01
Full Text Available In the stock market, some popular technical analysis indicators (e.g., Bollinger bands, RSI, ROC, etc. are widely used to forecast the direction of prices. The validity is shown by observed relative frequency of certain statistics, using the daily (hourly, weekly, etc. stock prices as samples. However, those samples are not independent. In earlier research, the stationary property and the law of large numbers related to those observations under Black-Scholes stock price model and stochastic volatility model have been discussed. Since the fitness of both Black-Scholes model and short-range dependent process has been questioned, we extend the above results to fractional Black-Scholes model with Hurst parameter H>1/2, under which the stock returns follow a kind of long-range dependent process. We also obtain the rate of convergence.
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Fiorino, Claudio, E-mail: fiorino.claudio@hsr.it [Department of Medical Physics, San Raffaele Scientific Institute, Milan (Italy); Cozzarini, Cesare [Department of Radiotherapy, San Raffaele Scientific Institute, Milan (Italy); Rancati, Tiziana [Prostate Cancer Program, Fondazione Istituto di Ricovero e Cura a Carattere Scientifico Istituto Nazionale dei Tumori, Milan (Italy); Briganti, Alberto [Department of Urology, San Raffaele Scientific Institute, Milan (Italy); Cattaneo, Giovanni Mauro; Mangili, Paola [Department of Medical Physics, San Raffaele Scientific Institute, Milan (Italy); Di Muzio, Nadia Gisella [Department of Radiotherapy, San Raffaele Scientific Institute, Milan (Italy); Calandrino, Riccardo [Department of Medical Physics, San Raffaele Scientific Institute, Milan (Italy)
2014-12-01
Purpose: To fit urinary toxicity data of patients treated with postprostatectomy radiation therapy with the linear quadratic (LQ) model with/without introducing a time factor. Methods and Materials: Between 1993 and 2010, 1176 patients were treated with conventional fractionation (1.8 Gy per fraction, median 70.2 Gy, n=929) or hypofractionation (2.35-2.90 Gy per fraction, n=247). Data referred to 2004-2010 (when all schemes were in use, n=563; conventional fractionation: 316; hypofractionation: 247) were fitted as a logit function of biological equivalent dose (BED), according to the LQ model with/without including a time factor γ (fixing α/β = 5 Gy). The 3-year risks of severe urethral stenosis, incontinence, and hematuria were considered as endpoints. Best-fit parameters were derived, and the resulting BEDs were taken in multivariable backward logistic models, including relevant clinical variables, considering the whole population. Results: The 3-year incidences of severe stenosis, incontinence, and hematuria were, respectively, 6.6%, 4.8%, and 3.3% in the group treated in 2004-2010. The best-fitted α/β values were 0.81 Gy and 0.74 Gy for incontinence and hematuria, respectively, with the classic LQ formula. When fixing α/β = 5 Gy, best-fit values for γ were, respectively, 0.66 Gy/d and 0.85 Gy/d. Sensitivity analyses showed reasonable values for γ (0.6-1.0 Gy/d), with comparable goodness of fit for α/β values between 3.5 and 6.5 Gy. Likelihood ratio tests showed that the fits with/without including γ were equivalent. The resulting multivariable backward logistic models in the whole population included BED, pT4, and use of antihypertensives (area under the curve [AUC] = 0.72) for incontinence and BED, pT4, and year of surgery (AUC = 0.80) for hematuria. Stenosis data could not be fitted: a 4-variable model including only clinical factors (acute urinary toxicity, pT4, year of surgery, and use of antihypertensives) was suggested (AUC
Directory of Open Access Journals (Sweden)
Cheng Xu
2015-01-01
Full Text Available In this manuscript, the local fractional arbitrary Euler-Lagrange formula are utilized to address the diffusion model of fractal heat and mass transfer in a fluidized bed based on the Fick's law with local fractional vector calculus. This article has been corrected. Link to the correction 10.2298/TSCI150923149E
A rational fraction polynomials model to study vertical dynamic wheel-rail interaction
Correa, N.; Vadillo, E. G.; Santamaria, J.; Gómez, J.
2012-04-01
This paper presents a model designed to study vertical interactions between wheel and rail when the wheel moves over a rail welding. The model focuses on the spatial domain, and is drawn up in a simple fashion from track receptances. The paper obtains the receptances from a full track model in the frequency domain already developed by the authors, which includes deformation of the rail section and propagation of bending, elongation and torsional waves along an infinite track. Transformation between domains was secured by applying a modified rational fraction polynomials method. This obtains a track model with very few degrees of freedom, and thus with minimum time consumption for integration, with a good match to the original model over a sufficiently broad range of frequencies. Wheel-rail interaction is modelled on a non-linear Hertzian spring, and consideration is given to parametric excitation caused by the wheel moving over a sleeper, since this is a moving wheel model and not a moving irregularity model. The model is used to study the dynamic loads and displacements emerging at the wheel-rail contact passing over a welding defect at different speeds.
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Araujo, Elaine Bortoleti de
1995-07-01
The present work reflects the clinical interest for labelling diamino dithiol compounds with technetium-99m. Both chosen compounds, L,L-Ethylene dicysteine (L,L-EC) and L,L-Ethylene dicysteine diethyl esther (L,L-ECD) were obtained with relative good yield and characterized by IR and NMR. The study of labelling conditions with technetium-99m showed the influence of the type and mass of reducing agent as well as the pH on the formation of complexes with desired biological characteristics. Radiochemical purity was determined by thin layer chromatography (TLC) and high performance liquid chromatography (HPLC). Lyophilised kits of L,L-EC and L,L-ECD for labelling with {sup 99m}Tc were obtained, with stability superior to 120 days, when stored under refrigeration, enabling the kits marketing. The ideal formulation of the kits as well as the use of liquid nitrogen in the freezing process, determined the lyophilization success. Distribution biological studies of the {sup 99m}Tc complexes were performed on mice by invasive method and on bigger animals by scintigraphic evaluation. Biological distribution studies of the complex {sup 99m}Tc-L,L-EC showed fast blood clearance, with the elimination of about 90% of the administered dose after 60 minutes, almost exclusively by the urinary system. The biological distribution results were adjusted to a three compartmental distribution model, as expected for a radiopharmaceutical designed to renal dynamic studies, with tubular elimination. The complex interaction with renal tubular receptors is related with structural characteristics of the compound, more specifically with the presence and location of polar groups. In comparison with {sup 99m}Tc-L,L-EC, biological studies of the complex {sup 99m}Tc -L,L-ECD showed different distribution aspects, despite some structural similarities. The presence of ethyl groups confers to the complex neutrality and lipophilicity. It cross the intact blood brain barrier and is retained in the brain
Fractional charge separation in the hard-core Bose Hubbard Model on the Kagome Lattice
Zhang, Xue Feng; Eggert, Sebastian
2013-03-01
We consider the hard core Bose Hubbard Model on a Kagome lattice with fixed (open) boundary conditions on two edges. We find that the fixed boundary conditions lift the degeneracy and freeze the system at 1/3 and 2/3 filling at small hopping. At larger hopping strengths, fractional charges spontaneously separate and are free to move to the edges of the system, which leads to a novel compressible phase with solid order. The compressibility is due to excitations on the edge which display a chrial symmetry breaking that is reminiscent of the quantum Hall effect. Large scale Monte Carlo simulations confirm the analytical calculations.
Quantifying Arsenic Leaching from Soils Using a Fractional-Derivative Model
Lu, B.; Zhang, Y.; LU, B.
2015-12-01
Arsenic leaching from soils can exhibit multiple-rate kinetics due to the heterogeneity nature of the medium, motivating the development of a fractional-order derivative model (FDM). The sorption-desorption process in saturated natural soils may not be limited to be a single rate or can reach equilibrium quickly, even at the laboratory scale. Applications of the FDM show that the multi-rate mass transfer quantifies the multi-stage desorption in Arsenic leaching characterized by the heavy late-time tailing behavior.
Unsteady flow of viscoelastic fluid between two cylinders using fractional Maxwell model
Institute of Scientific and Technical Information of China (English)
Muhammad Jamil; Constantin Fetecau; Corina Fetecau
2012-01-01
The unsteady flow of an incompressible fractional Maxwell fluid between two infinite coaxial cylinders is studied by means of integral transforms.The motion of the fluid is due to the inner cylinder that applies a time dependent torsional shear to the fluid.The exact solutions for velocity and shear stress are presented in series form in terms of some generalized functions.They can easily be particularized to give similar solutions for Maxwell and Newtonian fluids.Finally,the influence of pertinent parameters on the fluid motion,as well as a comparison between models,is highlighted by graphical illustrations.
Ruedig, Elizabeth; Caffrey, Emily; Hess, Catherine; Higley, Kathryn
2014-08-01
Simple, ellipsoidal geometries have long been the standard for estimating radiation dose rates in non-human biota (NHB). With the introduction of a regulatory protection standard that emphasizes protection of NHB as its own end point, there has been interest in improved models for the calculation of dose rates in NHB. Here, we describe the creation of a voxelized model for a rainbow trout (Oncorhynchus mykiss), a freshwater aquatic salmonid. Absorbed fractions (AFs) for both photon and electron sources were tabulated at electron energies of 0.1, 0.2, 0.4, 0.5, 0.7, 1.0, 1.5, 2.0, and 4.0 MeV and photon energies of 0.01, 0.015, 0.02, 0.03, 0.05, 0.1, 0.2, 0.5, 1.0, 1.5, 2.0, and 4.0 MeV. A representative set of the data is made available in this publication; the entire set of absorbed fractions is available as electronic supplementary materials. These results are consistent with previous voxelized models and reinforce the well-understood relationship between the AF and the target's mass and location, as well as the energy of the incident radiation.
Financial analysis of technology acquisition using fractionated lasers as a model.
Jutkowitz, Eric; Carniol, Paul J; Carniol, Alan R
2010-08-01
Ablative fractional lasers are among the most advanced and costly devices on the market. Yet, there is a dearth of published literature on the cost and potential return on investment (ROI) of such devices. The objective of this study was to provide a methodological framework for physicians to evaluate ROI. To facilitate this analysis, we conducted a case study on the potential ROI of eight ablative fractional lasers. In the base case analysis, a 5-year lease and a 3-year lease were assumed as the purchase option with a $0 down payment and 3-month payment deferral. In addition to lease payments, service contracts, labor cost, and disposables were included in the total cost estimate. Revenue was estimated as price per procedure multiplied by total number of procedures in a year. Sensitivity analyses were performed to account for variability in model assumptions. Based on the assumptions of the model, all lasers had higher ROI under the 5-year lease agreement compared with that for the 3-year lease agreement. When comparing results between lasers, those with lower operating and purchase cost delivered a higher ROI. Sensitivity analysis indicates the model is most sensitive to purchase method. If physicians opt to purchase the device rather than lease, they can significantly enhance ROI. ROI analysis is an important tool for physicians who are considering making an expensive device acquisition. However, physicians should not rely solely on ROI and must also consider the clinical benefits of a laser.
Energy Technology Data Exchange (ETDEWEB)
DePaolo, D.
2010-10-15
A surface reaction kinetic model is developed for predicting Ca isotope fractionation and metal/Ca ratios of calcite as a function of rate of precipitation from aqueous solution. The model is based on the requirements for dynamic equilibrium; i.e. proximity to equilibrium conditions is determined by the ratio of the net precipitation rate (R{sub p}) to the gross forward precipitation rate (R{sub f}), for conditions where ionic transport to the growing crystal surface is not rate-limiting. The value of R{sub p} has been experimentally measured under varying conditions, but the magnitude of R{sub f} is not generally known, and may depend on several factors. It is posited that, for systems with no trace constituents that alter the surface chemistry, R{sub f} can be estimated from the bulk far-from-equilibrium dissolution rate of calcite (R{sub b} or k{sub b}), since at equilibrium R{sub f} = R{sub b}, and R{sub p} = 0. Hence it can be inferred that R{sub f} {approx} R{sub p} + R{sub b}. The dissolution rate of pure calcite is measureable and is known to be a function of temperature and pH. At given temperature and pH, equilibrium precipitation is approached when R{sub p} (= R{sub f} - R{sub b}) << R{sub b}. For precipitation rates high enough that R{sub p} >> R{sub b}, both isotopic and trace element partitioning are controlled by the kinetics of ion attachment to the mineral surface, which tend to favor more rapid incorporation of the light isotopes of Ca and discriminate weakly between trace metals and Ca. With varying precipitation rate, a transition region between equilibrium and kinetic control occurs near R{sub p} {approx} R{sub b} for Ca isotopic fractionation. According to this model, Ca isotopic data can be used to estimate R{sub f} for calcite precipitation. Mechanistic models for calcite precipitation indicate that the molecular exchange rate is not constant at constant T and pH, but rather is dependent also on solution saturation state and hence R{sub p
Exact results for spin dynamics and fractionalization in the Kitaev Model.
Baskaran, G; Mandal, Saptarshi; Shankar, R
2007-06-15
We present certain exact analytical results for dynamical spin correlation functions in the Kitaev Model. It is the first result of its kind in nontrivial quantum spin models. The result is also novel: in spite of the presence of gapless propagating Majorana fermion excitations, dynamical two spin correlation functions are identically zero beyond nearest neighbor separation. This shows existence of a gapless but short range spin liquid. An unusual, all energy scale fractionalization of a spin-flip quanta, into two infinitely massive pi fluxes and a dynamical Majorana fermion, is shown to occur. As the Kitaev Model exemplifies topological quantum computation, our result presents new insights into qubit dynamics and generation of topological excitations.
Biot-JKD model: simulation of 1D transient poroelastic waves with fractional derivatives
Blanc, Emilie; Lombard, Bruno
2012-01-01
A time-domain numerical modeling of Biot poroelastic waves is presented. The viscous dissipation occurring in the pores is described using the dynamic permeability model developed by Johnson-Koplik-Dashen (JKD). Some of the coefficients in the Biot-JKD model are proportional to the square root of the frequency: in the time-domain, these coefficients introduce order 1/2 shifted fractional derivatives involving a convolution product. Based on a diffusive representation, the convolution kernel is replaced by a finite number of memory variables that satisfy local-in-time ordinary differential equations. Thanks to the dispersion relation, the coefficients in the diffusive representation are obtained by performing an optimization procedure in the frequency range of interest. A splitting strategy is then applied numerically: the propagative part of Biot-JKD equations is discretized using a fourth-order ADER scheme on a Cartesian grid, whereas the diffusive part is solved exactly. Comparisons with analytical solution...
Institute of Scientific and Technical Information of China (English)
HU Zhen-qi; HE Fen-qin; YIN Jian-zhong; LU Xia; TANG Shi-lu; WANG Lin-lin; LI Xiao-jing
2007-01-01
The objective of this paper is to improve the monitoring speed and precision of fractional vegetation cover (fc). It mainly focuses onfc estimation when fcmax andfcmin are not approximately equal to 100% and 0%, respectively due to using remote sensing image with medium or low spatial resolution. Meanwhile, we present a new method offc estimation based on a random set offc maximum and minimum values from digital camera (DC) survey data and a dimidiate pixel model. The results show that this is a convenient, efficient and accurate method forfc monitoring, with the maximum error -0.172 and correlation coefficient of 0.974 between DC survey data and the estimated value of the remote sensing model. The remaining DC survey data can be used as verification data for the precision of thefc estimation. In general, the estimation offc based on DC survey data and a remote sensing model is a brand-new development trend and deserves further extensive utilization.
Directory of Open Access Journals (Sweden)
Yunfeng Jiang
2016-07-01
Full Text Available A fractional derivative system identification approach for modeling battery dynamics is presented in this paper, where fractional derivatives are applied to approximate non-linear dynamic behavior of a battery system. The least squares-based state-variable filter (LSSVF method commonly used in the identification of continuous-time models is extended to allow the estimation of fractional derivative coefficents and parameters of the battery models by monitoring a charge/discharge demand signal and a power storage/delivery signal. In particular, the model is combined by individual fractional differential models (FDMs, where the parameters can be estimated by a least-squares algorithm. Based on experimental data, it is illustrated how the fractional derivative model can be utilized to predict the dynamics of the energy storage and delivery of a lithium iron phosphate battery (LiFePO 4 in real-time. The results indicate that a FDM can accurately capture the dynamics of the energy storage and delivery of the battery over a large operating range of the battery. It is also shown that the fractional derivative model exhibits improvements on prediction performance compared to standard integer derivative model, which in beneficial for a battery management system.
Yang, Qingxia; Xu, Jun; Cao, Binggang; Li, Xiuqing
2017-01-01
Identification of internal parameters of lithium-ion batteries is a useful tool to evaluate battery performance, and requires an effective model and algorithm. Based on the least square genetic algorithm, a simplified fractional order impedance model for lithium-ion batteries and the corresponding parameter identification method were developed. The simplified model was derived from the analysis of the electrochemical impedance spectroscopy data and the transient response of lithium-ion batteries with different states of charge. In order to identify the parameters of the model, an equivalent tracking system was established, and the method of least square genetic algorithm was applied using the time-domain test data. Experiments and computer simulations were carried out to verify the effectiveness and accuracy of the proposed model and parameter identification method. Compared with a second-order resistance-capacitance (2-RC) model and recursive least squares method, small tracing voltage fluctuations were observed. The maximum battery voltage tracing error for the proposed model and parameter identification method is within 0.5%; this demonstrates the good performance of the model and the efficiency of the least square genetic algorithm to estimate the internal parameters of lithium-ion batteries. PMID:28212405
Yang, Qingxia; Xu, Jun; Cao, Binggang; Li, Xiuqing
2017-01-01
Identification of internal parameters of lithium-ion batteries is a useful tool to evaluate battery performance, and requires an effective model and algorithm. Based on the least square genetic algorithm, a simplified fractional order impedance model for lithium-ion batteries and the corresponding parameter identification method were developed. The simplified model was derived from the analysis of the electrochemical impedance spectroscopy data and the transient response of lithium-ion batteries with different states of charge. In order to identify the parameters of the model, an equivalent tracking system was established, and the method of least square genetic algorithm was applied using the time-domain test data. Experiments and computer simulations were carried out to verify the effectiveness and accuracy of the proposed model and parameter identification method. Compared with a second-order resistance-capacitance (2-RC) model and recursive least squares method, small tracing voltage fluctuations were observed. The maximum battery voltage tracing error for the proposed model and parameter identification method is within 0.5%; this demonstrates the good performance of the model and the efficiency of the least square genetic algorithm to estimate the internal parameters of lithium-ion batteries.
Sulfur Isotope Fractionation in Magmatic Systems：Models of Rayleigh Distillation and Selective Flux
Institute of Scientific and Technical Information of China (English)
郑永飞
1990-01-01
The effect of Rayleigh distillation by outgassing of SO2 and H2S on the isotopic composition of sulfur remaining in silicate melts is quantitatively modelled.A threshold mole fraction of sulfur in sulfide component of the melts is reckoned to be of critical importance in shifting the δ34S of the melts mith respect to the original magmas.The partial equilibrium fractionation in a magmatic system is evaluated by assuming that a non-equilibrium flux of sulfur occurs between magmatic volatiles and the melts,while an equilibrium fractionation is approached between sulfate and sulfide within the melts.The results show that under high fo2 conditions,the sulfate/sulfide ratio in a melt entds to increase,and the δ34S value of sulfur in a solidified rock might then be shifted in the positive direction.This may either be due to Rayleigh outgassing in case the mole fraction of sulfide is less than the threshold,or due to a unidirectional increase in δ34S value of the sulfate with decreaing temperature,Conversely,at low fo2,the sulfate/sulfide ratio tends to decrease and the δ34S value of total sulfur could be driven in the negative direction,either because of the Rayleigh outgassing in case the mole fraction of sulfide is greater than the threshold,or because of a unidirectional decrease inδ34S value of the sulfide.To establish isotopic equilibrium between sulfate and sulfide,the HM,QFM or WM buffers in the magmatic system are suggested to provide the redox couple that could simultaneously reduce the sulfate and oxidize the sulfide.CaO present in the silicatte Melts is also called upon to participate in the chemical equilibrium between sulfate and sulfide,Consequently,the δ34S value of an igneous rock could considerably deviate from that of its original magma due to the influence of oxygen fugacity and temperature at the time of magma solidification.
