Analysis of the deterministic and stochastic SIRS epidemic models with nonlinear incidence
Liu, Qun; Chen, Qingmei
2015-06-01
In this paper, the deterministic and stochastic SIRS epidemic models with nonlinear incidence are introduced and investigated. For deterministic system, the basic reproductive number R0 is obtained. Furthermore, if R0 ≤ 1, then the disease-free equilibrium is globally asymptotically stable and if R0 > 1, then there is a unique endemic equilibrium which is globally asymptotically stable. For stochastic system, to begin with, we verify that there is a unique global positive solution starting from the positive initial value. Then when R0 > 1, we prove that stochastic perturbations may lead the disease to extinction in scenarios where the deterministic system is persistent. When R0 ≤ 1, a result on fluctuation of the solution around the disease-free equilibrium of deterministic model is obtained under appropriate conditions. At last, if the intensity of the white noise is sufficiently small and R0 > 1, then there is a unique stationary distribution to stochastic system.
Deterministic nonlinear systems a short course
Anishchenko, Vadim S; Strelkova, Galina I
2014-01-01
This text is a short yet complete course on nonlinear dynamics of deterministic systems. Conceived as a modular set of 15 concise lectures it reflects the many years of teaching experience by the authors. The lectures treat in turn the fundamental aspects of the theory of dynamical systems, aspects of stability and bifurcations, the theory of deterministic chaos and attractor dimensions, as well as the elements of the theory of Poincare recurrences.Particular attention is paid to the analysis of the generation of periodic, quasiperiodic and chaotic self-sustained oscillations and to the issue of synchronization in such systems. This book is aimed at graduate students and non-specialist researchers with a background in physics, applied mathematics and engineering wishing to enter this exciting field of research.
Streamflow disaggregation: a nonlinear deterministic approach
Directory of Open Access Journals (Sweden)
B. Sivakumar
2004-01-01
Full Text Available This study introduces a nonlinear deterministic approach for streamflow disaggregation. According to this approach, the streamflow transformation process from one scale to another is treated as a nonlinear deterministic process, rather than a stochastic process as generally assumed. The approach follows two important steps: (1 reconstruction of the scalar (streamflow series in a multi-dimensional phase-space for representing the transformation dynamics; and (2 use of a local approximation (nearest neighbor method for disaggregation. The approach is employed for streamflow disaggregation in the Mississippi River basin, USA. Data of successively doubled resolutions between daily and 16 days (i.e. daily, 2-day, 4-day, 8-day, and 16-day are studied, and disaggregations are attempted only between successive resolutions (i.e. 2-day to daily, 4-day to 2-day, 8-day to 4-day, and 16-day to 8-day. Comparisons between the disaggregated values and the actual values reveal excellent agreements for all the cases studied, indicating the suitability of the approach for streamflow disaggregation. A further insight into the results reveals that the best results are, in general, achieved for low embedding dimensions (2 or 3 and small number of neighbors (less than 50, suggesting possible presence of nonlinear determinism in the underlying transformation process. A decrease in accuracy with increasing disaggregation scale is also observed, a possible implication of the existence of a scaling regime in streamflow.
Deterministic behavioural models for concurrency
DEFF Research Database (Denmark)
Sassone, Vladimiro; Nielsen, Mogens; Winskel, Glynn
1993-01-01
This paper offers three candidates for a deterministic, noninterleaving, behaviour model which generalizes Hoare traces to the noninterleaving situation. The three models are all proved equivalent in the rather strong sense of being equivalent as categories. The models are: deterministic labelled...
Deterministic aspects of nonlinear modulation instability
van Groesen, E; Karjanto, N
2011-01-01
Different from statistical considerations on stochastic wave fields, this paper aims to contribute to the understanding of (some of) the underlying physical phenomena that may give rise to the occurrence of extreme, rogue, waves. To that end a specific deterministic wavefield is investigated that develops extreme waves from a uniform background. For this explicitly described nonlinear extension of the Benjamin-Feir instability, the soliton on finite background of the NLS equation, the global down-stream evolving distortions, the time signal of the extreme waves, and the local evolution near the extreme position are investigated. As part of the search for conditions to obtain extreme waves, we show that the extreme wave has a specific optimization property for the physical energy, and comment on the possible validity for more realistic situations.
The human ECG nonlinear deterministic versus stochastic aspects
Kantz, H; Kantz, Holger; Schreiber, Thomas
1998-01-01
We discuss aspects of randomness and of determinism in electrocardiographic signals. In particular, we take a critical look at attempts to apply methods of nonlinear time series analysis derived from the theory of deterministic dynamical systems. We will argue that deterministic chaos is not a likely explanation for the short time variablity of the inter-beat interval times, except for certain pathologies. Conversely, densely sampled full ECG recordings possess properties typical of deterministic signals. In the latter case, methods of deterministic nonlinear time series analysis can yield new insights.
Modeling of deterministic chaotic systems
Energy Technology Data Exchange (ETDEWEB)
Lai, Y. [Department of Physics and Astronomy and Department of Mathematics, The University of Kansas, Lawrence, Kansas 66045 (United States); Grebogi, C. [Institute for Plasma Research, University of Maryland, College Park, Maryland 20742 (United States); Grebogi, C.; Kurths, J. [Department of Physics and Astrophysics, Universitaet Potsdam, Postfach 601553, D-14415 Potsdam (Germany)
1999-03-01
The success of deterministic modeling of a physical system relies on whether the solution of the model would approximate the dynamics of the actual system. When the system is chaotic, situations can arise where periodic orbits embedded in the chaotic set have distinct number of unstable directions and, as a consequence, no model of the system produces reasonably long trajectories that are realized by nature. We argue and present physical examples indicating that, in such a case, though the model is deterministic and low dimensional, statistical quantities can still be reliably computed. {copyright} {ital 1999} {ital The American Physical Society}
A deterministic width function model
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C. E. Puente
2003-01-01
Full Text Available Use of a deterministic fractal-multifractal (FM geometric method to model width functions of natural river networks, as derived distributions of simple multifractal measures via fractal interpolating functions, is reported. It is first demonstrated that the FM procedure may be used to simulate natural width functions, preserving their most relevant features like their overall shape and texture and their observed power-law scaling on their power spectra. It is then shown, via two natural river networks (Racoon and Brushy creeks in the United States, that the FM approach may also be used to closely approximate existing width functions.
Solute Transport in a Heterogeneous Aquifer: A Nonlinear Deterministic Dynamical Analysis
Sivakumar, B.; Harter, T.; Zhang, H.
2003-04-01
Stochastic approaches are widely used for modeling and prediction of uncertainty in groundwater flow and transport processes. An important reason for this is our belief that the dynamics of the seemingly complex and highly irregular subsurface processes are essentially random in nature. However, the discovery of nonlinear deterministic dynamical theory has revealed that random-looking behavior could also be the result of simple deterministic mechanisms influenced by only a few nonlinear interdependent variables. The purpose of the present study is to introduce this theory to subsurface solute transport process, in an attempt to investigate the possibility of understanding the transport dynamics in a much simpler, deterministic, manner. To this effect, salt transport process in a heterogeneous aquifer medium is studied. Specifically, time series of arrival time of salt particles are analyzed. These time series are obtained by integrating a geostatistical (transition probability/Markov chain) model with a groundwater flow model (MODFLOW) and a salt transport (Random Walk Particle) model. The (dynamical) behavior of the transport process (nonlinear deterministic or stochastic) is identified using standard statistical techniques (e.g. autocorrelation function, power spectrum) as well as specific nonlinear deterministic dynamical techniques (e.g. phase-space diagram, correlation dimension method). The sensitivity of the salt transport dynamical behavior to the hydrostratigraphic parameters (i.e. number, volume proportions, mean lengths, and juxtapositional tendencies of facies) used in the transition probability/Markov chain model is also studied. The results indicate that the salt transport process may exhibit very simple (i.e. deterministic) to very complex (i.e. stochastic) dynamical behavior, depending upon the above parameters (i.e. characteristics of the aquifer medium). Efforts towards verification and strengthening of the present results and prediction of salt
Deterministic quantum nonlinear optics with single atoms and virtual photons
Kockum, Anton Frisk; Miranowicz, Adam; Macrı, Vincenzo; Savasta, Salvatore; Nori, Franco
2017-06-01
We show how analogs of a large number of well-known nonlinear-optics phenomena can be realized with one or more two-level atoms coupled to one or more resonator modes. Through higher-order processes, where virtual photons are created and annihilated, an effective deterministic coupling between two states of such a system can be created. In this way, analogs of three-wave mixing, four-wave mixing, higher-harmonic and -subharmonic generation (i.e., up- and down-conversion), multiphoton absorption, parametric amplification, Raman and hyper-Raman scattering, the Kerr effect, and other nonlinear processes can be realized. In contrast to most conventional implementations of nonlinear optics, these analogs can reach unit efficiency, only use a minimal number of photons (they do not require any strong external drive), and do not require more than two atomic levels. The strength of the effective coupling in our proposed setups becomes weaker the more intermediate transition steps are needed. However, given the recent experimental progress in ultrastrong light-matter coupling and improvement of coherence times for engineered quantum systems, especially in the field of circuit quantum electrodynamics, we estimate that many of these nonlinear-optics analogs can be realized with currently available technology.