Tan, Cheng; Liang, Zhi-Shan
2016-03-01
In this paper, based on the fact that the inductors and capacitors are of fractional order in nature, the four-order mathematical model of the fractional order quadratic Boost converter in type I and type II discontinuous conduction mode (DCM) — DCM is established by using fractional calculus theory. Direct current (DC) analysis is conducted by using the DC equivalent model and the transfer functions are derived from the corresponding alternating current (AC) equivalent model. The DCM-DCM regions of type I and type II are obtained and the relations between the regions and the orders are found. The influence of the orders on the performance of the quadratic Boost converter in DCM-DCM is verified by numerical and circuit simulations. Simulation results demonstrate the correctness of the fractional order model and the efficiency of the proposed theoretical analysis.
Energy Technology Data Exchange (ETDEWEB)
Morais, A. P. [Biomedical Engineering Program, COPPE, Rio de Janeiro (Brazil); Salgado de Oliveira University, Marechal Deodoro Street, 217 – Centro, Niterói, Rio de Janeiro (Brazil); Pino, A. V. [Biomedical Engineering Program, COPPE, Rio de Janeiro (Brazil); Souza, M. N. [Biomedical Engineering Program, COPPE, Rio de Janeiro (Brazil); Electronics Department at Polytechnic School, Federal University of Rio de Janeiro, Centro de Tecnologia Bloco H sala 217, Ilha do Fundão, Rio de Janeiro (Brazil)
2016-08-15
This in vitro study evaluated the diagnostic performance of an alternative electric bioimpedance spectroscopy technique (BIS-STEP) detect questionable occlusal carious lesions. Six specialists carried out the visual (V), radiography (R), and combined (VR) exams of 57 sound or non-cavitated occlusal carious lesion teeth classifying the occlusal surfaces in sound surface (H), enamel caries (EC), and dentinal caries (DC). Measurements were based on the current response to a step voltage excitation (BIS-STEP). A fractional electrical model was used to predict the current response in the time domain and to estimate the model parameters: Rs and Rp (resistive parameters), and C and α (fractional parameters). Histological analysis showed caries prevalence of 33.3% being 15.8% hidden caries. Combined examination obtained the best traditional diagnostic results with specificity = 59.0%, sensitivity = 70.9%, and accuracy = 60.8%. There were statistically significant differences in bioimpedance parameters between the H and EC groups (p = 0.016) and between the H and DC groups (Rs, p = 0.006; Rp, p = 0.022, and α, p = 0.041). Using a suitable threshold for the Rs, we obtained specificity = 60.7%, sensitivity = 77.9%, accuracy = 73.2%, and 100% of detection for deep lesions. It can be concluded that BIS-STEP method could be an important tool to improve the detection and management of occlusal non-cavitated primary caries and pigmented sites.
Energy Technology Data Exchange (ETDEWEB)
Choi, A. S.; Flach, G. P.; Martino, C. J.; Zamecnik, J. R.; Harris, M. K.; Wilmarth, W. R.; Calloway, T. B.
2005-03-23
In order to accelerate waste treatment and disposal of Hanford tank waste by 2028, the Department of Energy (DOE) and CH2M Hill Hanford Group (CHG), Inc. are evaluating alternative technologies which will be used in conjunction with the Waste Treatment Plant (WTP) to safely pretreat and immobilize the tank waste. Several technologies (Bulk Vitrification and Steam Reforming) are currently being evaluated for immobilizing the pretreated waste. Since the WTP does not have sufficient capacity to pretreat all the waste going to supplemental treatment by the 2028 milestone, two technologies (Selective Dissolution and Fractional Crystallization) are being considered for pretreatment of salt waste. The scope of this task was to: (1) evaluate the recent Savannah River Site (SRS) Tank 41 dissolution campaign and other literature to provide a more complete understanding of selective dissolution, (2) provide an update on the progress of salt dissolution and modeling activities at SRS, (3) investigate SRS experience and outside literature sources on industrial equipment and experimental results of previous fractional crystallization processes, and (4) evaluate recent Hanford AP104 boildown experiments and modeling results and recommend enhancements to the Environmental Simulation Program (ESP) to improve its predictive capabilities. This report provides a summary of this work and suggested recommendations.
Muñiz-Lerma, Jose Alberto; Paliwal, Manas; Jung, In-Ho; Brochu, Mathieu
2017-04-01
A one-dimensional numerical solidification model has been developed to predict the recovery and refining efficiency of fractional crystallization applied to a blend of aircraft Al scraps with variations of Fe and Si. The model incorporates the effective partition coefficient depending on the degree of melt stirring. Moreover, the kinetic factors that affect the formation of primary Al FCC during fractional crystallization such as solidification velocity, thermal gradient, cooling rate, and solute back-diffusion are taken into account. The simulation results suggest that the optimum solidification velocities that are able to yield the highest refining can be ranged between 1.0 × 10-6 and 1.0 × 10-5 m/s with medium to high stirring levels. The maximum recovery of refined Al has been estimated to be 31 wt pct of the initial scrap when the process is carried out at 1 × 10-6 m/s and the initial concentrations of Fe and Si are 1 and 2 pct, respectively.
Emergent chiral spin liquid: fractional quantum Hall effect in a kagome Heisenberg model.
Gong, Shou-Shu; Zhu, Wei; Sheng, D N
2014-09-10
The fractional quantum Hall effect (FQHE) realized in two-dimensional electron systems under a magnetic field is one of the most remarkable discoveries in condensed matter physics. Interestingly, it has been proposed that FQHE can also emerge in time-reversal invariant spin systems, known as the chiral spin liquid (CSL) characterized by the topological order and the emerging of the fractionalized quasiparticles. A CSL can naturally lead to the exotic superconductivity originating from the condense of anyonic quasiparticles. Although CSL was highly sought after for more than twenty years, it had never been found in a spin isotropic Heisenberg model or related materials. By developing a density-matrix renormalization group based method for adiabatically inserting flux, we discover a FQHE in a spin-½ isotropic kagome Heisenberg model. We identify this FQHE state as the long-sought CSL with a uniform chiral order spontaneously breaking time reversal symmetry, which is uniquely characterized by the half-integer quantized topological Chern number protected by a robust excitation gap. The CSL is found to be at the neighbor of the previously identified Z2 spin liquid, which may lead to an exotic quantum phase transition between two gapped topological spin liquids.
Muñiz-Lerma, Jose Alberto; Paliwal, Manas; Jung, In-Ho; Brochu, Mathieu
2017-01-01
A one-dimensional numerical solidification model has been developed to predict the recovery and refining efficiency of fractional crystallization applied to a blend of aircraft Al scraps with variations of Fe and Si. The model incorporates the effective partition coefficient depending on the degree of melt stirring. Moreover, the kinetic factors that affect the formation of primary Al FCC during fractional crystallization such as solidification velocity, thermal gradient, cooling rate, and solute back-diffusion are taken into account. The simulation results suggest that the optimum solidification velocities that are able to yield the highest refining can be ranged between 1.0 × 10-6 and 1.0 × 10-5 m/s with medium to high stirring levels. The maximum recovery of refined Al has been estimated to be 31 wt pct of the initial scrap when the process is carried out at 1 × 10-6 m/s and the initial concentrations of Fe and Si are 1 and 2 pct, respectively.
Morais, A. P.; Pino, A. V.; Souza, M. N.
2016-08-01
This in vitro study evaluated the diagnostic performance of an alternative electric bioimpedance spectroscopy technique (BIS-STEP) detect questionable occlusal carious lesions. Six specialists carried out the visual (V), radiography (R), and combined (VR) exams of 57 sound or non-cavitated occlusal carious lesion teeth classifying the occlusal surfaces in sound surface (H), enamel caries (EC), and dentinal caries (DC). Measurements were based on the current response to a step voltage excitation (BIS-STEP). A fractional electrical model was used to predict the current response in the time domain and to estimate the model parameters: Rs and Rp (resistive parameters), and C and α (fractional parameters). Histological analysis showed caries prevalence of 33.3% being 15.8% hidden caries. Combined examination obtained the best traditional diagnostic results with specificity = 59.0%, sensitivity = 70.9%, and accuracy = 60.8%. There were statistically significant differences in bioimpedance parameters between the H and EC groups (p = 0.016) and between the H and DC groups (Rs, p = 0.006; Rp, p = 0.022, and α, p = 0.041). Using a suitable threshold for the Rs, we obtained specificity = 60.7%, sensitivity = 77.9%, accuracy = 73.2%, and 100% of detection for deep lesions. It can be concluded that BIS-STEP method could be an important tool to improve the detection and management of occlusal non-cavitated primary caries and pigmented sites.
Hamiltonian Analysis of Gauged $CP^{1}$ Model, the Hopf term, and fractional spin
Chakraborty, B
1998-01-01
Recently it was shown by Cho and Kimm that the gauged $CP^1$ model, obtained by gauging the global $SU(2)$ group and adding a corresponding Chern-Simons term, has got its own soliton. These solitons are somewhat distinct from those of pure $CP^1$ model as they cannot always be characterised by $\\pi_2(CP^1)=Z$. In this paper, we first carry out a detailed Hamiltonian analysis of this gauged $CP^1$ model. This reveals that the model has only $SU(2)$ as the gauge invariance, rather than $SU(2) \\times U(1)$. The $U(1)$ gauge invariance of the original (ungauged) $CP^1$ model is actually contained in the $SU(2)$ group itself. Then we couple the Hopf term associated to these solitons and again carry out its Hamiltonian analysis. The symplectic structures, along with the structures of the constraints of these two models (with or without Hopf term) are found to be essentially the same. The model with a Hopf term is shown to have fractional spin which, when computed in the radiation gauge, is found to depend not only ...
Institute of Scientific and Technical Information of China (English)
TAN Wenchang; XU Mingyu
2004-01-01
The fractional calculus approach in the constitutive relationship model of a generalized second grade fluid is introduced. Exact analytical solutions are obtained for a class of unsteady flows for the generalized second grade fluid with the fractional derivative model between two parallel plates by using the Laplace transform and Fourier transform for fractional calculus. The unsteady flows are generated by the impulsive motion or periodic oscillation of one of the plates. In addition, the solutions of the shear stresses at the plates are also determined.
Lee, Geum Seon; Yim, Dongsool; Cheong, Jae Hoon; Kang, Tae Jin
2012-12-01
Our previous report showed that Hydnocarpi Semen (HS) extract has wound repair activity at ulcer lesion in diabetic mice. In this study, fractions of n-Hexane, ethylacetate (EtOAc), and butanol (BuOH) from HS crude extract were evaluated for their wound healing activity by using in vivo diabetic ulcer models and in vitro acute inflammation model. Although n-Hexane and EtOAc fractions promote wound healing in mice with ulcer, the BuOH fraction exhibited the most potent wound healing activity and the wound area score significantly decreased after treatment of BuOH fraction even at dose of 2 mg/kg. BuOH fraction stimulated macrophages to increase the production of nitric oxide (NO) and TNF-α. The BuOH fraction also enhanced the production of TGF-β and VEGF, which were involved in fibroblast activation and angiogenesis. The mRNA expression and activation of MMP-9 were increased by three fractions and the activity was higher in BuOH fraction-treated group compared to the other groups. The mechanism that the HS helps to promote healing of diabetic ulcer is possibly associated with the production of TNF-α, a proinflammatory cytokine, as well as the secretion of VEGF, TGF-β, and MMP-9, which were involved in proliferation of capillaries and fibroblasts. These results suggest that HS can be a new candidate material for the treatment of wound in skin ulcer.
Directory of Open Access Journals (Sweden)
Jagdev Singh
2017-07-01
Full Text Available In this paper, we propose a new numerical algorithm, namely q-homotopy analysis Sumudu transform method (q-HASTM, to obtain the approximate solution for the nonlinear fractional dynamical model of interpersonal and romantic relationships. The suggested algorithm examines the dynamics of love affairs between couples. The q-HASTM is a creative combination of Sumudu transform technique, q-homotopy analysis method and homotopy polynomials that makes the calculation very easy. To compare the results obtained by using q-HASTM, we solve the same nonlinear problem by Adomian’s decomposition method (ADM. The convergence of the q-HASTM series solution for the model is adapted and controlled by auxiliary parameter ℏ and asymptotic parameter n. The numerical results are demonstrated graphically and in tabular form. The result obtained by employing the proposed scheme reveals that the approach is very accurate, effective, flexible, simple to apply and computationally very nice.
Fractional Response Models - A Replication Exercise of Papke and Wooldridge (1996
Directory of Open Access Journals (Sweden)
Harald Oberhofer
2012-09-01
Full Text Available This paper replicates the estimates of a fractional response model for share data reported in the seminal paper of Leslie E. Papke and Jeffrey M. Wooldridge published in the Journal of Applied Econometrics 11(6, 1996, pp.619-632. We have been able to replicate all of the reported estimation results concerning the determinants of employee participation rates in 401(k pension plans using the standard routines provided in Stata. As an alternative, we estimate a two-part model that is capable of coping with the excessive number of boundary values equalling one in the data. The estimated marginal effects are similar to those derived in the paper. A small-scale Monte Carlo simulation exercise suggests that the RESET tests proposed by Papke and Wooldridge in their robust form are useful for detecting neglected non-linearities in small samples.
Energy Technology Data Exchange (ETDEWEB)
Choi, Seo-Woo; Kim, Soree; Jung, YounJoon, E-mail: yjjung@snu.ac.kr [Department of Chemistry, Seoul National University, Seoul 151-747 (Korea, Republic of)
2015-06-28
Kinetically constrained models have gained much interest as models that assign the origins of interesting dynamic properties of supercooled liquids to dynamical facilitation mechanisms that have been revealed in many experiments and numerical simulations. In this work, we investigate the dynamic heterogeneity in the fragile-to-strong liquid via Monte Carlo method using the model that linearly interpolates between the strong liquid-like behavior and the fragile liquid-like behavior by an asymmetry parameter b. When the asymmetry parameter is sufficiently small, smooth fragile-to-strong transition is observed both in the relaxation time and the diffusion constant. Using these physical quantities, we investigate fractional Stokes-Einstein relations observed in this model. When b is fixed, the system shows constant power law exponent under the temperature change, and the exponent has the value between that of the Frederickson-Andersen model and the East model. Furthermore, we investigate the dynamic length scale of our systems and also find the crossover relation between the relaxation time. We ascribe the competition between energetically favored symmetric relaxation mechanism and entropically favored asymmetric relaxation mechanism to the fragile-to-strong crossover behavior.
Berezowski, Tomasz; Chormański, Jarosław; Nossent, Jiri; Batelaan, Okke
2014-05-01
Distributed hydrological models enhance the analysis and explanation of environmental processes. As more spatial input data and time series become available, more analysis is required of the sensitivity of the data on the simulations. Most research so far focussed on the sensitivity of precipitation data in distributed hydrological models. However, these results can not be compared until a universal approach to quantify the sensitivity of a model to spatial data is available. The frequently tested and used remote sensing data for distributed models is snow cover. Snow cover fraction (SCF) remote sensing products are easily available from the internet, e.g. MODIS snow cover product MOD10A1 (daily snow cover fraction at 500m spatial resolution). In this work a spatial sensitivity analysis (SA) of remotely sensed SCF from MOD10A1 was conducted with the distributed WetSpa model. The aim is to investigate if the WetSpa model is differently subjected to SCF uncertainty in different areas of the model domain. The analysis was extended to look not only at SA quantities but also to relate them to the physical parameters and processes in the study area. The study area is the Biebrza River catchment, Poland, which is considered semi natural catchment and subject to a spring snow melt regime. Hydrological simulations are performed with the distributed WetSpa model, with a simulation period of 2 hydrological years. For the SA the Latin-Hypercube One-factor-At-a-Time (LH-OAT) algorithm is used, with a set of different response functions in regular 4 x 4 km grid. The results show that the spatial patterns of sensitivity can be easily interpreted by co-occurrence of different landscape features. Moreover, the spatial patterns of the SA results are related to the WetSpa spatial parameters and to different physical processes. Based on the study results, it is clear that spatial approach of SA can be performed with the proposed algorithm and the MOD10A1 SCF is spatially sensitive in
Compartmentalized metabolic engineering for biochemical and biofuel production.
Huttanus, Herbert M; Feng, Xueyang
2017-06-01
Sub-cellular compartments create specialized reaction chambers in eukaryotes. These compartments provide favorable micro-environments for many metabolic processes. Recently, metabolic engineers have explored the concept of pathway compartmentalization to enhance the performance of metabolic pathways. This strategy offers many unique advantages, including (i) increased local concentrations of enzymes and substrates, (ii) accessing alternate substrate pools, (iii) separation from competing reactions, and (iv) isolation of harmful intermediates or conditions needed for the pathway. In this review, the method of localizing metabolic pathways into specific organelles as well as the benefits of pathway compartmentalization in terms of enhancing the production of value-added chemicals is discussed. Copyright © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Intracellular compartmentalization of skeletal muscle glycogen metabolism and insulin signalling
DEFF Research Database (Denmark)
Prats Gavalda, Clara; Gomez-Cabello, Alba; Vigelsø Hansen, Andreas
2011-01-01
compartmentalization in the regulation of skeletal muscle glycogen metabolism and insulin signalling. As a result, a hypothetical regulatory mechanism is proposed by which cells could direct glycogen resynthesis towards different pools of glycogen particles depending on the metabolic needs. Furthermore, we discuss......The interest in skeletal muscle metabolism and insulin signalling has increased exponentially in recent years as a consequence of their role in the development of type 2 diabetes mellitus. Despite this, the exact mechanisms involved in the regulation of skeletal muscle glycogen metabolism...... and insulin signalling transduction remain elusive. We believe that one of the reasons is that the role of intracellular compartmentalization as a regulator of metabolic pathways and signalling transduction has been rather ignored. This paper briefly reviews the literature to discuss the role of intracellular...
Barriers in the brain: resolving dendritic spine morphology and compartmentalization
2014-01-01
Dendritic spines are micron-sized protrusions that harbor the majority of excitatory synapses in the central nervous system. The head of the spine is connected to the dendritic shaft by a 50–400 nm thin membrane tube, called the spine neck, which has been hypothesized to confine biochemical and electric signals within the spine compartment. Such compartmentalization could minimize interspinal crosstalk and thereby support spine-specific synapse plasticity. However, to what extent compartmenta...
Compartmentalized Droplets for Continuous Flow Liquid-Liquid Interface Catalysis.
Zhang, Ming; Wei, Lijuan; Chen, Huan; Du, Zhiping; Binks, Bernard P; Yang, Hengquan
2016-08-17
To address the limitations of batch organic-aqueous biphasic catalysis, we develop a conceptually novel method termed Flow Pickering Emulsion, or FPE, to process biphasic reactions in a continuous flow fashion. This method involves the compartmentalization of bulk water into micron-sized droplets based on a water-in-oil Pickering emulsion, which are packed into a column reactor. The compartmentalized water droplets can confine water-soluble catalysts, thus "immobilizing" the catalyst in the column reactor, while the interstices between the droplets allow the organic (oil) phase to flow. Key fundamental principles underpinning this method such as the oil phase flow behavior, the stability of compartmentalized droplets and the confinement capability of these droplets toward water-soluble catalysts are experimentally and theoretically investigated. As a proof of this concept, case studies including a sulfuric acid-catalyzed addition reaction, a heteropolyacid-catalyzed ring opening reaction and an enzyme-catalyzed chiral reaction demonstrate the generality and versatility of the FPE method. Impressively, in addition to the excellent durability, the developed FPE reactions exhibit up to 10-fold reaction efficiency enhancement in comparison to the existing batch reactions, indicating a unique flow interface catalysis effect. This study opens up a new avenue to allow conventional biphasic catalysis reactions to access more sustainable and efficient flow chemistry using an innovative liquid-liquid interface protocol.