Directory of Open Access Journals (Sweden)
MANFREDI, P.
2014-11-01
Full Text Available This paper extends recent literature results concerning the statistical simulation of circuits affected by random electrical parameters by means of the polynomial chaos framework. With respect to previous implementations, based on the generation and simulation of augmented and deterministic circuit equivalents, the modeling is extended to generic and ?black-box? multi-terminal nonlinear subcircuits describing complex devices, like those found in integrated circuits. Moreover, based on recently-published works in this field, a more effective approach to generate the deterministic circuit equivalents is implemented, thus yielding more compact and efficient models for nonlinear components. The approach is fully compatible with commercial (e.g., SPICE-type circuit simulators and is thoroughly validated through the statistical analysis of a realistic interconnect structure with a 16-bit memory chip. The accuracy and the comparison against previous approaches are also carefully established.
A passive dynamic walking robot that has a deterministic nonlinear gait.
Kurz, Max J; Judkins, Timothy N; Arellano, Chris; Scott-Pandorf, Melissa
2008-01-01
There is a growing body of evidence that the step-to-step variations present in human walking are related to the biomechanics of the locomotive system. However, we still have limited understanding of what biomechanical variables influence the observed nonlinear gait variations. It is necessary to develop reliable models that closely resemble the nonlinear gait dynamics in order to advance our knowledge in this scientific field. Previously, Goswami et al. [1998. A study of the passive gait of a compass-like biped robot: symmetry and chaos. International Journal of Robotic Research 17(12)] and Garcia et al. [1998. The simplest walking model: stability, complexity, and scaling. Journal of Biomechanical Engineering 120(2), 281-288] have demonstrated that passive dynamic walking computer models can exhibit a cascade of bifurcations in their gait pattern that lead to a deterministic nonlinear gait pattern. These computer models suggest that the intrinsic mechanical dynamics may be at least partially responsible for the deterministic nonlinear gait pattern; however, this has not been shown for a physical walking robot. Here we use the largest Laypunov exponent and a surrogation analysis method to confirm and extend Garcia et al.'s and Goswami et al.'s original results to a physical passive dynamic walking robot. Experimental outcomes from our walking robot further support the notion that the deterministic nonlinear step-to-step variations present in gait may be partly governed by the intrinsic mechanical dynamics of the locomotive system. Furthermore the nonlinear analysis techniques used in this investigation offer novel methods for quantifying the nature of the step-to-step variations found in human and robotic gait.
Introducing Synchronisation in Deterministic Network Models
DEFF Research Database (Denmark)
Schiøler, Henrik; Jessen, Jan Jakob; Nielsen, Jens Frederik D.;
2006-01-01
The paper addresses performance analysis for distributed real time systems through deterministic network modelling. Its main contribution is the introduction and analysis of models for synchronisation between tasks and/or network elements. Typical patterns of synchronisation are presented leading....... The suggested models are intended for incorporation into an existing analysis tool a.k.a. CyNC based on the MATLAB/SimuLink framework for graphical system analysis and design....
Bayesian Uncertainty Analyses Via Deterministic Model
Krzysztofowicz, R.
2001-05-01
Rational decision-making requires that the total uncertainty about a variate of interest (a predictand) be quantified in terms of a probability distribution, conditional on all available information and knowledge. Suppose the state-of-knowledge is embodied in a deterministic model, which is imperfect and outputs only an estimate of the predictand. Fundamentals are presented of three Bayesian approaches to producing a probability distribution of the predictand via any deterministic model. The Bayesian Processor of Output (BPO) quantifies the total uncertainty in terms of a posterior distribution, conditional on model output. The Bayesian Processor of Ensemble (BPE) quantifies the total uncertainty in terms of a posterior distribution, conditional on an ensemble of model output. The Bayesian Forecasting System (BFS) decomposes the total uncertainty into input uncertainty and model uncertainty, which are characterized independently and then integrated into a predictive distribution.