Field Testing of Compartmentalization Methods for Multifamily Construction
Energy Technology Data Exchange (ETDEWEB)
Ueno, K. [Building Science Corporation, Westford, MA (United States); Lstiburek, J. [Building Science Corporation, Westford, MA (United States)
2015-03-01
The 2012 IECC has an airtightness requirement of 3 air changes per hour at 50 Pascals test pressure for both single-family and multifamily construction in Climate Zones 3-8. Other programs (LEED, ASHRAE 189, ASHRAE 62.2) have similar or tighter compartmentalization requirements, driving the need for easier and more effective methods of compartmentalization in multifamily buildings. Builders and practitioners have found that fire-resistance rated wall assemblies are a major source of difficulty in air sealing/compartmentalization, particularly in townhouse construction. This problem is exacerbated when garages are “tucked in” to the units and living space is located over the garages. In this project, Building Science Corporation examined the taping of exterior sheathing details to improve air sealing results in townhouse and multifamily construction, when coupled with a better understanding of air leakage pathways. Current approaches are cumbersome, expensive, time consuming, and ineffective; these details were proposed as a more effective and efficient method. The effectiveness of these air sealing methods was tested with blower door testing, including “nulled” or “guarded” testing (adjacent units run at equal test pressure to null out inter-unit air leakage, or “pressure neutralization”). Pressure diagnostics were used to evaluate unit-to-unit connections and series leakage pathways (i.e., air leakage from exterior, into the fire-resistance rated wall assembly, and to the interior).
DEFF Research Database (Denmark)
Tan, Qihua; Thomassen, Mads; Hjelmborg, Jacob V B
2011-01-01
among fractional polynomial models with power terms from a set of fixed values that offer a wide range of curve shapes and suggests a best fitting model. After a limited simulation study, the model has been applied to our human in vivo irritated epidermis data with missing observations to investigate......-course pattern in a gene by gene manner. We introduce a growth curve model with fractional polynomials to automatically capture the various time-dependent expression patterns and meanwhile efficiently handle missing values due to incomplete observations. For each gene, our procedure compares the performances...... time-dependent transcriptional responses to a chemical irritant. Our method was able to identify the various nonlinear time-course expression trajectories. The integration of growth curves with fractional polynomials provides a flexible way to model different time-course patterns together with model...
Modelling groundwater fractal flow with fractional differentiation via Mittag-Leffler law
Ahokposi, D. P.; Atangana, Abdon; Vermeulen, D. P.
2017-04-01
Modelling the flow of groundwater within a network of fractures is perhaps one of the most difficult exercises within the field of geohydrology. This physical problem has attracted the attention of several scientists across the globe. Already two different types of differentiations have been used to attempt modelling this problem including the classical and the fractional differentiation. In this paper, we employed the most recent concept of differentiation based on the non-local and non-singular kernel called the generalized Mittag-Leffler function, to reshape the model of groundwater fractal flow. We presented the existence of positive solution of the new model. Using the fixed-point approach, we established the uniqueness of the positive solution. We solve the new model with three different numerical schemes including implicit, explicit and Crank-Nicholson numerical methods. Experimental data collected from four constant discharge tests conducted in a typical fractured crystalline rock aquifer of the Northern Limb (Bushveld Complex) in the Limpopo Province (South Africa) are compared with the numerical solutions. It is worth noting that the four boreholes (BPAC1, BPAC2, BPAC3, and BPAC4) are located on Faults.
Black holes in multi-fractional and Lorentz-violating models
Calcagni, Gianluca; Rodríguez Fernández, David; Ronco, Michele
2017-05-01
We study static and radially symmetric black holes in the multi-fractional theories of gravity with q-derivatives and with weighted derivatives, frameworks where the spacetime dimension varies with the probed scale and geometry is characterized by at least one fundamental length ℓ _*. In the q-derivatives scenario, one finds a tiny shift of the event horizon. Schwarzschild black holes can present an additional ring singularity, not present in general relativity, whose radius is proportional to ℓ _*. In the multi-fractional theory with weighted derivatives, there is no such deformation, but non-trivial geometric features generate a cosmological-constant term, leading to a de Sitter-Schwarzschild black hole. For both scenarios, we compute the Hawking temperature and comment on the resulting black-hole thermodynamics. In the case with q-derivatives, black holes can be hotter than usual and possess an additional ring singularity, while in the case with weighted derivatives they have a de Sitter hair of purely geometric origin, which may lead to a solution of the cosmological constant problem similar to that in unimodular gravity. Finally, we compare our findings with other Lorentz-violating models.
Black holes in multi-fractional and Lorentz-violating models
Energy Technology Data Exchange (ETDEWEB)
Calcagni, Gianluca [CSIC, Instituto de Estructura de la Materia, Madrid (Spain); Rodriguez Fernandez, David [Universidad de Oviedo, Department of Physics, Oviedo (Spain); Ronco, Michele [Universita di Roma ' ' La Sapienza' ' , Dipartimento di Fisica, Rome (Italy); INFN, Rome (Italy)
2017-05-15
We study static and radially symmetric black holes in the multi-fractional theories of gravity with q-derivatives and with weighted derivatives, frameworks where the spacetime dimension varies with the probed scale and geometry is characterized by at least one fundamental length l{sub *}. In the q-derivatives scenario, one finds a tiny shift of the event horizon. Schwarzschild black holes can present an additional ring singularity, not present in general relativity, whose radius is proportional to l{sub *}. In the multi-fractional theory with weighted derivatives, there is no such deformation, but non-trivial geometric features generate a cosmological-constant term, leading to a de Sitter-Schwarzschild black hole. For both scenarios, we compute the Hawking temperature and comment on the resulting black-hole thermodynamics. In the case with q-derivatives, black holes can be hotter than usual and possess an additional ring singularity, while in the case with weighted derivatives they have a de Sitter hair of purely geometric origin, which may lead to a solution of the cosmological constant problem similar to that in unimodular gravity. Finally, we compare our findings with other Lorentz-violating models. (orig.)
Black holes in multi-fractional and Lorentz-violating models.
Calcagni, Gianluca; Rodríguez Fernández, David; Ronco, Michele
2017-01-01
We study static and radially symmetric black holes in the multi-fractional theories of gravity with q-derivatives and with weighted derivatives, frameworks where the spacetime dimension varies with the probed scale and geometry is characterized by at least one fundamental length [Formula: see text]. In the q-derivatives scenario, one finds a tiny shift of the event horizon. Schwarzschild black holes can present an additional ring singularity, not present in general relativity, whose radius is proportional to [Formula: see text]. In the multi-fractional theory with weighted derivatives, there is no such deformation, but non-trivial geometric features generate a cosmological-constant term, leading to a de Sitter-Schwarzschild black hole. For both scenarios, we compute the Hawking temperature and comment on the resulting black-hole thermodynamics. In the case with q-derivatives, black holes can be hotter than usual and possess an additional ring singularity, while in the case with weighted derivatives they have a de Sitter hair of purely geometric origin, which may lead to a solution of the cosmological constant problem similar to that in unimodular gravity. Finally, we compare our findings with other Lorentz-violating models.
Fdez-Güelfo, L A; Álvarez-Gallego, C; Sales Márquez, D; Romero García, L I
2011-01-01
Solid retention time (SRT) is a very important operational variable in continuous and semicontinuous waste treatment processes since the organic matter removal efficiency--expressed in terms of percentage of Dissolved Organic Carbon (% DOC) or Volatile Solids (% VS) removed--and the biogas or methane production are closely related with the SRT imposed. Optimum SRT is depending on the waste characteristics and the microorganisms involved in the process and, hence, it should be determined specifically in each case. In this work a series of experiments were carried out to determine the effect of SRT, from 40 to 8 days, on the performance of the dry (30% Total Solids) thermophilic (55°C) anaerobic digestion of organic fraction of Municipal Solid Wastes (OFMSW) operating at semicontinuous regime of feeding. The experimental results show than 15days is the optimum SRT (the best between all proved) for this process. Besides, data of organic matter concentration and methane production versus SRT have been used to obtain the kinetic parameters of the kinetic model of Romero García (1991): the maximum specific growth rate of the microorganisms (μmax=0.580 days(-1)) and the fraction of substrate non-biodegradable (α=0.268).
Wille, Marie-Luise; Langton, Christian M
2016-02-01
The acceptance of broadband ultrasound attenuation (BUA) for the assessment of osteoporosis suffers from a limited understanding of both ultrasound wave propagation through cancellous bone and its exact dependence upon the material and structural properties. It has recently been proposed that ultrasound wave propagation in cancellous bone may be described by a concept of parallel sonic rays; the transit time of each ray defined by the proportion of bone and marrow propagated. A Transit Time Spectrum (TTS) describes the proportion of sonic rays having a particular transit time, effectively describing the lateral inhomogeneity of transit times over the surface aperture of the receive ultrasound transducer. The aim of this study was to test the hypothesis that the solid volume fraction (SVF) of simplified bone:marrow replica models may be reliably estimated from the corresponding ultrasound transit time spectrum. Transit time spectra were derived via digital deconvolution of the experimentally measured input and output ultrasonic signals, and compared to predicted TTS based on the parallel sonic ray concept, demonstrating agreement in both position and amplitude of spectral peaks. Solid volume fraction was calculated from the TTS; agreement between true (geometric calculation) with predicted (computer simulation) and experimentally-derived values were R(2)=99.9% and R(2)=97.3% respectively. It is therefore envisaged that ultrasound transit time spectroscopy (UTTS) offers the potential to reliably estimate bone mineral density and hence the established T-score parameter for clinical osteoporosis assessment.
Fractional Market Model and its Verification on the Warsaw STOCK Exchange
Kozłowska, Marzena; Kasprzak, Andrzej; Kutner, Ryszard
We analyzed the rising and relaxation of the cusp-like local peaks superposed with oscillations which were well defined by the Warsaw Stock Exchange index WIG in a daily time horizon. We found that the falling paths of all index peaks were described by a generalized exponential function or the Mittag-Leffler (ML) one superposed with various types of oscillations. However, the rising paths (except the first one of WIG which rises exponentially and the most important last one which rises again according to the ML function) can be better described by bullish anti-bubbles or inverted bubbles.2-4 The ML function superposed with oscillations is a solution of the nonhomogeneous fractional relaxation equation which defines here our Fractional Market Model (FMM) of index dynamics which can be also called the Rheological Model of Market. This solution is a generalized analog of an exactly solvable fractional version of the Standard or Zener Solid Model of viscoelastic materials commonly used in modern rheology.5 For example, we found that the falling paths of the index can be considered to be a system in the intermediate state lying between two complex ones, defined by short and long-time limits of the Mittag-Leffler function; these limits are given by the Kohlrausch-Williams-Watts (KWW) law for the initial times, and the power-law or the Nutting law for asymptotic time. Some rising paths (i.e., the bullish anti-bubbles) are a kind of log-periodic oscillations of the market in the bullish state initiated by a crash. The peaks of the index can be viewed as precritical or precrash ones since: (i) the financial market changes its state too early from the bullish to bearish one before it reaches a scaling region (defined by the diverging power-law of return per unit time), and (ii) they are affected by a finite size effect. These features could be a reminiscence of a significant risk aversion of the investors and their finite number, respectively. However, this means that the
Dauser, T.; García, J.; Walton, , D. J.; Eikmann, W.; Kallman, T.; McClintock, J.; Wilms, J.
2016-05-01
Aims: The only relativistic reflection model that implements a parameter relating the intensity incident on an accretion disk to the observed intensity is relxill. The parameter used in earlier versions of this model, referred to as the reflection strength, is unsatisfactory; it has been superseded by a parameter that provides insight into the accretion geometry, namely the reflection fraction. The reflection fraction is defined as the ratio of the coronal intensity illuminating the disk to the coronal intensity that reaches the observer. Methods: The relxill model combines a general relativistic ray-tracing code and a photoionization code to compute the component of radiation reflected from an accretion that is illuminated by an external source. The reflection fraction is a particularly important parameter for relativistic models with well-defined geometry, such as the lamp post model, which is a focus of this paper. Results: Relativistic spectra are compared for three inclinations and for four values of the key parameter of the lamp post model, namely the height above the black hole of the illuminating, on-axis point source. In all cases, the strongest reflection is produced for low source heights and high spin. A low-spin black hole is shown to be incapable of producing enhanced relativistic reflection. Results for the relxill model are compared to those obtained with other models and a Monte Carlo simulation. Conclusions: Fitting data by using the relxill model and the recently implemented reflection fraction, the geometry of a system can be constrained. The reflection fraction is independent of system parameters such as inclination and black hole spin. The reflection-fraction parameter was implemented with the name refl_frac in all flavours of the relxill model, and the non-relativistic reflection model xillver, in v0.4a (18 January 2016).
Directory of Open Access Journals (Sweden)
Feng Hou
2016-01-01
Full Text Available The triaxial creep tests of frozen silty clay mixed with sands were performed under different pressures, and the test results demonstrated that, under the low confining pressure, when the shear stress is lower than the long-term strength, the test specimen exhibits an attenuation creep because the strengthening effect is greater than the weakening effect. When the shear stress is higher than the long-term strength, the test specimen exhibits a nonattenuation creep due to the level of the strengthening and weakening effects change in different stages. As the confining pressure increases, the test specimens only exhibit an attenuation creep because of the enhancing strengthening effect. Both the hardening parameter and the damage variable were introduced to describe the strengthening and weakening effects, respectively, and a new creep constitutive model for frozen soil considering these effects was put forward based on the theory of elastoviscoplastic and the fractional derivative. Finally, the model parameters were analyzed and their determination method was also provided to reveal the trend of parameters according to the triaxial test results. The calculated results of the constitutive model show that the proposed model can describe the whole creep process of frozen soil well.
Modeling the Process of Particle Fractionation in a Pneumatic Centrifugal Apparatus
Shvab, A. V.; Evseev, N. S.
2016-07-01
The present investigation pertains to simulation of the aerodynamics of a two-phase nonisothermal twisted turbulent flow in the vortex chamber of an air-centrifugal classifier. The gas phase dynamics was determined with the aid of Reynolds equations whose closure was based on the Wilcox turbulence model. The motion of the solid phase of an ultradisperse powder is simulated by a combination of calculations of the motion trajectories of particular particles in a Lagrangian coordinate system. The influence of turbulent diffusion of particles and of other factors on the efficiency of the segregation of particle fractions by size is shown. The reliability of the results obtained is confirmed by test studies and by comparing numerical results with well-known experimental data.
Shock-Wave Heating Model for Chondrule Formation: Prevention of Isotopic Fractionation
Miura, H; Miura, Hitoshi; Nakamoto, Taishi
2006-01-01
Chondrules are considered to have much information on dust particles and processes in the solar nebula. It is naturally expected that protoplanetary disks observed in present star forming regions have similar dust particles and processes, so study of chondrule formation may provide us great information on the formation of the planetary systems. Evaporation during chondrule melting may have resulted in depletion of volatile elements in chondrules. However, no evidence for a large degree of heavy-isotope enrichment has been reported in chondrules. In order to meet this observed constraint, the rapid heating rate at temperatures below the silicate solidus is required to suppress the isotopic fractionation. We have developed a new shock-wave heating model taking into account the radiative transfer of the dust thermal continuum emission and the line emission of gas molecules and calculated the thermal history of chondrules. We have found that optically-thin shock waves for the thermal continuum emission from dust ...
Haptic feedback control in medical robots through fractional viscoelastic tissue model.
Kobayashi, Yo; Moreira, Pedro; Liu, Chao; Poignet, Philippe; Zemiti, Nabil; Fujie, Masakatsu G
2011-01-01
In this paper, we discuss the design of an adaptive control system for robot-assisted surgery with haptic feedback. Through a haptic device, the surgeon teleoperates the medical instrument in free space, fixed on a remote robot or in contact. In free space, the surgeon feels the motion of the robot. In the present paper, we evaluated the performance of the controller on viscoelastic tissue, modeled by a fractional derivative equation. In addition, we propose a novel controller using an integer formalization process that is suitable for these tissue properties. The simulation results suggested that performance, in terms of force control and telepresence, became poorer when the conventional controller, which was designed for elastic target object, was applied to the viscoelastic tissues. In contrast, the results suggested that our proposed controller maintained its performance on the viscoelastic tissues.
A novel crowd flow model based on linear fractional stable motion
Wei, Juan; Zhang, Hong; Wu, Zhenya; He, Junlin; Guo, Yangyong
2016-03-01
For the evacuation dynamics in indoor space, a novel crowd flow model is put forward based on Linear Fractional Stable Motion. Based on position attraction and queuing time, the calculation formula of movement probability is defined and the queuing time is depicted according to linear fractal stable movement. At last, an experiment and simulation platform can be used for performance analysis, studying deeply the relation among system evacuation time, crowd density and exit flow rate. It is concluded that the evacuation time and the exit flow rate have positive correlations with the crowd density, and when the exit width reaches to the threshold value, it will not effectively decrease the evacuation time by further increasing the exit width.
Alvarez-Silva, María Camila; Álvarez-Yela, Astrid Catalina; Gómez-Cano, Fabio; Zambrano, María Mercedes; Husserl, Johana; Danies, Giovanna; Restrepo, Silvia; González-Barrios, Andrés Fernando
2017-01-01
Soil microbial communities are responsible for a wide range of ecological processes and have an important economic impact in agriculture. Determining the metabolic processes performed by microbial communities is crucial for understanding and managing ecosystem properties. Metagenomic approaches allow the elucidation of the main metabolic processes that determine the performance of microbial communities under different environmental conditions and perturbations. Here we present the first compartmentalized metabolic reconstruction at a metagenomics scale of a microbial ecosystem. This systematic approach conceives a meta-organism without boundaries between individual organisms and allows the in silico evaluation of the effect of agricultural intervention on soils at a metagenomics level. To characterize the microbial ecosystems, topological properties, taxonomic and metabolic profiles, as well as a Flux Balance Analysis (FBA) were considered. Furthermore, topological and optimization algorithms were implemented to carry out the curation of the models, to ensure the continuity of the fluxes between the metabolic pathways, and to confirm the metabolite exchange between subcellular compartments. The proposed models provide specific information about ecosystems that are generally overlooked in non-compartmentalized or non-curated networks, like the influence of transport reactions in the metabolic processes, especially the important effect on mitochondrial processes, as well as provide more accurate results of the fluxes used to optimize the metabolic processes within the microbial community.
Density-driven free-convection model for isotopically fractionated geogenic nitrate in sabkha brine
Wood, Warren W.; Böhlke, John Karl
2017-01-01
Subsurface brines with high nitrate (NO3−) concentration are common in desert environments as atmospheric nitrogen is concentrated by the evaporation of precipitation and little nitrogen uptake. However, in addition to having an elevated mean concentration of ∼525 mg/L (as N), NO3− in the coastal sabkhas of Abu Dhabi is enriched in 15N (mean δ15N ∼17‰), which is an enigma. A NO3− solute mass balance analysis of the sabkha aquifer system suggests that more than 90% of the nitrogen is from local atmospheric deposition and the remainder from ascending brine. In contrast, isotopic mass balances based on Δ17O, δ15N, and δ18O data suggest approximately 80 to 90% of the NO3− could be from ascending brine. As the sabkha has essentially no soil, no vegetation, and no anthropogenic land or water use, we propose to resolve this apparent contradiction with a density-driven free-convection transport model. In this conceptual model, the density of rain is increased by solution of surface salts, transporting near-surface oxygenated NO3− bearing water downward where it encounters reducing conditions and mixes with oxygen-free ascending geologic brines. In this environment, NO3− is partially reduced to nitrogen gas (N2), thus enriching the remaining NO3− in heavy isotopes. The isotopically fractionated NO3− and nitrogen gas return to the near-surface oxidizing environment on the upward displacement leg of the free-convection cycle, where the nitrogen gas is released to the atmosphere and new NO3− is added to the system from atmospheric deposition. This recharge/recycling process has operated over many cycles in the 8000-year history of the shallow aquifer, progressively concentrating and isotopically fractionating the NO3−.