Dynamic optimization deterministic and stochastic models
Hinderer, Karl; Stieglitz, Michael
2016-01-01
This book explores discrete-time dynamic optimization and provides a detailed introduction to both deterministic and stochastic models. Covering problems with finite and infinite horizon, as well as Markov renewal programs, Bayesian control models and partially observable processes, the book focuses on the precise modelling of applications in a variety of areas, including operations research, computer science, mathematics, statistics, engineering, economics and finance. Dynamic Optimization is a carefully presented textbook which starts with discrete-time deterministic dynamic optimization problems, providing readers with the tools for sequential decision-making, before proceeding to the more complicated stochastic models. The authors present complete and simple proofs and illustrate the main results with numerous examples and exercises (without solutions). With relevant material covered in four appendices, this book is completely self-contained.
Piecewise deterministic processes in biological models
Rudnicki, Ryszard
2017-01-01
This book presents a concise introduction to piecewise deterministic Markov processes (PDMPs), with particular emphasis on their applications to biological models. Further, it presents examples of biological phenomena, such as gene activity and population growth, where different types of PDMPs appear: continuous time Markov chains, deterministic processes with jumps, processes with switching dynamics, and point processes. Subsequent chapters present the necessary tools from the theory of stochastic processes and semigroups of linear operators, as well as theoretical results concerning the long-time behaviour of stochastic semigroups induced by PDMPs and their applications to biological models. As such, the book offers a valuable resource for mathematicians and biologists alike. The first group will find new biological models that lead to interesting and often new mathematical questions, while the second can observe how to include seemingly disparate biological processes into a unified mathematical theory, and...
Influence of Deterministic Attachments for Large Unifying Hybrid Network Model
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
Large unifying hybrid network model (LUHPM) introduced the deterministic mixing ratio fd on the basis of the harmonious unification hybrid preferential model, to describe the influence of deterministic attachment to the network topology characteristics,
Stochastic Modeling and Deterministic Limit of Catalytic Surface Processes
DEFF Research Database (Denmark)
Starke, Jens; Reichert, Christian; Eiswirth, Markus;
2007-01-01
of stochastic origin can be observed in experiments. The models include a new approach to the platinum phase transition, which allows for a unification of existing models for Pt(100) and Pt(110). The rich nonlinear dynamical behavior of the macroscopic reaction kinetics is investigated and shows good agreement......Three levels of modeling, microscopic, mesoscopic and macroscopic are discussed for the CO oxidation on low-index platinum single crystal surfaces. The introduced models on the microscopic and mesoscopic level are stochastic while the model on the macroscopic level is deterministic. It can...... with low pressure experiments. Furthermore, for intermediate pressures, noise-induced pattern formation, which has not been captured by earlier models, can be reproduced in stochastic simulations with the mesoscopic model....
Deterministic and stochastic evolution equations for fully dispersive and weakly nonlinear waves
DEFF Research Database (Denmark)
Eldeberky, Y.; Madsen, Per A.
1999-01-01
This paper presents a new and more accurate set of deterministic evolution equations for the propagation of fully dispersive, weakly nonlinear, irregular, multidirectional waves. The equations are derived directly from the Laplace equation with leading order nonlinearity in the surface boundary c...
Directory of Open Access Journals (Sweden)
Alessandro Boianelli
Full Text Available When grown on glucose and beta-glucosides, S. pneumoniae shows sequential use of sugars resulting in diauxic growth with variable time extent of the lag phase separating the biphasic growth curve. The pneumococcal beta-glucoside uptake locus containing the PTS transporter spr0276-82, is regulated by a multi-domain transcriptional regulator CelR. In this work, we address the contribution of phosphorylation of the phosphorylable cysteine in the EIIB domain of CelR to diauxic lag. Utilising site-directed mutagenesis of the phosphorylable amino acids in the EIIB and EIIA domains of CelR, we show that the EIIB domain activation is linked to the duration of the lag phase. Analysis of mutants for other PTS systems indicates that a second beta-glucoside PTS (spr0505, not able to support growth on cellobiose, is responsible for the lag during diauxic growth. A mathematical model of the process is devised together with a nonlinear identification procedure which provides model parameter estimates characterizing the single phases of bacterial growth. Parameter identification performed on data recorded in appropriate experiments on mutants allows for establishing a relationship between a specific model parameter, the EIIB domain and the time extent of the diauxic lag. The experimental results and the related insights provided by the mathematical model provide evidence that the conflicting activation of the CelR regulator is at the origin of the lag phase during sequential growth on glucose and cellobiose. This data is the first description of diauxic lag regulation involving two PTS and a multidomain regulator and could serve as a promising approach for studying the S. pneumoniae growth process on complex carbon sources as possibly encountered in the human host.