Institute of Scientific and Technical Information of China (English)
Yang Ning-Ning; Liu Chong-Xin; Wu Chao-Jun
2012-01-01
In this paper,the fractional-order mathematical model and the fractional-order state-space averaging model of the Buck-Boost converter in continuous conduction mode (CCM) are established based on the fractional calculus and the Adomian decomposition method.Some dynamical properties of the current-mode controlled fractional-order BuckBoost converter are analysed.The simulation is accomplished by using SIMULINK.Numerical simulations are presented to verify the analytical results and we find that bifurcation points will be moved backward as α and β vary.At the same time,the simulation results show that the converter goes through different routes to chaos.
Energy Technology Data Exchange (ETDEWEB)
Wennberg, Berit M.; Baumann, Pia; Gagliardi, Giovanna (Dept. of Medical Physics, Karolinska Univ. Hospital and the Karolinska Inst., Stockholm (Sweden)), e-mail: berit.wennberg@karolinska.se (and others)
2011-05-15
Background. In SBRT of lung tumours no established relationship between dose-volume parameters and the incidence of lung toxicity is found. The aim of this study is to compare the LQ model and the universal survival curve (USC) to calculate biologically equivalent doses in SBRT to see if this will improve knowledge on this relationship. Material and methods. Toxicity data on radiation pneumonitis grade 2 or more (RP2+) from 57 patients were used, 10.5% were diagnosed with RP2+. The lung DVHs were corrected for fractionation (LQ and USC) and analysed with the Lyman- Kutcher-Burman (LKB) model. In the LQ-correction alpha/beta = 3 Gy was used and the USC parameters used were: alpha/beta = 3 Gy, D{sub 0} = 1.0 Gy, n = 10, alpha 0.206 Gy-1 and d{sub T} = 5.8 Gy. In order to understand the relative contribution of different dose levels to the calculated NTCP the concept of fractional NTCP was used. This might give an insight to the questions of whether 'high doses to small volumes' or 'low doses to large volumes' are most important for lung toxicity. Results and Discussion. NTCP analysis with the LKB-model using parameters m = 0.4, D50 = 30 Gy resulted for the volume dependence parameter (n) with LQ correction n = 0.87 and with USC correction n = 0.71. Using parameters m = 0.3, D{sub 50} = 20 Gy n = 0.93 with LQ correction and n 0.83 with USC correction. In SBRT of lung tumours, NTCP modelling of lung toxicity comparing models (LQ,USC) for fractionation correction, shows that low dose contribute less and high dose more to the NTCP when using the USC-model. Comparing NTCP modelling of SBRT data and data from breast cancer, lung cancer and whole lung irradiation implies that the response of the lung is treatment specific. More data are however needed in order to have a more reliable modelling
Directory of Open Access Journals (Sweden)
Yu Zhang
2015-10-01
Full Text Available In this article, we begin with the non-homogeneous model for the non-differentiable heat flow, which is described using the local fractional vector calculus, from the first law of thermodynamics in fractal media point view. We employ the local fractional variational iteration algorithm II to solve the fractal heat equations. The obtained results show the non-differentiable behaviors of temperature fields of fractal heat flow defined on Cantor sets.
A generic interference model for uplink OFDMA networks with fractional frequency reuse
Tabassum, Hina
2014-03-01
Fractional frequency reuse (FFR) has emerged as a viable solution to coordinate and mitigate cochannel interference (CCI) in orthogonal frequency-division multiple-access (OFDMA)-based wireless cellular networks. The incurred CCI in cellular networks with FFR is highly uncertain and varies as a function of various design parameters that include the user scheduling schemes, the transmit power distribution among multiple allocated subcarriers, the partitioning of the cellular region into cell-edge and cell-center zones, the allocation of spectrum within each zone, and the channel reuse factors. To this end, this paper derives a generic analytical model for uplink CCI in multicarrier OFDMA networks with FFR. The derived expressions capture several network design parameters and are applicable to any composite fading-channel models. The accuracy of the derivations is verified via Monte Carlo simulations. Moreover, their usefulness is demonstrated by obtaining closed-form expressions for the Rayleigh fading-channel model and by evaluating important network performance metrics such as ergodic capacity. Numerical results provide useful system design guidelines and highlight the trade-offs associated with the deployment of FFR schemes in OFDMA-based networks. © 2013 IEEE.
Directory of Open Access Journals (Sweden)
Wei Wang
2013-01-01
Full Text Available The precipitation of wax/solid paraffin during production, transportation, and processing of crude oil is a serious problem. It is essential to have a reliable model to predict the wax appearance temperature and the amount of solid precipitated at different conditions. This paper presents a work to predict the solid precipitation based on solid-liquid equilibrium with regular solution-molecular thermodynamic theory and characterization of the crude oil plus fraction. Due to the differences of solubility characteristics between solid and liquid phase, the solubility parameters of liquid and solid phase are calculated by a modified model. The heat capacity change between solid and liquid phase is considered and estimated in the thermodynamic model. An activity coefficient based thermodynamic method combined with two characteristic methods to calculate wax precipitation in crude oil, especially heavy oil, has been tested with experimental data. The results show that the wax appearance temperature and the amount of weight precipitated can be predicted well with the experimental data.
The role of fractional calculus in modeling biological phenomena: A review
Ionescu, C.; Lopes, A.; Copot, D.; Machado, J. A. T.; Bates, J. H. T.
2017-10-01
This review provides the latest developments and trends in the application of fractional calculus (FC) in biomedicine and biology. Nature has often showed to follow rather simple rules that lead to the emergence of complex phenomena as a result. Of these, the paper addresses the properties in respiratory lung tissue, whose natural solutions arise from the midst of FC in the form of non-integer differ-integral solutions and non-integer parametric models. Diffusion of substances in human body, e.g. drug diffusion, is also a phenomena well known to be captured with such mathematical models. FC has been employed in neuroscience to characterize the generation of action potentials and spiking patters but also in characterizing bio-systems (e.g. vegetable tissues). Despite the natural complexity, biological systems belong as well to this class of systems, where FC has offered parsimonious yet accurate models. This review paper is a collection of results and literature reports who are essential to any versed engineer with multidisciplinary applications and bio-medical in particular.
The emergence of nonuniform spatiotemporal fractionation schemes within the standard BED model
Energy Technology Data Exchange (ETDEWEB)
Unkelbach, Jan, E-mail: junkelbach@mgh.harvard.edu; Papp, Dávid [Department of Radiation Oncology, Massachusetts General Hospital and Harvard Medical School, Boston, Massachusetts 02114 (United States)
2015-05-15
Purpose: Nonuniform spatiotemporal radiotherapy fractionation schemes, i.e., delivering distinct dose distributions in different fractions can potentially improve the therapeutic ratio. This is possible if the dose distributions are designed such that similar doses are delivered to normal tissues (exploit the fractionation effect) while hypofractionating subregions of the tumor. In this paper, the authors develop methodology for treatment planning with nonuniform fractions and demonstrate this concept in the context of intensity-modulated proton therapy (IMPT). Methods: Treatment planning is performed by simultaneously optimizing (possibly distinct) IMPT dose distributions for multiple fractions. This is achieved using objective and constraint functions evaluated for the cumulative biologically equivalent dose (BED) delivered at the end of treatment. BED based treatment planning formulations lead to nonconvex optimization problems, such that local gradient based algorithms require adequate starting positions to find good local optima. To that end, the authors develop a combinatorial algorithm to initialize the pencil beam intensities. Results: The concept of nonuniform spatiotemporal fractionation schemes is demonstrated for a spinal metastasis patient treated in two fractions using stereotactic body radiation therapy. The patient is treated with posterior oblique beams with the kidneys being located in the entrance region of the beam. It is shown that a nonuniform fractionation scheme that hypofractionates the central part of the tumor allows for a skin and kidney BED reduction of approximately 10%–20%. Conclusions: Nonuniform spatiotemporal fractionation schemes represent a novel approach to exploit fractionation effects that deserves further exploration for selected disease sites.
Subcellular compartmentation of glutathione in dicotyledonous plants
Müller, Maria
2010-01-01
This study describes the subcellular distribution of glutathione in roots and leaves of different plant species (Arabidopsis, Cucurbita, and Nicotiana). Glutathione is an important antioxidant and redox buffer which is involved in many metabolic processes including plant defense. Thus information on the subcellular distribution in these model plants especially during stress situations provides a deeper insight into compartment specific defense reactions and reflects the occurrence of compartment specific oxidative stress. With immunogold cytochemistry and computer-supported transmission electron microscopy glutathione could be localized in highest contents in mitochondria, followed by nuclei, peroxisomes, the cytosol, and plastids. Within chloroplasts and mitochondria, glutathione was restricted to the stroma and matrix, respectively, and did not occur in the lumen of cristae and thylakoids. Glutathione was also found at the membrane and in the lumen of the endoplasmic reticulum. It was also associated with the trans and cis side of dictyosomes. None or only very little glutathione was detected in vacuoles and the apoplast of mesophyll and root cells. Additionally, glutathione was found in all cell compartments of phloem vessels, vascular parenchyma cells (including vacuoles) but was absent in xylem vessels. The specificity of this method was supported by the reduction of glutathione labeling in all cell compartments (up to 98%) of the glutathione-deficient Arabidopsis thaliana rml1 mutant. Additionally, we found a similar distribution of glutathione in samples after conventional fixation and rapid microwave-supported fixation. Thus, indicating that a redistribution of glutathione does not occur during sample preparation. Summing up, this study gives a detailed insight into the subcellular distribution of glutathione in plants and presents solid evidence for the accuracy and specificity of the applied method. PMID:20186447
Estimation of pharmacokinetic parameters from non-compartmental variables using Microsoft Excel.
Dansirikul, Chantaratsamon; Choi, Malcolm; Duffull, Stephen B
2005-06-01
This study was conducted to develop a method, termed 'back analysis (BA)', for converting non-compartmental variables to compartment model dependent pharmacokinetic parameters for both one- and two-compartment models. A Microsoft Excel spreadsheet was implemented with the use of Solver and visual basic functions. The performance of the BA method in estimating pharmacokinetic parameter values was evaluated by comparing the parameter values obtained to a standard modelling software program, NONMEM, using simulated data. The results show that the BA method was reasonably precise and provided low bias in estimating fixed and random effect parameters for both one- and two-compartment models. The pharmacokinetic parameters estimated from the BA method were similar to those of NONMEM estimation.
Bentil, Sarah A; Dupaix, Rebecca B
2014-02-01
The ability of the fractional Zener constitutive model to predict the behavior of postmortem swine brain tissue was examined in this work. Understanding tissue behavior attributed to degradation is invaluable in many fields such as the forensic sciences or cases where only cadaveric tissue is available. To understand how material properties change with postmortem age, the fractional Zener model was considered as it includes parameters to describe brain stiffness and also the parameter α, which quantifies the viscoelasticity of a material. The relationship between the viscoelasticity described by α and tissue degradation was examined by fitting the model to data collected in a previous study (Bentil, 2013). This previous study subjected swine neural tissue to in vitro unconfined compression tests using four postmortem age groups (week). All samples were compressed to a strain level of 10% using two compressive rates: 1mm/min and 5mm/min. Statistical analysis was used as a tool to study the influence of the fractional Zener constants on factors such as tissue degradation and compressive rate. Application of the fractional Zener constitutive model to the experimental data showed that swine neural tissue becomes less stiff with increased postmortem age. The fractional Zener model was also able to capture the nonlinear viscoelastic features of the brain tissue at low strain rates. The results showed that the parameter α was better correlated with compressive rate than with postmortem age. © 2013 Published by Elsevier Ltd.
Can a Time Fractional-Derivative Model Capture Scale-Dependent Dispersion in Saturated Soils?
Garrard, Rhiannon M; Zhang, Yong; Wei, Song; Sun, HongGuang; Qian, Jiazhong
2017-07-10
Time nonlocal transport models such as the time fractional advection-dispersion equation (t-fADE) were proposed to capture well-documented non-Fickian dynamics for conservative solutes transport in heterogeneous media, with the underlying assumption that the time nonlocality (which means that the current concentration change is affected by previous concentration load) embedded in the physical models can release the effective dispersion coefficient from scale dependency. This assumption, however, has never been systematically examined using real data. This study fills this historical knowledge gap by capturing non-Fickian transport (likely due to solute retention) documented in the literature (Huang et al. 1995) and observed in our laboratory from small to intermediate spatial scale using the promising, tempered t-fADE model. Fitting exercises show that the effective dispersion coefficient in the t-fADE, although differing subtly from the dispersion coefficient in the standard advection-dispersion equation, increases nonlinearly with the travel distance (varying from 0.5 to 12 m) for both heterogeneous and macroscopically homogeneous sand columns. Further analysis reveals that, while solute retention in relatively immobile zones can be efficiently captured by the time nonlocal parameters in the t-fADE, the motion-independent solute movement in the mobile zone is affected by the spatial evolution of local velocities in the host medium, resulting in a scale-dependent dispersion coefficient. The same result may be found for the other standard time nonlocal transport models that separate solute retention and jumps (i.e., displacement). Therefore, the t-fADE with a constant dispersion coefficient cannot capture scale-dependent dispersion in saturated porous media, challenging the application for stochastic hydrogeology methods in quantifying real-world, preasymptotic transport. Hence improvements on time nonlocal models using, for example, the novel subordination
Fractional-order elastic models of cartilage: A multi-scale approach
Magin, Richard L.; Royston, Thomas J.
2010-03-01
The objective of this research is to develop new quantitative methods to describe the elastic properties (e.g., shear modulus, viscosity) of biological tissues such as cartilage. Cartilage is a connective tissue that provides the lining for most of the joints in the body. Tissue histology of cartilage reveals a multi-scale architecture that spans a wide range from individual collagen and proteoglycan molecules to families of twisted macromolecular fibers and fibrils, and finally to a network of cells and extracellular matrix that form layers in the connective tissue. The principal cells in cartilage are chondrocytes that function at the microscopic scale by creating nano-scale networks of proteins whose biomechanical properties are ultimately expressed at the macroscopic scale in the tissue's viscoelasticity. The challenge for the bioengineer is to develop multi-scale modeling tools that predict the three-dimensional macro-scale mechanical performance of cartilage from micro-scale models. Magnetic resonance imaging (MRI) and MR elastography (MRE) provide a basis for developing such models based on the nondestructive biomechanical assessment of cartilage in vitro and in vivo. This approach, for example, uses MRI to visualize developing proto-cartilage structure, MRE to characterize the shear modulus of such structures, and fractional calculus to describe the dynamic behavior. Such models can be extended using hysteresis modeling to account for the non-linear nature of the tissue. These techniques extend the existing computational methods to predict stiffness and strength, to assess short versus long term load response, and to measure static versus dynamic response to mechanical loads over a wide range of frequencies (50-1500 Hz). In the future, such methods can perhaps be used to help identify early changes in regenerative connective tissue at the microscopic scale and to enable more effective diagnostic monitoring of the onset of disease.
DEFF Research Database (Denmark)
Nielsen, Joakim Refslund; Dellwik, Ebba; Hahmann, Andrea N.
2014-01-01
A method is presented for development of satellite green vegetation fraction (GVF) time series for use in the Weather Research and Forecasting (WRF) model. The GVF data is in the WRF model used to describe the temporal evolution of many land surface parameters, in addition to the evolution...
Tavakoli-Kakhki, Mahsan; Haeri, Mohammad
2011-07-01
Fractional order PI and PID controllers are the most common fractional order controllers used in practice. In this paper, a simple analytical method is proposed for tuning the parameters of these controllers. The proposed method is useful in designing fractional order PI and PID controllers for control of complicated fractional order systems. To achieve the goal, at first a reduction technique is presented for approximating complicated fractional order models. Then, based on the obtained reduced models some analytical rules are suggested to determine the parameters of fractional order PI and PID controllers. Finally, numerical results are given to show the efficiency of the proposed tuning algorithm.
DEFF Research Database (Denmark)
Jala, Ram Chandra Reddy; Guo, Zheng; Bjerring, Thomas;
2010-01-01
A multi-stage temperature-programmed fractionating crystallization process was carried out to examine the effects of the presence of stearic acid (SA), oleic acid (OA), and linoleic acid (LA) on the separation of elaidic acid (EA). The results showed that the efficiency of fractionating crystalli......A multi-stage temperature-programmed fractionating crystallization process was carried out to examine the effects of the presence of stearic acid (SA), oleic acid (OA), and linoleic acid (LA) on the separation of elaidic acid (EA). The results showed that the efficiency of fractionating...
Branovets, Jelena; Sepp, Mervi; Kotlyarova, Svetlana; Jepihhina, Natalja; Sokolova, Niina; Aksentijevic, Dunja; Lygate, Craig A; Neubauer, Stefan; Vendelin, Marko; Birkedal, Rikke
2013-08-15
Disruption of the creatine kinase (CK) system in hearts of CK-deficient mice leads to changes in the ultrastructure and regulation of mitochondrial respiration. We expected to see similar changes in creatine-deficient mice, which lack the enzyme guanidinoacetate methyltransferase (GAMT) to produce creatine. The aim of this study was to characterize the changes in cardiomyocyte mitochondrial organization, regulation of respiration, and intracellular compartmentation associated with GAMT deficiency. Three-dimensional mitochondrial organization was assessed by confocal microscopy. On populations of permeabilized cardiomyocytes, we recorded ADP and ATP kinetics of respiration, competition between mitochondria and pyruvate kinase for ADP produced by ATPases, ADP kinetics of endogenous pyruvate kinase, and ATP kinetics of ATPases. These data were analyzed by mathematical models to estimate intracellular compartmentation. Quantitative analysis of morphological and kinetic data as well as derived model fits showed no difference between GAMT-deficient and wild-type mice. We conclude that inactivation of the CK system by GAMT deficiency does not alter mitochondrial organization and intracellular compartmentation in relaxed cardiomyocytes. Thus, our results suggest that the healthy heart is able to preserve cardiac function at a basal level in the absence of CK-facilitated energy transfer without compromising intracellular organization and the regulation of mitochondrial energy homeostasis. This raises questions on the importance of the CK system as a spatial energy buffer in unstressed cardiomyocytes.
Energy Technology Data Exchange (ETDEWEB)
Minard, Kevin R.; Holtom, Gary R.; Kathmann, Loel E.; Majors, Paul D.; Thrall, Brian D.; Wind, Robert A.
2004-09-01
Apoptosis and necrosis is induced in monolayer cultures of Chinese hamster ovary cells using okadaic acid and hydrogen peroxide (H2O2) respectively, and the effect on water diffusion and compartmentalization is examined using pulsed-field-gradient (PFG) 1H-NMR and simultaneous confocal microscopy. In PFG experiments characterized by a fixed diffusion time (< 4.7 msec) and variable b-values (0-27,000 s/mm2) 1H-NMR data collected with untreated cells exhibits multi-exponential behavior. Analysis using a slow-exchange model reveals two distinct cellular water compartments with different apparent diffusion coefficients (0.56, 0.06 x 10-3 mm2/sec) and volume fractions (0.96, 0.04). During the first 12 hours of either necrosis or apoptosis the amount of water in the smallest compartment increases two-fold prior to significant changes in cell density or plasma membrane integrity. Over the same period water content in the largest compartment decreases by over a factor of two in apoptotic cells, in accordance with observed cell shrinkage, and changes little in necrotic counterparts where only slight swelling is evident. PFG 1H-NMR therefore serves as a sensitive indicator of early cell death in monolayer cultures and can distinguish apoptosis from necrosis. Measurements of restricted diffusion and water exchange are also presented to elucidate compartment origins and justify model assumptions.
Energy Technology Data Exchange (ETDEWEB)
Brossard, N.; Croset, M.; Lecerf, J.; Lagarde, M. [Institut National des Sciences Appliquees (INSA), 69 - Villeurbanne (France); Pachiaudi, C.; Normand, S.; Riou, J.P. [Faculte de Medecine, 69 - Lyon (France); Chirouze, V.; Tayot, J.L. [IMEDEX, 69 - Chaponost (France)
1994-12-31
In order to study the compartmental metabolism of the 22:6n-3 fatty acid, and particularly the role of the transport plasmatic forms for the tissue uptake (especially brain), a technique is developed using carbon 13 stable isotope and an isotopic mass spectrometry coupled to gaseous chromatography technique. This method has been validated in rat with docosahexaenoic acid enriched in {sup 13}C and esterified in triglycerides. The compartmental metabolism is monitored by measuring the variation of 22:6n-3 isotopic enrichment in the various lipoprotein lipidic fractions, in blood globules and in the brain. 1 fig., 1 tab., 12 refs.
DEFF Research Database (Denmark)
Manfredi, Simone; Tonini, Davide; Christensen, Thomas Højlund
2011-01-01
with composting (for “organics”) and incineration (for “recyclable paper”). This however requires high degree of control over gas and leachate emissions, high gas collection efficiency and extensive gas utilization at the landfill. For the other waste fractions, recycling and incineration are favourable, although......, by means of LCA-modelling, aims at comparing the environmental performance of three major management options (landfilling, recycling and incineration or composting) for a number of individual waste fractions. The landfilling option is here approached comprehensively, accounting for all technical...... quantification of the landfill impacts when comparing management options for selected waste fractions.Results from the life-cycle impact assessment (LCIA) show that the environmental performance estimated for landfilling with energy recovery of the fractions “organics” and “recyclable paper” is comparable...
Akram, Ghazala; Batool, Fiza
2017-05-01
The (G'/G) -expansion method is utilized for a reliable treatment of space-time fractional biological population model. The method has been applied in the sense of the Jumarie's modified Riemann-Liouville derivative. Three classes of exact traveling wave solutions, hyperbolic, trigonometric and rational solutions of the associated equation are characterized with some free parameters. A generalized fractional complex transform is applied to convert the fractional equations to ordinary differential equations which subsequently resulted in number of exact solutions. It should be mentioned that the (G'/G) -expansion method is very effective and convenient for solving nonlinear partial differential equations of fractional order whose balancing number is a negative integer.
Akram, Ghazala; Batool, Fiza
2017-10-01
The (G'/G)-expansion method is utilized for a reliable treatment of space-time fractional biological population model. The method has been applied in the sense of the Jumarie's modified Riemann-Liouville derivative. Three classes of exact traveling wave solutions, hyperbolic, trigonometric and rational solutions of the associated equation are characterized with some free parameters. A generalized fractional complex transform is applied to convert the fractional equations to ordinary differential equations which subsequently resulted in number of exact solutions. It should be mentioned that the (G'/G)-expansion method is very effective and convenient for solving nonlinear partial differential equations of fractional order whose balancing number is a negative integer.
Directory of Open Access Journals (Sweden)
Pietro Bia
2016-01-01
Full Text Available The interaction of electromagnetic fields and biological tissues has become a topic of increasing interest for new research activities in bioelectrics, a new interdisciplinary field combining knowledge of electromagnetic theory, modeling, and simulations, physics, material science, cell biology, and medicine. In particular, the feasibility of pulsed electromagnetic fields in RF and mm-wave frequency range has been investigated with the objective to discover new noninvasive techniques in healthcare. The aim of this contribution is to illustrate a novel Finite-Difference Time-Domain (FDTD scheme for simulating electromagnetic pulse propagation in arbitrary dispersive biological media. The proposed method is based on the fractional calculus theory and a general series expansion of the permittivity function. The spatial dispersion effects are taken into account, too. The resulting formulation is explicit, it has a second-order accuracy, and the need for additional storage variables is minimal. The comparison between simulation results and those evaluated by using an analytical method based on the Fourier transformation demonstrates the accuracy and effectiveness of the developed FDTD model. Five numerical examples showing the plane wave propagation in a variety of dispersive media are examined.
Grünwald-Letnikov operators for fractional relaxation in Havriliak-Negami models
Garrappa, Roberto
2016-09-01
Several classes of differential and integral operators of non integer order have been proposed in the past to model systems exhibiting anomalous and hereditary properties. A wide range of complex and heterogeneous systems are described in terms of laws of Havriliak-Negami type involving a special fractional relaxation whose behavior in the time-domain can not be represented by any of the existing operators. In this work we introduce new integral and differential operators for the description of Havriliak-Negami models in the time-domain. In particular we propose a formulation of Grünwald-Letnikov type which turns out to be effective not only to provide a theoretical characterization of the operators associated to Havriliak-Negami systems but also for computational purposes. We study some properties of the new operators and, by means of some numerical experiments, we present their use in practical computation and we show the superiority with respect to the few other approaches previously proposed in literature.
The iDuo Bi-compartmental Knee Replacement: Our Early Experience.
Directory of Open Access Journals (Sweden)
Peter Jemmett
2016-12-01
Our early results suggest that the iDuo knee is a good option for those with isolated bi-compartmental disease and outcome scores are comparable with those reported for the BKA. This bi-compartmental design may bridge the gap between the uni-compartmental and total knee replacement. The choice between monolithic or modular designs remains in debate. We will continue to use this prosthesis for a carefully selected group of patients.
Mvogo, Alain; Tambue, Antoine; Ben-Bolie, Germain H.; Kofané, Timoléon C.
2016-10-01
We investigate localized wave solutions in a network of Hindmarsh-Rose neural model taking into account the long-range diffusive couplings. We show by a specific analytical technique that the model equations in the infrared limit (wave number k → 0) can be governed by the complex fractional Ginzburg-Landau (CFGL) equation. According to the stiffness of the system, we propose both the semi and the linearly implicit Riesz fractional finite-difference schemes to solve efficiently the CFGL equation. The obtained fractional numerical solutions for the nerve impulse reveal localized short impulse properties. We also show the equivalence between the continuous CFGL and the discrete Hindmarsh-Rose models for relatively large network.
Functional compartmentalization of the human superficial masseter muscle.
Directory of Open Access Journals (Sweden)
Rodrigo A Guzmán-Venegas
Full Text Available Some muscles have demonstrated a differential recruitment of their motor units in relation to their location and the nature of the motor task performed; this involves functional compartmentalization. There is little evidence that demonstrates the presence of a compartmentalization of the superficial masseter muscle during biting. The aim of this study was to describe the topographic distribution of the activity of the superficial masseter (SM muscle's motor units using high-density surface electromyography (EMGs at different bite force levels. Twenty healthy natural dentate participants (men: 4; women: 16; age 20±2 years; mass: 60±12 kg, height: 163±7 cm were selected from 316 volunteers and included in this study. Using a gnathodynamometer, bites from 20 to 100% maximum voluntary bite force (MVBF were randomly requested. Using a two-dimensional grid (four columns, six electrodes located on the dominant SM, EMGs in the anterior, middle-anterior, middle-posterior and posterior portions were simultaneously recorded. In bite ranges from 20 to 60% MVBF, the EMG activity was higher in the anterior than in the posterior portion (p-value = 0.001.The center of mass of the EMG activity was displaced towards the posterior part when bite force increased (p-value = 0.001. The topographic distribution of EMGs was more homogeneous at high levels of MVBF (p-value = 0.001. The results of this study show that the superficial masseter is organized into three functional compartments: an anterior, a middle and a posterior compartment. However, this compartmentalization is only seen at low levels of bite force (20-60% MVBF.
Functional compartmentalization of the human superficial masseter muscle.
Guzmán-Venegas, Rodrigo A; Biotti Picand, Jorge L; de la Rosa, Francisco J Berral
2015-01-01
Some muscles have demonstrated a differential recruitment of their motor units in relation to their location and the nature of the motor task performed; this involves functional compartmentalization. There is little evidence that demonstrates the presence of a compartmentalization of the superficial masseter muscle during biting. The aim of this study was to describe the topographic distribution of the activity of the superficial masseter (SM) muscle's motor units using high-density surface electromyography (EMGs) at different bite force levels. Twenty healthy natural dentate participants (men: 4; women: 16; age 20±2 years; mass: 60±12 kg, height: 163±7 cm) were selected from 316 volunteers and included in this study. Using a gnathodynamometer, bites from 20 to 100% maximum voluntary bite force (MVBF) were randomly requested. Using a two-dimensional grid (four columns, six electrodes) located on the dominant SM, EMGs in the anterior, middle-anterior, middle-posterior and posterior portions were simultaneously recorded. In bite ranges from 20 to 60% MVBF, the EMG activity was higher in the anterior than in the posterior portion (p-value = 0.001).The center of mass of the EMG activity was displaced towards the posterior part when bite force increased (p-value = 0.001). The topographic distribution of EMGs was more homogeneous at high levels of MVBF (p-value = 0.001). The results of this study show that the superficial masseter is organized into three functional compartments: an anterior, a middle and a posterior compartment. However, this compartmentalization is only seen at low levels of bite force (20-60% MVBF).
Energy Technology Data Exchange (ETDEWEB)
Cimpan, Emil
2004-09-15
water fraction. The model intended to employ existent formulas of the medium parameters worked out by Maxwell, Bruggeman and Ramu and Rao. However, to calculate the loss due to the induced eddy currents within the medium in the particular case of the oil continuous phase, other mathematical models expressing (equivalent) medium conductivity and permittivity were required and developed in this work. Although the resonance frequency of the coil was decreasing with increasing medium conductivity, this variation was not as significant as the variation of the coil impedance. This raised the question as to whether coils having the same self-resonance frequency in different media could be constructed. This was worth investigating because it could simplify the mathematical modelling. This was indeed the case and coils featuring approximately the same resonance frequency in different media were made. Concluding, the measuring device based on the HFMFT, which was constructed, investigated and described in this work can be developed into a practical instrument for monitoring the water fraction in multiphase flows. The overall measurement accuracy when using this technique would depend on the analytical models expressing the medium parameters and circumscribing the HFMFT itself. When the mathematical modelling of the HFMFT was finalised, it was understood that many other applications of the technique were also possible. Some of these applications, which might be of interest such as a conductivity meter and a three-component ratio meter, are briefly discussed.
Septins and the lateral compartmentalization of eukaryotic membranes.
Caudron, Fabrice; Barral, Yves
2009-04-01
Eukaryotic cells from neurons and epithelial cells to unicellular fungi frequently rely on cellular appendages such as axons, dendritic spines, cilia, and buds for their biology. The emergence and differentiation of these appendages depend on the formation of lateral diffusion barriers at their bases to insulate their membranes from the rest of the cell. Here, we review recent progress regarding the molecular mechanisms and functions of such barriers. This overview underlines the importance and conservation of septin-dependent diffusion barriers, which coordinately compartmentalize both plasmatic and internal membranes. We discuss their role in memory establishment and the control of cellular aging.
Intracellular compartmentalization of skeletal muscle glycogen metabolism and insulin signalling
DEFF Research Database (Denmark)
Prats Gavalda, Clara; Gomez-Cabello, Alba; Vigelsø Hansen, Andreas
2011-01-01
The interest in skeletal muscle metabolism and insulin signalling has increased exponentially in recent years as a consequence of their role in the development of type 2 diabetes mellitus. Despite this, the exact mechanisms involved in the regulation of skeletal muscle glycogen metabolism...... compartmentalization in the regulation of skeletal muscle glycogen metabolism and insulin signalling. As a result, a hypothetical regulatory mechanism is proposed by which cells could direct glycogen resynthesis towards different pools of glycogen particles depending on the metabolic needs. Furthermore, we discuss...... the role of skeletal muscle transverse tubules as potential modulators of tissue insulin responsiveness....
DEFF Research Database (Denmark)
Christensen, Bent Jesper; Kruse, Robinson; Sibbertsen, Philipp
We consider hypothesis testing in a general linear time series regression framework when the possibly fractional order of integration of the error term is unknown. We show that the approach suggested by Vogelsang (1998a) for the case of integer integration does not apply to the case of fractional...
An economical and environmentally friendly whey protein fractionation process was developed using supercritical carbon dioxide (sCO2) as an acid to produce enriched fractions of alpha-lactalbumin (alpha-La) and beta-lactoglobulin (beta-Lg) from a commercial whey protein isolate (WPI) containing 55% ...
Spinal cord tolerance to reirradiation with single-fraction radiosurgery: a swine model.
Medin, P.M.; Foster, R.D.; Kogel, A.J. van der; Sayre, J.W.; McBride, W.H.; Solberg, T.D.
2012-01-01
PURPOSE: This study was performed to determine swine spinal cord tolerance to single-fraction, partial-volume irradiation 1 year after receiving uniform irradiation to 30 Gy in 10 fractions. METHODS AND MATERIALS: A 10-cm length of spinal cord (C3-T1) was uniformly irradiated to 30 Gy in 10 consecut
DEFF Research Database (Denmark)
Hattel, Jesper Henri; Pryds, Nini
2006-01-01
In this paper, the relationship between the Gas to Melt Ratio (GMR) and the solid fraction of an evolving billet surface is investigated numerically. The basis for the analysis is a recently developed integrated procedure for modelling the entire spray forming process. This model includes...... is the summation of “local” droplet size distributions along the r-axis of the spray cone. The criterion for a successful process has been a predefined process window characterised by a desired solid fraction range at a certain distance from the atomizer. Inside this process window, the gas and melt flows have...
Experimental studies and model analysis of noble gas fractionation in porous media
Ding, Xin; Kennedy, B. Mack.; Evans, William C.; Stonestrom, David A.
2016-01-01
The noble gases, which are chemically inert under normal terrestrial conditions but vary systematically across a wide range of atomic mass and diffusivity, offer a multicomponent approach to investigating gas dynamics in unsaturated soil horizons, including transfer of gas between saturated zones, unsaturated zones, and the atmosphere. To evaluate the degree to which fractionation of noble gases in the presence of an advective–diffusive flux agrees with existing theory, a simple laboratory sand column experiment was conducted. Pure CO2 was injected at the base of the column, providing a series of constant CO2 fluxes through the column. At five fixed sampling depths within the system, samples were collected for CO2 and noble gas analyses, and ambient pressures were measured. Both the advection–diffusion and dusty gas models were used to simulate the behavior of CO2 and noble gases under the experimental conditions, and the simulations were compared with the measured depth-dependent concentration profiles of the gases. Given the relatively high permeability of the sand column (5 ´ 10−11 m2), Knudsen diffusion terms were small, and both the dusty gas model and the advection–diffusion model accurately predicted the concentration profiles of the CO2 and atmospheric noble gases across a range of CO2 flux from ?700 to 10,000 g m−2 d−1. The agreement between predicted and measured gas concentrations demonstrated that, when applied to natural systems, the multi-component capability provided by the noble gases can be exploited to constrain component and total gas fluxes of non-conserved (CO2) and conserved (noble gas) species or attributes of the soil column relevant to gas transport, such as porosity, tortuosity, and gas saturation.
Hiniker, Susan M; Modlin, Leslie A; Choi, Clara Y; Atalar, Banu; Seiger, Kira; Binkley, Michael S; Harris, Jeremy P; Liao, Yaping Joyce; Fischbein, Nancy; Wang, Lei; Ho, Anthony; Lo, Anthony; Chang, Steven D; Harsh, Griffith R; Gibbs, Iris C; Hancock, Steven L; Li, Gordon; Adler, John R; Soltys, Scott G
2016-04-01
Patients with tumors adjacent to the optic nerves and chiasm are frequently not candidates for single-fraction stereotactic radiosurgery (SRS) due to concern for radiation-induced optic neuropathy. However, these patients have been successfully treated with hypofractionated SRS over 2-5 days, though dose constraints have not yet been well defined. We reviewed the literature on optic tolerance to radiation and constructed a dose-response model for visual pathway tolerance to SRS delivered in 1-5 fractions. We analyzed optic nerve and chiasm dose-volume histogram (DVH) data from perioptic tumors, defined as those within 3mm of the optic nerves or chiasm, treated with SRS from 2000-2013 at our institution. Tumors with subsequent local progression were excluded from the primary analysis of vision outcome. A total of 262 evaluable cases (26 with malignant and 236 with benign tumors) with visual field and clinical outcomes were analyzed. Median patient follow-up was 37 months (range: 2-142 months). The median number of fractions was 3 (1 fraction n = 47, 2 fraction n = 28, 3 fraction n = 111, 4 fraction n = 10, and 5 fraction n = 66); doses were converted to 3-fraction equivalent doses with the linear quadratic model using α/β = 2Gy prior to modeling. Optic structure dose parameters analyzed included Dmin, Dmedian, Dmean, Dmax, V30Gy, V25Gy, V20Gy, V15Gy, V10Gy, V5Gy, D50%, D10%, D5%, D1%, D1cc, D0.50cc, D0.25cc, D0.20cc, D0.10cc, D0.05cc, D0.03cc. From the plan DVHs, a maximum-likelihood parameter fitting of the probit dose-response model was performed using DVH Evaluator software. The 68% CIs, corresponding to one standard deviation, were calculated using the profile likelihood method. Of the 262 analyzed, 2 (0.8%) patients experienced common terminology criteria for adverse events grade 4 vision loss in one eye, defined as vision of 20/200 or worse in the affected eye. One of these patients had received 2 previous courses of radiotherapy to the optic structures
Wilms, Matthias; Werner, René; Yamamoto, Tokihiro; Handels, Heinz; Ehrhardt, Jan
2017-06-26
Correspondence modelling between low-dimensional breathing signals and internal organ motion is a prerequisite for application of advanced techniques in radiotherapy of moving targets. Patient-specific correspondence models can, for example, be built prior to treatment based on a planning 4D CT and simultaneously acquired breathing signals. Reliability of pre-treatment-built models depends, however, on the degree of patient-specific inter-fraction motion variations. This study investigates whether motion estimation accuracy in the presence of inter-fraction motion variations can be improved using correspondence models that incorporate motion information from different patients. The underlying assumption is that inter-patient motion variations resemble patient-specific inter-fraction motion variations for subpopulations of patients with similar breathing characteristics. The hypothesis is tested by integrating a sparse manifold clustering approach into a regression-based correspondence modelling framework that allows for automated identification of patient subpopulations. The evaluation is based on a total of 73 lung 4D CT data sets, including two cohorts of patients with repeat 4D CT scans (cohort 1: 14 patients; cohort 2: ten patients). The results are consistent for both cohorts: The subpopulation-based modelling approach outperforms general population modelling (models built on all data sets available) as well as pre-treatment-built models trained on only the patient-specific motion information. The results thereby support the hypothesis and illustrate the potential of subpopulation-based correspondence modelling.