Chaos theory as a bridge between deterministic and stochastic views for hydrologic modeling
Sivakumar, B.
2009-04-01
Two modeling approaches are prevalent in hydrology: deterministic and stochastic. The deterministic approach may be supported on the basis of the ‘permanent' nature of the ocean-earth-atmosphere structure and the ‘cyclical' nature of mechanisms that take place within it. The stochastic approach may be favored because of the ‘highly irregular and complex nature' of hydrologic phenomena and our ‘limited ability to observe' the detailed variations. With these two contrasting concepts, asking the question whether hydrologic phenomena are better modeled using a deterministic approach or a stochastic approach is meaningless. In fact, for most (if not all) hydrologic phenomena, both the deterministic approach and the stochastic approach are complementary to each other. This may be supported by our observation of both ‘deterministic' and ‘random' nature of hydrologic phenomena at ‘one or more scales' in time and/or space; for instance, there exists a significant deterministic nature in river flow in the form of seasonality and annual cycle, whereas the interactions of the various mechanisms involved in the river flow phenomenon and their various degrees of nonlinearity bring randomness. It is reasonable, therefore, to argue that use of an integrated modeling approach that incorporates both the deterministic and the stochastic components will produce greater success compared to either a deterministic approach or a stochastic approach independently. This study discusses the role of chaos theory as a potential avenue to the formulation of an integrated deterministic-stochastic approach. Through presentation of its fundamental principles (nonlinear interdependence, hidden determinism and order, sensitivity to initial conditions) and their relevance in hydrologic systems, the study contends that chaos theory can serve as a bridge between the deterministic and stochastic ‘extreme' views and offer a ‘middle-ground' approach. Specific examples of chaos theory
Deterministically Driven Avalanche Models of Solar Flares
Strugarek, Antoine; Charbonneau, Paul; Joseph, Richard; Pirot, Dorian
2014-08-01
We develop and discuss the properties of a new class of lattice-based avalanche models of solar flares. These models are readily amenable to a relatively unambiguous physical interpretation in terms of slow twisting of a coronal loop. They share similarities with other avalanche models, such as the classical stick-slip self-organized critical model of earthquakes, in that they are driven globally by a fully deterministic energy-loading process. The model design leads to a systematic deficit of small-scale avalanches. In some portions of model space, mid-size and large avalanching behavior is scale-free, being characterized by event size distributions that have the form of power-laws with index values, which, in some parameter regimes, compare favorably to those inferred from solar EUV and X-ray flare data. For models using conservative or near-conservative redistribution rules, a population of large, quasiperiodic avalanches can also appear. Although without direct counterparts in the observational global statistics of flare energy release, this latter behavior may be relevant to recurrent flaring in individual coronal loops. This class of models could provide a basis for the prediction of large solar flares.
Deterministically Driven Avalanche Models of Solar Flares
Strugarek, Antoine; Joseph, Richard; Pirot, Dorian
2014-01-01
We develop and discuss the properties of a new class of lattice-based avalanche models of solar flares. These models are readily amenable to a relatively unambiguous physical interpretation in terms of slow twisting of a coronal loop. They share similarities with other avalanche models, such as the classical stick--slip self-organized critical model of earthquakes, in that they are driven globally by a fully deterministic energy loading process. The model design leads to a systematic deficit of small scale avalanches. In some portions of model space, mid-size and large avalanching behavior is scale-free, being characterized by event size distributions that have the form of power-laws with index values, which, in some parameter regimes, compare favorably to those inferred from solar EUV and X-ray flare data. For models using conservative or near-conservative redistribution rules, a population of large, quasiperiodic avalanches can also appear. Although without direct counterparts in the observational global st...