Free vibrations of a taut cable with a general viscoelastic damper modeled by fractional derivatives
Sun, Limin; Chen, Lin
2015-01-01
This study extends dynamic understanding of a taut cable with a viscous damper at arbitrary location to that with a general linear viscoelastic (VE) damper portrayed by a five-parameter fractional derivative model (FDM). The FDM is able to describe a generalized relationship between force and deformation of viscoelastic dampers (material) in a wide frequency range, which can simulate a practical damper including its support condition or a secondary tie between neighboring cables. Free vibrations of the passively controlled cable system have then been formulated analytically through complex modal analysis. For the restricted case that the FDM is installed close to one cable anchorage, asymptotic solutions for the system complex frequency and modal damping are presented; explicit formulas have also been derived to determine the maximal attainable damping and corresponding optimum FDM parameters, based on which effects of frequency-dependent damper properties are appreciated. Considering the FDM located at arbitrary location, the three distinct regimes of frequency evolutions observed for a cable with a viscous damper have been generalized to that with a VE damper; also, new characteristics of the regime diagram and the frequency evolution in each regime are observed.
Directory of Open Access Journals (Sweden)
Liang Cui
2015-07-01
Full Text Available Irrigation water management is crucial for agricultural production and livelihood security in many regions and countries throughout the world. In this study, a two-stage stochastic fractional programming (TSFP method is developed for planning an agricultural water resources management system under uncertainty. TSFP can provide an effective linkage between conflicting economic benefits and the associated penalties; it can also balance conflicting objectives and maximize the system marginal benefit with per unit of input under uncertainty. The developed TSFP method is applied to a real case of agricultural water resources management of the Zhangweinan River Basin China, which is one of the main food and cotton producing regions in north China and faces serious water shortage. The results demonstrate that the TSFP model is advantageous in balancing conflicting objectives and reflecting complicated relationships among multiple system factors. Results also indicate that, under the optimized irrigation target, the optimized water allocation rate of Minyou Channel and Zhangnan Channel are 57.3% and 42.7%, respectively, which adapts the changes in the actual agricultural water resources management problem. Compared with the inexact two-stage water management (ITSP method, TSFP could more effectively address the sustainable water management problem, provide more information regarding tradeoffs between multiple input factors and system benefits, and help the water managers maintain sustainable water resources development of the Zhangweinan River Basin.
Fractional derivative and hereditary combined model for memory effects on flexible polyurethane foam
Elfarhani, Makram; Jarraya, Abdessalem; Abid, Said; Haddar, Mohamed
2016-06-01
In a quasi-static regime with cyclic loading, the force-displacement curve of flexible polyurethane exhibits complicated behavior: nonlinearity, visco-elasticity, hysteresis, residual force, etc. Beside nonlinearity and visco-elasticity, this material displays high dependence on the displacement rate and past loading history. Its dependence on compression rate helps to appropriately identify the force-displacement curve. Based on the new curve identification, the overall foam response is assumed to be a composite of a nonlinear elastic component and a visco-elastic component. The elastic component is expressed as a polynomial function in displacement, while the visco-elastic one is formulated according to the hereditary approach to represent the foam visco-elastic damping force during the loading phase and according to the fractional derivative approach during unloading to represent the visco-elastic residual force in the material. The focus of this study was to develop mathematical formulations and identification parameters to faithfully characterize the visco-elastic behavior of flexible polyurethane foam under multi-cycle compressive tests. A parameter calibration methodology based on the separation of the measurement data of each component force was established. This optimization process helps to avoid the parameter values admixture problem during the phase of numeric calculations of the same component force. The validity of the model results is checked according to the simulation accuracy, the physical significance of results and their agreement with the obtained force-displacement curve identification.
Pseudo Phase Plane and Fractional Calculus modeling of western global economic downturn
Tenreiro Machado, J. A.; Mata, Maria Eugénia
2015-05-01
This paper applies Pseudo Phase Plane (PPP) and Fractional Calculus (FC) mathematical tools for modeling world economies. A challenging global rivalry among the largest international economies began in the early 1970s, when the post-war prosperity declined. It went on, up to now. If some worrying threatens may exist actually in terms of possible ambitious military aggression, invasion, or hegemony, countries' PPP relative positions can tell something on the current global peaceful equilibrium. A global political downturn of the USA on global hegemony in favor of Asian partners is possible, but can still be not accomplished in the next decades. If the 1973 oil chock has represented the beginning of a long-run recession, the PPP analysis of the last four decades (1972-2012) does not conclude for other partners' global dominance (Russian, Brazil, Japan, and Germany) in reaching high degrees of similarity with the most developed world countries. The synergies of the proposed mathematical tools lead to a better understanding of the dynamics underlying world economies and point towards the estimation of future states based on the memory of each time series.
Abdulhameed, M.; Vieru, D.; Roslan, R.
2017-10-01
This paper investigates the electro-magneto-hydrodynamic flow of the non-Newtonian behavior of biofluids, with heat transfer, through a cylindrical microchannel. The fluid is acted by an arbitrary time-dependent pressure gradient, an external electric field and an external magnetic field. The governing equations are considered as fractional partial differential equations based on the Caputo-Fabrizio time-fractional derivatives without singular kernel. The usefulness of fractional calculus to study fluid flows or heat and mass transfer phenomena was proven. Several experimental measurements led to conclusion that, in such problems, the models described by fractional differential equations are more suitable. The most common time-fractional derivative used in Continuum Mechanics is Caputo derivative. However, two disadvantages appear when this derivative is used. First, the definition kernel is a singular function and, secondly, the analytical expressions of the problem solutions are expressed by generalized functions (Mittag-Leffler, Lorenzo-Hartley, Robotnov, etc.) which, generally, are not adequate to numerical calculations. The new time-fractional derivative Caputo-Fabrizio, without singular kernel, is more suitable to solve various theoretical and practical problems which involve fractional differential equations. Using the Caputo-Fabrizio derivative, calculations are simpler and, the obtained solutions are expressed by elementary functions. Analytical solutions of the biofluid velocity and thermal transport are obtained by means of the Laplace and finite Hankel transforms. The influence of the fractional parameter, Eckert number and Joule heating parameter on the biofluid velocity and thermal transport are numerically analyzed and graphic presented. This fact can be an important in Biochip technology, thus making it possible to use this analysis technique extremely effective to control bioliquid samples of nanovolumes in microfluidic devices used for biological
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Jorge A. Orrego-Ruiz
2014-06-01
Full Text Available In this work, prediction models of Saturates, Aromatics, Resins and Asphaltenes fractions (SARA from thirty-seven vacuum residues of representative Colombian crudes and eighteen fractions of molecular distillation process were obtained. Mid-Infrared (MIR Attenuated Total Reflection (ATR spectroscopy in combination with partial least squares (PLS regression analysis was used to estimate accurately SARA analysis in these kind of samples. Calibration coefficients of prediction models were for saturates, aromatics, resins and asphaltenes fractions, 0.99, 0.96, 0.97 and 0.99, respectively. This methodology permits to control the molecular distillation process since small differences in chemical composition can be detected. Total time elapsed to give the SARA analysis per sample is 10 minutes.
Stevens, Adam H.; Patel, Manish R.; Lewis, Stephen R.
2017-01-01
We calculate transport timescales of martian methane and investigate the effect of potential release mechanisms into the atmosphere using a numerical model that includes both Fickian and Knudsen diffusion. The incorporation of Knudsen diffusion, which improves on a Fickian description of transport given the low permeability of the martian regolith, means that transport timescales from sources collocated with a putative martian water table are very long, up to several million martian years. Transport timescales also mean that any temporally varying source process, even in the shallow subsurface, would not result in a significant, observable variation in atmospheric methane concentration since changes resulting from small variations in flux would be rapidly obscured by atmospheric transport. This means that a short-lived 'plume' of methane, as detected by Mumma et al. (2009) and Webster et al. (2014), cannot be reconciled with diffusive transport from any reasonable depth and instead must invoke alternative processes such as fracturing or convective plumes. It is shown that transport through the martian regolith will cause a significant change in the isotopic composition of the gas, meaning that methane release from depth will produce an isotopic signature in the atmosphere that could be significantly different than the source composition. The deeper the source, the greater the change, and the change in methane composition in both δ13C and δD approaches -1000 ‰ for sources at a depth greater than around 1 km. This means that signatures of specific sources, in particular the methane produced by biogenesis that is generally depleted in 13CH4 and CH3D, could be obscured. We find that an abiogenic source of methane could therefore display an isotopic fractionation consistent with that expected for biogenic source processes if the source was at sufficient depth. The only unambiguous inference that can be made from measurements of methane isotopes alone is a measured
Institute of Scientific and Technical Information of China (English)
HE Hailun; SONG Jinbao; Patrick J. Lynett; LI Shuang
2009-01-01
Fractional energy losses of waves due to wave breaking when passing over a submerged bar are studied systematically using a modified numerical code that is based on the high-order Boussinesq-type equations. The model is first tested by the additional experimental data, and the model's capability of simulating the wave transformation over both gentle slope and steep slope is demonstrated. Then, the model's breaking index is replaced and tested. The new breaking index, which is optimized from the several breaking indices, is not sensitive to the spatial grid length and includes the bottom slopes. Numerical tests show that the modified model with the new breaking index is more stable and efficient for the shallow-water wave breaking. Finally, the modified model is used to study the fractional energy losses for the regular waves propagating and breaking over a submerged bar. Our results have revealed that how the nonlinearity and the dispersion of the incident waves as well as the dimensionless bar height (normalized by water depth) dominate the fractional energy losses. It is also found that the bar slope (limited to gentle slopes that less than 1:10) and the dimensionless bar length (normalized by incident wave length) have negligible effects on the fractional energy losses.
Super-resolution Microscopy Reveals Compartmentalization of Peroxisomal Membrane Proteins.
Galiani, Silvia; Waithe, Dominic; Reglinski, Katharina; Cruz-Zaragoza, Luis Daniel; Garcia, Esther; Clausen, Mathias P; Schliebs, Wolfgang; Erdmann, Ralf; Eggeling, Christian
2016-08-12
Membrane-associated events during peroxisomal protein import processes play an essential role in peroxisome functionality. Many details of these processes are not known due to missing spatial resolution of technologies capable of investigating peroxisomes directly in the cell. Here, we present the use of super-resolution optical stimulated emission depletion microscopy to investigate with sub-60-nm resolution the heterogeneous spatial organization of the peroxisomal proteins PEX5, PEX14, and PEX11 around actively importing peroxisomes, showing distinct differences between these peroxins. Moreover, imported protein sterol carrier protein 2 (SCP2) occupies only a subregion of larger peroxisomes, highlighting the heterogeneous distribution of proteins even within the peroxisome. Finally, our data reveal subpopulations of peroxisomes showing only weak colocalization between PEX14 and PEX5 or PEX11 but at the same time a clear compartmentalized organization. This compartmentalization, which was less evident in cases of strong colocalization, indicates dynamic protein reorganization linked to changes occurring in the peroxisomes. Through the use of multicolor stimulated emission depletion microscopy, we have been able to characterize peroxisomes and their constituents to a yet unseen level of detail while maintaining a highly statistical approach, paving the way for equally complex biological studies in the future.
FE FORMULATION FOR THE VISCOELASTIC BODY MODELED BY FRACTIONAL CONSTITUTIVE LAW
Institute of Scientific and Technical Information of China (English)
Zhang Wei(张卫); Nobuyuki Shimizu
2001-01-01
This paper presents finite element (FE) fornulation of the viscoelastic materials described by fractional constitutive law. The time-domain threedimensional constitutive equation is constructed. The FE equations are set up by treating the fractional operator as a special case of the hereditary integration. The equations are solved by numerical integration method. The numerical algorithm de veloped by the authors for Liouville-Riemann's fractional derivative was adopted to formulate FE procedures and extended to solve the more general case of the hereditary integration. The numerical examples were given to show the correctness and effectiveness of the integration algorithm.
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G. I. Vasilieva
2010-01-01
Full Text Available The article presents experimental data on regulatory effect of neutrophilokine helper fractions on the macrophage (Mph functional activity in the course of antiplague immunity formation. It has revealed that these fractions content biologically active, low-molecular weight peptides. They stimulate Mph killing activity by increasing phagosome-lysosome fusion, thus boosting transformation of monocytes to Mph, and causing redistribution of macrophage subpopulations in the total cellular pool. The helper effect of neutrophilokine fractions upon functional activity of MPh is more pronounced during secondary immune response.
Institute of Scientific and Technical Information of China (English)
HUANG; Guanhua; HUANG; Quanzhong; ZHAN; Hongbin
2005-01-01
The newly developed Fractional Advection-Dispersion Equation (FADE), which is FADE was extended and used in this paper for modelling adsorbing contaminant transport by adding an adsorbing term. A parameter estimation method and its corresponding FORTRAN based program named FADEMain were developed on the basis of Nonlinear Least Square Algorithm and the analytical solution for one-dimensional FADE under the conditions of step input and steady state flow. Data sets of adsorbing contaminants Cd and NH4+-N transport in short homogeneous soil columns and conservative solute NaCI transport in a long homogeneous soil column, respectively were used to estimate the transport parameters both by FADEMain and the advection-dispersion equation (ADE) based program CXTFIT2.1. Results indicated that the concentration simulated by FADE agreed well with the measured data. Compared to the ADE model, FADE can provide better simulation for the concentration in the initial lower concentration part and the late higher concentration part of the breakthrough curves for both adsorbing contaminants. The dispersion coefficients for ADE were from 0.13 to 7.06 cm2/min, while the dispersion coefficients for FADE ranged from 0.119 to 3.05 cm1.856/min for NaCI transport in the long homogeneous soil column. We found that the dispersion coefficient of FADE increased with the transport distance, and the relationship between them can be quantified with an exponential function. Less scale-dependent was also found for the dispersion coefficient of FADE with respect to ADE.
Gerstenfeld, Edward P; Lavi, Nimrod; Bazan, Victor; Gojraty, Sattar; Kim, Steven J; Michele, John
2011-07-01
Complex fractionated atrial electrograms (CFEs) have been described as a target during atrial fibrillation (AF) ablation; however, the mechanism leading to CFEs is poorly understood. We used noncontact mapping in a canine model of AF to determine the activation patterns in areas of CFEs. Sustained AF was induced in 10 canines with 10-12 weeks of atrial tachy-pacing at 440 ppm. A roving mapping catheter and noncontact multielectrode array (MEA) were deployed in the left atrium (LA). NavX software was used to construct a contact bipolar CFE LA map. The MEA was then used to reconstruct wavefront propagation in proximity to CFE regions. Wavefront propagation was assessed during three separate recording segments for each site. There were 34 CFE regions identified (3.4/dog) and 102 noncontact CFE regional activation sequences studied. The CFE regions were stereotypically located at the junctions of (1) the left pulmonary vein (PV)/posterior LA, (2) right inferior PV/posterior LA, (3) right superior PV/anterior LA, and (4) the LA roof. The majority (47%) of CFE recordings were characterized by wavefront collision, usually between circulating LA wavefronts and entry/exit from the PVs. Thirty-eight (38%) CFE recordings were noted to be the central functional barrier of a reentrant wavefront. Ablation through CFE regions due to reentry led to AF termination and noninducibility in 3/5 animals. In this pacing-induced AF model, common causes of CFEs include: (1) wavefront collision, (2) conduction through channels of functional block, (3) reentry. The vast majority of these CFE regions were caused by wavefront collision rather than true "drivers" of AF. ©2011, The Authors. Journal compilation ©2011 Wiley Periodicals, Inc.
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Ruilan Dong
Full Text Available The objectives of this trial were to develop multiple linear regression (MLR models and three-layer Levenberg-Marquardt back propagation (BP3 neural network models using the Cornell Net Carbohydrate and Protein System (CNCPS carbohydrate fractions as dietary variables for predicting in vitro rumen volatile fatty acid (VFA production and further compare MLR and BP3 models. Two datasets were established for the trial, of which the first dataset containing 45 feed mixtures with concentrate/roughage ratios of 10∶90, 20∶80, 30∶70, 40∶60, and 50∶50 were used for establishing the models and the second dataset containing 10 feed mixtures with the same concentrate/roughage ratios with the first dataset were used for testing the models. The VFA production of feed samples was determined using an in vitro incubation technique. The CNCPS carbohydrate fractions (g, i.e. CA (sugars, CB1 (starch and pectin, CB2 (available cell wall of feed samples were calculated based on chemical analysis. The performance of MLR models and BP3 models were compared using a paired t-test, the determination coefficient (R2 and the root mean square prediction error (RMSPE between observed and predicted values. Statistical analysis indicated that VFA production (mmol was significantly correlated with CNCPS carbohydrate fractions (g CA, CB1, and CB2 in a multiple linear pattern. Compared with MLR models, BP3 models were more accurate in predicting acetate, propionate, and total VFA production while similar in predicting butyrate production. The trial indicated that both MLR and BP3 models were suitable for predicting in vitro rumen VFA production of feed mixtures using CNCPS carbohydrate fractions CA, CB1, and CB2 as input dietary variables while BP3 models showed greater accuracy for prediction.
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Kangning Xu
Full Text Available The loss and injury of neurons play an important role in the onset of various neurodegenerative diseases, while both microgliosis and astrocyte loss or dysfunction are significant causes of neuronal degeneration. Previous studies have suggested that an extract enriched panaxadiol saponins from ginseng has more neuroprotective potential than the total saponins of ginseng. The present study investigated whether a fraction of highly purified panaxadiol saponins (termed as Rb fraction was protective for both glia and neurons, especially GABAergic interneurons, against kainic acid (KA-induced excitotoxicity in rats. Rats received Rb fraction at 30 mg/kg (i.p., 40 mg/kg (i.p. or saline followed 40 min later by an intracerebroventricular injection of KA. Acute hippocampal injury was determined at 48 h after KA, and impairment of hippocampus-dependent learning and memory as well as delayed neuronal injury was determined 16 to 21 days later. KA injection produced significant acute hippocampal injuries, including GAD67-positive GABAergic interneuron loss in CA1, paralbumin (PV-positive GABAergic interneuron loss, pyramidal neuron degeneration and astrocyte damage accompanied with reactive microglia in both CA1 and CA3 regions of the hippocampus. There was also a delayed loss of GAD67-positive interneurons in CA1, CA3, hilus and dentate gyrus. Microgliosis also became more severe 21 days later. Accordingly, KA injection resulted in hippocampus-dependent spatial memory impairment. Interestingly, the pretreatment with Rb fraction at 30 or 40 mg/kg significantly protected the pyramidal neurons and GABAergic interneurons against KA-induced acute excitotoxicity and delayed injury. Rb fraction also prevented memory impairments and protected astrocytes from KA-induced acute excitotoxicity. Additionally, microglial activation, especially the delayed microgliosis, was inhibited by Rb fraction. Overall, this study demonstrated that Rb fraction protected both
Xu, Kangning; Zhang, Yufen; Wang, Yan; Ling, Peng; Xie, Xin; Jiang, Chenyao; Zhang, Zhizhen; Lian, Xiao-Yuan
2014-01-01
The loss and injury of neurons play an important role in the onset of various neurodegenerative diseases, while both microgliosis and astrocyte loss or dysfunction are significant causes of neuronal degeneration. Previous studies have suggested that an extract enriched panaxadiol saponins from ginseng has more neuroprotective potential than the total saponins of ginseng. The present study investigated whether a fraction of highly purified panaxadiol saponins (termed as Rb fraction) was protective for both glia and neurons, especially GABAergic interneurons, against kainic acid (KA)-induced excitotoxicity in rats. Rats received Rb fraction at 30 mg/kg (i.p.), 40 mg/kg (i.p. or saline followed 40 min later by an intracerebroventricular injection of KA. Acute hippocampal injury was determined at 48 h after KA, and impairment of hippocampus-dependent learning and memory as well as delayed neuronal injury was determined 16 to 21 days later. KA injection produced significant acute hippocampal injuries, including GAD67-positive GABAergic interneuron loss in CA1, paralbumin (PV)-positive GABAergic interneuron loss, pyramidal neuron degeneration and astrocyte damage accompanied with reactive microglia in both CA1 and CA3 regions of the hippocampus. There was also a delayed loss of GAD67-positive interneurons in CA1, CA3, hilus and dentate gyrus. Microgliosis also became more severe 21 days later. Accordingly, KA injection resulted in hippocampus-dependent spatial memory impairment. Interestingly, the pretreatment with Rb fraction at 30 or 40 mg/kg significantly protected the pyramidal neurons and GABAergic interneurons against KA-induced acute excitotoxicity and delayed injury. Rb fraction also prevented memory impairments and protected astrocytes from KA-induced acute excitotoxicity. Additionally, microglial activation, especially the delayed microgliosis, was inhibited by Rb fraction. Overall, this study demonstrated that Rb fraction protected both astrocytes and neurons
Shahbari, Juhaina Awawdeh; Peled, Irit
2015-01-01
This study investigates the effect of using a realistic situation with modeling characteristics in creating and resolving a cognitive conflict to promote understanding of a changing reference in fraction calculations. The study was conducted among 96 seventh graders divided into 2 experimental groups and 1 control group. The experimental groups…
Shahbari, Juhaina Awawdeh; Peled, Irit
2015-01-01
This study investigates the effect of using a realistic situation with modeling characteristics in creating and resolving a cognitive conflict to promote understanding of a changing reference in fraction calculations. The study was conducted among 96 seventh graders divided into 2 experimental groups and 1 control group. The experimental groups…
Davijani, Nafiseh Zare; Jahanfarnia, Gholamreza; Abharian, Amir Esmaeili
2017-01-01
One of the most important issues with respect to nuclear reactors is power control. In this study, we designed a fractional-order sliding mode controller based on a nonlinear fractional-order model of the reactor system in order to track the reference power trajectory and overcome uncertainties and external disturbances. Since not all of the variables in an operating reactor are measurable or specified in the control law, we propose a reduced-order fractional neutron point kinetic (ROFNPK) model based on measurable variables. In the design, we assume the differences between the approximated model and the real system is limited. We use the obtained model in the controller design process and use the Lyapunov method to perform a stability analysis of the closed-loop system. We simulate the proposed reduced-order fractional-order sliding mode controller (ROFOSMC) using Matlab/Simulink, and its performance is compared with that of a reduced order integer-order sliding mode controller (ROIOSMC). Our simulation results indicate an acceptable performance of the proposed approach in tracking the reference power trajectory with respect to ROIOSMC because of faster response of control effort signal and the smaller tracking error. Moreover, the results illustrate the capability of the controller in rejection of the disturbance and the noise signals and the robustness of controller against uncertainty.
Isolated hepatocytes and liver S9 fractions have been used to collect in vitro biotransformation data for fish as a means of improving modeled estimates of chemical bioaccumulation. To date, however, there have been few direct comparisons of these two methods. In the present st...
Lechleitner, Franziska A.; Jamieson, Robert A.; McIntyre, Cameron; Baldini, Lisa M.; Baldini, James U. L.; Eglinton, Timothy I.
2015-04-01
Over the past two decades, speleothems have become one of the most versatile and promising archives for the study of past continental climate. Very precise absolute dating is often possible using the U-Th method, resulting in paleoclimate records of exceptional resolution and accuracy. However, not all speleothems are amenable to this dating method for a variety of reasons (e.g. low U concentrations, high detrital Th etc). This has lead researchers to exclude many otherwise suitable speleothems and cave sites from further investigation. 14C-dating of speleothems has so far not been applicable, due to the 'dead carbon' problem. As drip water percolates through the karst, dissolving CaCO3, a variable amount of 14C-dead carbon is added to the solution. This results in a temporally variable and site-specific reservoir effect, ultimately undermining the development of speleothem 14C -chronologies. However, a number of recent studies have shown a clear link between karst hydrology and associated proxies (e.g., Mg/Ca and δ13C) and this 'dead carbon fraction' (DCF). We take advantage of this relationship to model DCF and its changes using Mg/Ca, δ13C and 14C data from published speleothem records. Using one record for calibration purposes, we build a transfer function for the DCF in relation to δ13C and Mg/Ca, which we then apply to other 14C records. Initial model results are promising; we are able to reconstruct general long-term average DCF within uncertainties of the calculated DCF from the U-Th chronology. Large shifts in DCF related to hydrology are also often detected. In a second step, we apply the model to a speleothem from southern Poland, which so far could not be dated, due to very low U-concentrations. To construct a 14C chronology, the stalagmite was sampled at 5 mm intervals. CaCO3 powders were graphitized and measured by Accelerator Mass Spectrometry (MICADAS) at ETH Zurich. Additional high-resolution (0.1 mm/sample) 14C measurements were performed on
Khalansky, D.; Popova, E.; Gladyshev, P.; Dushanov, E.; Kholmurodov, Kh.
2014-12-01
Aqueous electrolyte solutions play an important role in many electrophysical and chemical processes in aerospace technology and industrial applications. As noncovalent interactions, the interactions between ions are crucially important for biomolecular structures as well (protein structure folding, molecular level processes followed by ionic pair correlations, the formation of flexible hydrate shells, and so on). Specifically, ions (cations and anions with the same valence charges) can form stable pairs if their sizes match. The formation of ionic pairs can substantially affect the thermodynamic stabilities of proteins in the alkali salts physiologically present in the human body. Research aims and problems impose severe demands on readjustments of the ionic force fields and potential parameters developed to describe aqueous solutions and electrolytic systems. Ionic solutions and their interaction with biomolecules have been observed for over 100 years [1], but the behavior of such solutions remains poorly studied today. New data obtained in this work deals with parameterization strategies and adjustments for the ionic force fields of the alkali cations and halide anions that should be helpful in biomolecular research. Using molecular dynamics (MD) models, four electrolytic systems (HCl-H2O, LiCl-H2O, NaCl-H2O, and KCl-H2O) are investigated as binary mixtures of water and cations and anions, respectively. The intermolecular interaction parameters are varied for two of the four model electrolytes (HCl-H2O and NaCl-H2O) to simulate the possibility of different ionic shells forming during interaction with water. It is found that varying the potential parameters strongly affects the dynamic and structural characteristics of electrolyte systems. MD simulations are performed in the temperature range of 300 to 600 K with a step of 50 K. MD simulations for all electrolyte models (HCl-H2O, LiCl-H2O, NaCl-H2O, KCl-H2O) are also conducted for different molar fractions of
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Bahatdin Daşbaşı
2017-06-01
Full Text Available In this study, it is described the general forms of fractional-order differential equations and asymtotic stability of their system’s equilibria. In addition that, the stability analysis of equilibrium points of the local bacterial infection model which is fractional-order differential equation system, is made. Results of this analysis are supported via numerical simulations drawn by datas obtained from literature for mycobacterium tuberculosis and the antibiotics isoniazid (INH, rifampicin (RIF, streptomycin (SRT and pyrazinamide (PRZ used against this bacterial infection.
Energy Technology Data Exchange (ETDEWEB)
2015-01-01
The 2012 IECC has an airtightness requirement of 3 air changes per hour at 50 Pascals test pressure for both single family and multifamily construction in Climate Zones 3-8. Other programs (LEED, ASHRAE 189, ASHRAE 62.2) have similar or tighter compartmentalization requirements, thus driving the need for easier and more effective methods of compartmentalization in multifamily buildings.
Oost, J.; Hoekstra, Arjen Ysbert
2009-01-01
Compartmentalization of dike ring areas is currently seen as one of the promising options for managing or reducing the risk of flooding. Recently, several studies on the effectiveness of subdividing dike ring areas by means of compartmentalization dikes were published. These studies show that the
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Andrea Sorzia
2016-01-01
Full Text Available A tensile test until breakage and a creep and relaxation test on a polypropylene fibre are carried out and the resulting creep and stress relaxation curves are fit by a model adopting a fraction-exponential kernel in the viscoelastic operator. The models using fraction-exponential functions are simpler than the complex ones obtained from combination of dashpots and springs and, furthermore, are suitable for fitting experimental data with good approximation allowing, at the same time, obtaining inverse Laplace transform in closed form. Therefore, the viscoelastic response of polypropylene fibres can be modelled straightforwardly through analytical methods. Addition of polypropylene fibres greatly improves the tensile strength of composite materials with concrete matrix. The proposed analytical model can be employed for simulating the mechanical behaviour of composite materials with embedded viscoelastic fibres.
Das, Saptarshi
2014-01-01
In this paper, an incommensurate fractional order (FO) model has been proposed to generate ECG like waveforms. Earlier investigation of ECG like waveform generation is based on two identical Van-der Pol (VdP) family of oscillators which are coupled by time delays and gains. In this paper, we suitably modify the three state equations corresponding to the nonlinear cross-product of states, time delay coupling of the two oscillators and low-pass filtering, using the concept of fractional derivatives. Our results show that a wide variety of ECG like waveforms can be simulated from the proposed generalized models, characterizing heart conditions under different physiological conditions. Such generalization of the modelling of ECG waveforms may be useful to understand the physiological process behind ECG signal generation in normal and abnormal heart conditions. Along with the proposed FO models, an optimization based approach is also presented to estimate the VdP oscillator parameters for representing a realistic ...
Impact of Fractionation and Dose in a Multivariate Model for Radiation-Induced Chest Wall Pain
Energy Technology Data Exchange (ETDEWEB)
Din, Shaun U. [Department of Radiation Oncology, Memorial Sloan Kettering Cancer Center, New York, New York (United States); Williams, Eric L.; Jackson, Andrew [Department of Medical Physics, Memorial Sloan Kettering Cancer Center, New York, New York (United States); Rosenzweig, Kenneth E. [Department of Radiation Oncology, Mount Sinai Medical Center, New York, New York (United States); Wu, Abraham J.; Foster, Amanda [Department of Radiation Oncology, Memorial Sloan Kettering Cancer Center, New York, New York (United States); Yorke, Ellen D. [Department of Medical Physics, Memorial Sloan Kettering Cancer Center, New York, New York (United States); Rimner, Andreas, E-mail: rimnera@mskcc.org [Department of Radiation Oncology, Memorial Sloan Kettering Cancer Center, New York, New York (United States)
2015-10-01
Purpose: To determine the role of patient/tumor characteristics, radiation dose, and fractionation using the linear-quadratic (LQ) model to predict stereotactic body radiation therapy–induced grade ≥2 chest wall pain (CWP2) in a larger series and develop clinically useful constraints for patients treated with different fraction numbers. Methods and Materials: A total of 316 lung tumors in 295 patients were treated with stereotactic body radiation therapy in 3 to 5 fractions to 39 to 60 Gy. Absolute dose–absolute volume chest wall (CW) histograms were acquired. The raw dose-volume histograms (α/β = ∞ Gy) were converted via the LQ model to equivalent doses in 2-Gy fractions (normalized total dose, NTD) with α/β from 0 to 25 Gy in 0.1-Gy steps. The Cox proportional hazards (CPH) model was used in univariate and multivariate models to identify and assess CWP2 exposed to a given physical and NTD. Results: The median follow-up was 15.4 months, and the median time to development of CWP2 was 7.4 months. On a univariate CPH model, prescription dose, prescription dose per fraction, number of fractions, D83cc, distance of tumor to CW, and body mass index were all statistically significant for the development of CWP2. Linear-quadratic correction improved the CPH model significance over the physical dose. The best-fit α/β was 2.1 Gy, and the physical dose (α/β = ∞ Gy) was outside the upper 95% confidence limit. With α/β = 2.1 Gy, V{sub NTD99Gy} was most significant, with median V{sub NTD99Gy} = 31.5 cm{sup 3} (hazard ratio 3.87, P<.001). Conclusion: There were several predictive factors for the development of CWP2. The LQ-adjusted doses using the best-fit α/β = 2.1 Gy is a better predictor of CWP2 than the physical dose. To aid dosimetrists, we have calculated the physical dose equivalent corresponding to V{sub NTD99Gy} = 31.5 cm{sup 3} for the 3- to 5-fraction groups.
Wang, Xiao-Tian; Yan, Hai-Gang; Tang, Ming-Ming; Zhu, En-Hui
2010-02-01
A model for option pricing of fractional version of the Merton model with ‘Hurst exponent’ H being in [1/2,1) is established with transaction costs. In particular, for H∈(1/2,1) the minimal price Cmin(t,St) of an option under transaction costs is obtained, which displays that the timestep δt and the ‘Hurst exponent’ H play an important role in option pricing with transaction costs.
A survival model for fractionated radiotherapy with an application to prostate cancer
Energy Technology Data Exchange (ETDEWEB)
Zaider, Marco [Department of Medical Physics, Memorial Sloan-Kettering Cancer Center, New York, NY (United States)]. E-mail: Zaiderm@mskcc.org; Zelefsky, Michael J.; Leibel, Steven A. [Department of Radiation Oncology, Memorial Sloan-Kettering Cancer Center, New York, NY (United States); Hanin, Leonid G. [Department of Mathematics, Idaho State University, Pocatello, ID (United States); Tsodikov, Alexander D.; Yakovlev, Andrei Y. [Department of Oncological Sciences, Huntsman Cancer Institute, University of Utah, Salt Lake City, UT (United States)
2001-10-01
This paper explores the applicability of a mechanistic survival model, based on the distribution of clonogens surviving a course of fractionated radiation therapy, to clinical data on patients with prostate cancer. The study was carried out using data on 1100 patients with clinically localized prostate cancer who were treated with three-dimensional conformal radiation therapy. The patients were stratified by radiation dose (group 1: <67.5 Gy; group 2: 67.5-72.5 Gy; group 3: 72.5-77.5 Gy; group 4: 77.5-87.5 Gy) and prognosis category (favourable, intermediate and unfavourable as defined by pre-treatment PSA and Gleason score). A relapse was recorded when tumour recurrence was diagnosed or when three successive prostate specific antigen (PSA) elevations were observed from a post-treatment nadir PSA level. PSA relapse-free survival was used as the primary end point. The model, which is based on an iterated Yule process, is specified in terms of three parameters: the mean number of tumour clonogens that survive the treatment, the mean of the progression time of post-treatment tumour development and its standard deviation. The model parameters were estimated by the maximum likelihood method. The fact that the proposed model provides an excellent description both of the survivor function and of the hazard rate is prima facie evidence of the validity of the model because closeness of the two survivor functions (empirical and model-based) does not generally imply closeness of the corresponding hazard rates. The estimated cure probabilities for the favourable group are 0.80, 0.74 and 0.87 (for dose groups 1-3, respectively); for the intermediate group: 0.25, 0.51, 0.58 and 0.78 (for dose groups 1-4, respectively) and for the unfavourable group: 0.0, 0.27, 0.33 and 0.64 (for dose groups 1-4, respectively). The distribution of progression time to tumour relapse was found to be independent of prognosis group but dependent on dose. As the dose increases the mean progression
Animal-to-Human Extrapolation Using Compartmental Models
1991-01-01
capillary blood flow. In: Whipple. H. E,. et al., eds. Multi-corn- 2. Copenhaver . W. M.; Kelly, D. E.: Wood, R. L. Baileys textbook partment analysis...of tracer experiments. New York: New York Acad- of histology. 17th ed. Baltimore: The Williams & Wilkins Company; emy of Sciences ; 1972:92-105. (Ann
Tracking the weathering of basalts on Mars using lithium isotope fractionation models
Fairén, Alberto G.; Losa-Adams, Elisabeth; Gil-Lozano, Carolina; Gago-Duport, Luis; Uceda, Esther R.; Squyres, Steven W.; Rodríguez, J. Alexis P.; Davila, Alfonso F.; McKay, Christopher P.
2015-04-01
Lithium (Li), the lightest of the alkali elements, has geochemical properties that include high aqueous solubility (Li is the most fluid mobile element) and high relative abundance in basalt-forming minerals (values ranking between 0.2 and 12 ppm). Li isotopes are particularly subject to fractionation because the two stable isotopes of lithium—7Li and 6Li—have a large relative mass difference (˜15%) that results in significant fractionation between water and solid phases. The extent of Li isotope fractionation during aqueous alteration of basalt depends on the dissolution rate of primary minerals—the source of Li—and on the precipitation kinetics, leading to formation of secondary phases. Consequently, a detailed analysis of Li isotopic ratios in both solution and secondary mineral lattices could provide clues about past Martian weathering conditions, including weathering extent, temperature, pH, supersaturation, and evaporation rate of the initial solutions in contact with basalt rocks. In this paper, we discuss ways in which Martian aqueous processes could have lead to Li isotope fractionation. We show that Li isotopic data obtained by future exploration of Mars could be relevant to highlighting different processes of Li isotopic fractionation in the past, and therefore to understanding basalt weathering and environmental conditions early in the planet's history.
Directory of Open Access Journals (Sweden)
Qihua Tan
2011-01-01
Full Text Available Identifying the various gene expression response patterns is a challenging issue in expression microarray time-course experiments. Due to heterogeneity in the regulatory reaction among thousands of genes tested, it is impossible to manually characterize a parametric form for each of the time-course pattern in a gene by gene manner. We introduce a growth curve model with fractional polynomials to automatically capture the various time-dependent expression patterns and meanwhile efficiently handle missing values due to incomplete observations. For each gene, our procedure compares the performances among fractional polynomial models with power terms from a set of fixed values that offer a wide range of curve shapes and suggests a best fitting model. After a limited simulation study, the model has been applied to our human in vivo irritated epidermis data with missing observations to investigate time-dependent transcriptional responses to a chemical irritant. Our method was able to identify the various nonlinear time-course expression trajectories. The integration of growth curves with fractional polynomials provides a flexible way to model different time-course patterns together with model selection and significant gene identification strategies that can be applied in microarray-based time-course gene expression experiments with missing observations.
Del Bello, E.; Taddeucci, J.; De'Michieli Vitturi, M.; Scarlato, P.; Andronico, D.; Scollo, S.; Kueppers, U.
2015-12-01
We present the first report of experimental measurements of the enhanced settling velocity of volcanic particles as function of particle volume fraction. In order to investigate the differences in the aerodynamic behavior of ash particles when settling individually or in mass, we performed systematic large-scale ash settling experiments using natural basaltic and phonolitic ash. By releasing ash particles at different, controlled volumetric flow rates, in an unconstrained open space and at minimal air movement, we measured their terminal velocity, size, and particle volume fraction with a high-speed camera at 2000 fps. Enhanced settling velocities of individual particles increase with increasing particle volume fraction. This suggests that particle clustering during fallout may be one reason explaining larger than theoretical depletion rates of fine particles from volcanic ash clouds. We provide a quantitative empirical model that allows to calculate, from a given particle size and density, the enhanced velocity resulting from a given particle volume fraction. The proposed model has the potential to serve as a simple tool for the prediction of the terminal velocity of ash of an hypothetical distribution of ash of known particle size and volume fraction. This is of particular importance for advection-diffusion transport model of ash where generally a one-way coupling is adopted, considering only the flow effects on particles. To better quantify the importance of the enhanced settling velocity in ash dispersal, we finally introduced the new formulation in a Lagrangian model calculating for realistic eruptive conditions the resulting ash concentration in the atmosphere and on the ground.
Schwarcz, Attila; Bogner, Peter; Meric, Philippe; Correze, Jean-Loup; Berente, Zoltan; Pál, József; Gallyas, Ferenc; Doczi, Tamas; Gillet, Brigitte; Beloeil, Jean-Claude
2004-02-01
It is generally believed that the apparent diffusion coefficient (ADC) changes measured by diffusion-weighted imaging (DWI) in brain pathologies are related to alterations in the water compartments. The aim of this study was to elucidate the role of compartmentalization in DWI via biexponential analysis of the signal decay due to diffusion. DWI experiments were performed on mouse brain over an extended range of b-values (up to 10,000 mm(-2) s) under intact, global ischemic, and cold-injury conditions. DWI was additionally applied to centrifuged human erythrocyte samples with a negligible extracellular space. Biexponential signal decay was found to occur in the cortex of the intact mouse brain. During global ischemia, in addition to a drop in the ADC in both components, a shift from the volume fraction of the rapidly diffusing component to the slowly diffusing one was observed. In cold injury, the biexponential signal decay was still present despite the electron-microscopically validated disintegration of the membranes. The biexponential function was also applicable for fitting of the data obtained on erythrocyte samples. The results suggest that compartmentalization is not an essential feature of biexponential decay in diffusion experiments. Copyright 2004 Wiley-Liss, Inc.
Prass, Taiane S.; Bravo, Juan Martin; Clarke, Robin T.; Collischonn, Walter; Lopes, SíLvia R. C.
2012-05-01
The paper compares forecasts of mean monthly water levels up to six months ahead at Ladário, on the Upper Paraguay River, Brazil, estimated from two long-range dependence models. In one of them, the marked seasonal cycle was removed and a fractionally differenced model was fitted to the transformed series. In the other, a seasonal fractionally differenced model was fitted to water levels without transformation. Forecasts from both models for periods up to six months ahead were compared with forecasts given by simpler "short-range dependence" Box-Jenkins models, one fitted to the transformed series, the other a seasonal autoregressive moving average (ARMA) model. Estimates of parameters in the four models (two "long-range dependence", two "short-range dependence") were updated at six-monthly intervals over a 20 year period, and forecasts were compared using root mean square errors (rmse) between water-level forecasts and observed levels. As judged by rmse, performances of the two long-range dependence models, and of the ARMA (1,1) short-range dependence model, were very similar; all three out-performed the seasonal short-range dependence ARMA model. There was evidence that all models performed better during recession periods, than on the hydrograph rising limb.
A fractional model to describe the Brownian motion of particles and its analytical solution
Directory of Open Access Journals (Sweden)
Jing-Jing Yao
2015-12-01
Full Text Available In this article, we apply a relatively modified analytic iterative method for solving a time-fractional Fokker–Planck equation subject to given constraints. The utilized method is a numerical technique based on the generalization of residual error function and then applying the generalized Taylor series formula. This method can be used as an alternative to obtain analytic solutions of different types of fractional partial differential equations such as Fokker–Planck equation applied in mathematics, physics, and engineering. The solutions of our equation are calculated in the form of a rapidly convergent series with easily computable components. The validity, potentiality, and practical usefulness of the proposed method have been demonstrated by applying it to several numerical examples. The results reveal that the proposed methodology is very useful and simple in determination of solution of the Fokker–Planck equation of fractional order.
Apartment Compartmentalization With an Aerosol-Based Sealing Process
Energy Technology Data Exchange (ETDEWEB)
Maxwell, S. [Consortium for Advanced Residential Buildings, Norwalk, CT (United States); Berger, D. [Consortium for Advanced Residential Buildings, Norwalk, CT (United States); Harrington, C. [Consortium for Advanced Residential Buildings, Norwalk, CT (United States)
2015-03-01
Air sealing of building enclosures is a difficult and time-consuming process. Current methods in new construction require laborers to physically locate small and sometimes large holes in multiple assemblies and then manually seal each of them. The innovation demonstrated under this research study was the automated air sealing and compartmentalization of buildings through the use of an aerosolized sealant, developed by the Western Cooling Efficiency Center at University of California Davis. CARB sought to demonstrate this new technology application in a multifamily building in Queens, NY. The effectiveness of the sealing process was evaluated by three methods: air leakage testing of overall apartment before and after sealing, point-source testing of individual leaks, and pressure measurements in the walls of the target apartment during sealing.
Compartmentalization in penicillin G biosynthesis by Penicillium chrysogenum PQ-96.
Kurzątkowski, Wiesław; Staniszewska, Monika; Bondaryk, Małgorzata; Gębska-Kuczerowska, Anita
2014-01-01
The arrangement of organelles in the sub-apical productive non-growing vacuolated hyphal cells of the high- and the low-penicillin-pro- ducing strains Penicillium chrysogenum was compared using transmission electron microscopy. In the productive cells of the high-yielding strain the endoplasmic reticulum and the polyribosomes with associated peroxisomes are frequently arranged at the periphery of the cytoplasm and around the vacuoles. At the high activity of penicillin G biosynthesis the immuno-label of the cytosolic isopenicillin N synthase is concentrated at the polyribosomes arranged in the peripheral cytoplasm and along the tonoplast as well as around the peroxisomes. On the basis of the obtained results the compartmentalization of the pathway of penicillin G biosymthesis is discussed. The obtained results support the phenylacetic acid detoxification hypothesis of penicillin G biosynthesis.
Fractional Dynamics and Control
Machado, José; Luo, Albert
2012-01-01
Fractional Dynamics and Control provides a comprehensive overview of recent advances in the areas of nonlinear dynamics, vibration and control with analytical, numerical, and experimental results. This book provides an overview of recent discoveries in fractional control, delves into fractional variational principles and differential equations, and applies advanced techniques in fractional calculus to solving complicated mathematical and physical problems.Finally, this book also discusses the role that fractional order modeling can play in complex systems for engineering and science. Discusses how fractional dynamics and control can be used to solve nonlinear science and complexity issues Shows how fractional differential equations and models can be used to solve turbulence and wave equations in mechanics and gravity theories and Schrodinger’s equation Presents factional relaxation modeling of dielectric materials and wave equations for dielectrics Develops new methods for control and synchronization of...
A Spur-free Fractional-N Sigma-Delta PLL for GSM Applications: Linear Model and Simulations
DEFF Research Database (Denmark)
Cassia, Marco; Shah, Peter Jivan; Bruun, Erik
2003-01-01
A new PLL topology and a new simplified linear model are presented. The new ΣΔ fractional-N synthesizer presents no reference spurs and lowers the overall phase noise, thanks to the presence of a Sample/Hold block. With a new simulation methodology it is possible to perform very accurate simulati......A new PLL topology and a new simplified linear model are presented. The new ΣΔ fractional-N synthesizer presents no reference spurs and lowers the overall phase noise, thanks to the presence of a Sample/Hold block. With a new simulation methodology it is possible to perform very accurate...... simulations, whose results match closely those obtained with the linear PLL model developed....
Heart mitochondrial TTP synthesis and the compartmentalization of TMP.
Kamath, Vasudeva G; Hsiung, Chia-Heng; Lizenby, Zachary J; McKee, Edward E
2015-01-23
The primary pathway of TTP synthesis in the heart requires thymidine salvage by mitochondrial thymidine kinase 2 (TK2). However, the compartmentalization of this pathway and the transport of thymidine nucleotides are not well understood. We investigated the metabolism of [(3)H]thymidine or [(3)H]TMP as precursors of [(3)H]TTP in isolated intact or broken mitochondria from the rat heart. The results demonstrated that [(3)H]thymidine was readily metabolized by the mitochondrial salvage enzymes to TTP in intact mitochondria. The equivalent addition of [(3)H]TMP produced far less [(3)H]TTP than the amount observed with [(3)H]thymidine as the precursor. Using zidovudine to inhibit TK2, the synthesis of [(3)H]TTP from [(3)H]TMP was effectively blocked, demonstrating that synthesis of [(3)H]TTP from [(3)H]TMP arose solely from the dephosphorysynthase pathway that includes deoxyuridine triphosphatelation of [(3)H]TMP to [(3)H]thymidine. To determine the role of the membrane in TMP metabolism, mitochondrial membranes were disrupted by freezing and thawing. In broken mitochondria, [(3)H]thymidine was readily converted to [(3)H]TMP, but further phosphorylation was prevented even though the energy charge was well maintained by addition of oligomycin A, phosphocreatine, and creatine phosphokinase. The failure to synthesize TTP in broken mitochondria was not related to a loss of membrane potential or inhibition of the electron transport chain, as confirmed by addition of carbonyl cyanide 4-(trifluoromethoxy) phenylhydrazone and potassium cyanide, respectively, in intact mitochondria. In summary, these data, taken together, suggest that the thymidine salvage pathway is compartmentalized so that TMP kinase prefers TMP synthesized by TK2 over medium TMP and that this is disrupted in broken mitochondria.
2010-04-01
... 21 Food and Drugs 8 2010-04-01 2010-04-01 false Knee joint femorotibial (uni-compartmental) metal... Devices § 888.3535 Knee joint femorotibial (uni-compartmental) metal/polymer porous-coated uncemented prosthesis. (a) Identification. A knee joint femorotibial (uni-compartmental) metal/polymer...
Classifying CT Image Data Into Material Fractions by a Scale and Rotation Invariant Edge Model
Serlie, I.W.; Vos, F.M.; Truyen, R.; Post, F.H.; Van Vliet, L.J.
2007-01-01
A fully automated method is presented to classify 3-D CT data into material fractions. An analytical scale-invariant description relating the data value to derivatives around Gaussian blurred step edges—arch model—is applied to uniquely combine robustness to noise, global signal fluctuations, anisot
Wildschut, J.; Arentz, J.; Rasrendra, C. B.; Venderbosch, R. H.; Heeres, H. J.
2009-01-01
Fast pyrolysis oil can be upgraded by a catalytic hydrotreatment (250-400 degrees C, 100-200 bar) using heterogeneous catalysts such as Ru/C to hydrocarbon-like products that can serve as liquid transportation fuels. Insight into the complex reaction pathways of the various component fractions durin
Wave equation for generalized Zener model containing complex order fractional derivatives
Atanacković, Teodor M.; Janev, Marko; Konjik, Sanja; Pilipović, Stevan
2017-03-01
We study waves in a viscoelastic rod whose constitutive equation is of generalized Zener type that contains fractional derivatives of complex order. The restrictions following from the Second Law of Thermodynamics are derived. The initial boundary value problem for such materials is formulated and solution is presented in the form of convolution. Two specific examples are analyzed.
Wave equation for generalized Zener model containing complex order fractional derivatives
Atanacković, Teodor M.; Janev, Marko; Konjik, Sanja; Pilipović, Stevan
2017-01-01
We study waves in a viscoelastic rod whose constitutive equation is of generalized Zener type that contains fractional derivatives of complex order. The restrictions following from the Second Law of Thermodynamics are derived. The initial boundary value problem for such materials is formulated and solution is presented in the form of convolution. Two specific examples are analyzed.
Decomposition of fractional quantum Hall model states: product rule symmetries and approximations
Thomale, R.; Estienne, B.; Regnault, N.; Bernevig, B.A.
2011-01-01
We provide a detailed description of a product rule structure of the monomial (Slater) expansion coefficients of bosonic (fermionic) fractional quantum Hall (FQH) states derived recently, which we now extend to spin-singlet states. We show that the Haldane-Rezayi spin-singlet state can be obtained
Spinal cord tolerance to single-fraction partial-volume irradiation: a swine model
Medin, P.M.; Foster, R.D.; Kogel, A.J. van der; Sayre, J.W.; McBride, W.H.; Solberg, T.D.
2011-01-01
PURPOSE: To determine the spinal cord tolerance to single-fraction, partial-volume irradiation in swine. METHODS AND MATERIALS: A 5-cm-long cervical segment was irradiated in 38-47-week-old Yucatan minipigs using a dedicated, image-guided radiosurgery linear accelerator. The radiation was delivered
DEFF Research Database (Denmark)
Stegmann, Mikkel Bille; Pedersen, Dorthe
2005-01-01
Rapid and unsupervised quantitative analysis is of utmost importance to ensure clinical acceptance of many examinations using cardiac magnetic resonance imaging (MRI). We present a framework that aims at fulfilling these goals for the application of left ventricular ejection fraction estimation i...
DEFF Research Database (Denmark)
Cavaliere, Giuseppe; Nielsen, Morten Ørregaard; Taylor, Robert
We consider the problem of conducting estimation and inference on the parameters of univariate heteroskedastic fractionally integrated time series models. We first extend existing results in the literature, developed for conditional sum-of squares estimators in the context of parametric fractional...... time series models driven by conditionally homoskedastic shocks, to allow for conditional and unconditional heteroskedasticity both of a quite general and unknown form. Global consistency and asymptotic normality are shown to still obtain; however, the covariance matrix of the limiting distribution...... of the estimator now depends on nuisance parameters derived both from the weak dependence and heteroskedasticity present in the shocks. We then investigate classical methods of inference based on the Wald, likelihood ratio and Lagrange multiplier tests for linear hypotheses on either or both of the long and short...
Li, Jun-Bao
2012-09-01
This paper presents Gabor filter based optical image recognition using Fractional Power Polynomial model based Common Kernel Discriminant Locality Preserving Projection. This method tends to solve the nonlinear classification problem endured by optical image recognition owing to the complex illumination condition in practical applications, such as face recognition. The first step is to apply Gabor filter to extract desirable textural features characterized by spatial frequency, spatial locality and orientation selectivity to cope with the variations in illumination. In the second step we propose Class-wise Locality Preserving Projection through creating the nearest neighbor graph guided by the class labels for the textural features reduction. Finally we present Common Kernel Discriminant Vector with Fractional Power Polynomial model to reduce the dimensions of the textural features for recognition. For the performance evaluation on optical image recognition, we test the proposed method on a challenging optical image recognition problem, face recognition.
Directory of Open Access Journals (Sweden)
Youxin Luo
2013-07-01
Full Text Available Grey system theory is a scientific theory possessed with wide adaptability to study poor information. The construction method of the background value in multivariable grey model was analyzed. The trapezoid formula and extrapolation method using rational interpolation and numerical integration was proposed based on the theory of vector valued continued fractions. And a non-equidistant multivariable grey model MGRM(1,n was built through applying reciprocal accumulated generating operation. The model is suitable for building both equidistant and non-equidistant models, and it broadens the application range of the grey model and effectively increases both the fitting and the prediction precisions of the model. The applicability and the reliability of the model built were proven by real cases.
Karras, G; Billard, F; Lavorel, B; Siour, G; Hartmann, J -M; Faucher, O; Gershnabel, Erez; Prior, Yehiam; Averbukh, Ilya Sh
2016-01-01
We report the observation of fractional echoes in a double-pulse excited nonlinear system. Unlike standard echoes which appear periodically at delays which are integer multiple of the delay between the two exciting pulses, the fractional echoes appear at rational fractions of this delay. We discuss the mechanism leading to this phenomenon, and provide the first experimental demonstration of fractional echoes by measuring third harmonic generation in a thermal gas of CO2 molecules excited by a pair of femtosecond laser pulses.
Directory of Open Access Journals (Sweden)
Tatsuhiko Sato
Full Text Available We here propose a new model assembly for estimating the surviving fraction of cells irradiated with various types of ionizing radiation, considering both targeted and nontargeted effects in the same framework. The probability densities of specific energies in two scales, which are the cell nucleus and its substructure called a domain, were employed as the physical index for characterizing the radiation fields. In the model assembly, our previously established double stochastic microdosimetric kinetic (DSMK model was used to express the targeted effect, whereas a newly developed model was used to express the nontargeted effect. The radioresistance caused by overexpression of anti-apoptotic protein Bcl-2 known to frequently occur in human cancer was also considered by introducing the concept of the adaptive response in the DSMK model. The accuracy of the model assembly was examined by comparing the computationally and experimentally determined surviving fraction of Bcl-2 cells (Bcl-2 overexpressing HeLa cells and Neo cells (neomycin resistant gene-expressing HeLa cells irradiated with microbeam or broadbeam of energetic heavy ions, as well as the WI-38 normal human fibroblasts irradiated with X-ray microbeam. The model assembly reproduced very well the experimentally determined surviving fraction over a wide range of dose and linear energy transfer (LET values. Our newly established model assembly will be worth being incorporated into treatment planning systems for heavy-ion therapy, brachytherapy, and boron neutron capture therapy, given critical roles of the frequent Bcl-2 overexpression and the nontargeted effect in estimating therapeutic outcomes and harmful effects of such advanced therapeutic modalities.
Sato, Tatsuhiko; Hamada, Nobuyuki
2014-01-01
We here propose a new model assembly for estimating the surviving fraction of cells irradiated with various types of ionizing radiation, considering both targeted and nontargeted effects in the same framework. The probability densities of specific energies in two scales, which are the cell nucleus and its substructure called a domain, were employed as the physical index for characterizing the radiation fields. In the model assembly, our previously established double stochastic microdosimetric kinetic (DSMK) model was used to express the targeted effect, whereas a newly developed model was used to express the nontargeted effect. The radioresistance caused by overexpression of anti-apoptotic protein Bcl-2 known to frequently occur in human cancer was also considered by introducing the concept of the adaptive response in the DSMK model. The accuracy of the model assembly was examined by comparing the computationally and experimentally determined surviving fraction of Bcl-2 cells (Bcl-2 overexpressing HeLa cells) and Neo cells (neomycin resistant gene-expressing HeLa cells) irradiated with microbeam or broadbeam of energetic heavy ions, as well as the WI-38 normal human fibroblasts irradiated with X-ray microbeam. The model assembly reproduced very well the experimentally determined surviving fraction over a wide range of dose and linear energy transfer (LET) values. Our newly established model assembly will be worth being incorporated into treatment planning systems for heavy-ion therapy, brachytherapy, and boron neutron capture therapy, given critical roles of the frequent Bcl-2 overexpression and the nontargeted effect in estimating therapeutic outcomes and harmful effects of such advanced therapeutic modalities.
Phleps, Stefanie; Zibetti, Stefano; Budavári, Tamás
2013-01-01
The fraction of galaxies with red colours depends sensitively on environment, and on the way in which environment is measured. To distinguish competing theories for the quenching of star formation, a robust and complete description of environment is required, to be applied to a large sample of galaxies. The environment of galaxies can be described using the density field of neighbours on multiple scales - the multiscale density field. We are using the Millennium simulation and a simple HOD prescription which describes the multiscale density field of Sloan Digital Sky Survey DR7 galaxies to investigate the dependence of the fraction of red galaxies on the environment. Using a volume limited sample where we have sufficient galaxies in narrow density bins, we have more dynamic range in halo mass and density for satellite galaxies than for central galaxies. Therefore we model the red fraction of central galaxies as a constant while we use a functional form to describe the red fraction of satellites as a function ...
Verma, Neeraj; Singh, Anil P; Amresh, G; Sahu, P K; Rao, Ch V
2011-05-01
To evaluate the hepatoprotective potential of ethyl acetate fraction of Rhododendron arboreum (Family: Ericaceae) in Wistar rats against carbon tetrachloride (CCl(4))-induced liver damage in preventive and curative models. Fraction at a dose of 100, 200, and 400 mg/kg was administered orally once daily for 14 days in CCl(4)-treated groups (II, III, IV, V and VI). The serum levels of glutamic oxaloacetic transaminase (SGOT), glutamate pyruvate transaminase (SGPT), alkaline phosphatase (SALP), γ-glutamyltransferase (γ -GT), and bilirubin were estimated along with activities of glutathione S-transferase (GST), glutathione reductase, hepatic malondialdehyde formation, and glutathione content. The substantially elevated serum enzymatic activities of SGOT, SGPT, SALP, γ-GT, and bilirubin due to CCl(4) treatment were restored toward normal in a dose-dependent manner. Meanwhile, the decreased activities of GST and glutathione reductase were also restored toward normal. In addition, ethyl acetate fraction also significantly prevented the elevation of hepatic malondialdehyde formation and depletion of reduced glutathione content in the liver of CCl(4)-intoxicated rats in a dose-dependent manner. Silymarin used as standard reference also exhibited significant hepatoprotective activity on post-treatment against CCl(4)-induced hepatotoxicity in rats. The biochemical observations were supplemented with histopathological examination of rat liver sections. The results of this study strongly indicate that ethyl acetate fraction has a potent hepatoprotective action against CCl(4)-induced hepatic damage in rats.