Analysis of deterministic cyclic gene regulatory network models with delays
Ahsen, Mehmet Eren; Niculescu, Silviu-Iulian
2015-01-01
This brief examines a deterministic, ODE-based model for gene regulatory networks (GRN) that incorporates nonlinearities and time-delayed feedback. An introductory chapter provides some insights into molecular biology and GRNs. The mathematical tools necessary for studying the GRN model are then reviewed, in particular Hill functions and Schwarzian derivatives. One chapter is devoted to the analysis of GRNs under negative feedback with time delays and a special case of a homogenous GRN is considered. Asymptotic stability analysis of GRNs under positive feedback is then considered in a separate chapter, in which conditions leading to bi-stability are derived. Graduate and advanced undergraduate students and researchers in control engineering, applied mathematics, systems biology and synthetic biology will find this brief to be a clear and concise introduction to the modeling and analysis of GRNs.
Use of deterministic models in sports and exercise biomechanics research.
Chow, John W; Knudson, Duane V
2011-09-01
A deterministic model is a modeling paradigm that determines the relationships between a movement outcome measure and the biomechanical factors that produce such a measure. This review provides an overview of the use of deterministic models in biomechanics research, a historical summary of this research, and an analysis of the advantages and disadvantages of using deterministic models. The deterministic model approach has been utilized in technique analysis over the last three decades, especially in swimming, athletics field events, and gymnastics. In addition to their applications in sports and exercise biomechanics, deterministic models have been applied successfully in research on selected motor skills. The advantage of the deterministic model approach is that it helps to avoid selecting performance or injury variables arbitrarily and to provide the necessary theoretical basis for examining the relative importance of various factors that influence the outcome of a movement task. Several disadvantages of deterministic models, such as the use of subjective measures for the performance outcome, were discussed. It is recommended that exercise and sports biomechanics scholars should consider using deterministic models to help identify meaningful dependent variables in their studies.
Nonlinear dynamic analysis of atomic force microscopy under deterministic and random excitation
Energy Technology Data Exchange (ETDEWEB)
Pishkenari, Hossein Nejat [Center of Excellence in Design, Robotics and Automation (CEDRA), School of Mechanical Engineering, Sharif University of Technology, Tehran (Iran, Islamic Republic of); Behzad, Mehdi [Center of Excellence in Design, Robotics and Automation (CEDRA), School of Mechanical Engineering, Sharif University of Technology, Tehran (Iran, Islamic Republic of)], E-mail: m_behzad@sharif.edu; Meghdari, Ali [Center of Excellence in Design, Robotics and Automation (CEDRA), School of Mechanical Engineering, Sharif University of Technology, Tehran (Iran, Islamic Republic of)
2008-08-15
The atomic force microscope (AFM) system has evolved into a useful tool for direct measurements of intermolecular forces with atomic-resolution characterization that can be employed in a broad spectrum of applications. This paper is devoted to the analysis of nonlinear behavior of amplitude modulation (AM) and frequency modulation (FM) modes of atomic force microscopy. For this, the microcantilever (which forms the basis for the operation of AFM) is modeled as a single mode approximation and the interaction between the sample and cantilever is derived from a van der Waals potential. Using perturbation methods such as averaging, and Fourier transform nonlinear equations of motion are analytically solved and the advantageous results are extracted from this nonlinear analysis. The results of the proposed techniques for AM-AFM, clearly depict the existence of two stable and one unstable (saddle) solutions for some of exciting parameters under deterministic vibration. The basin of attraction of two stable solutions is different and dependent on the exciting frequency. From this analysis the range of the frequency which will result in a unique periodic response can be obtained and used in practical experiments. Furthermore the analytical responses determined by perturbation techniques can be used to detect the parameter region where the chaotic motion is avoided. On the other hand for FM-AFM, the relation between frequency shift and the system parameters can be extracted and used for investigation of the system nonlinear behavior. The nonlinear behavior of the oscillating tip can easily explain the observed shift of frequency as a function of tip sample distance. Also in this paper we have investigated the AM-AFM system response under a random excitation. Using two different methods we have obtained the statistical properties of the tip motion. The results show that we can use the mean square value of tip motion to image the sample when the excitation signal is random.
The cointegrated vector autoregressive model with general deterministic terms
DEFF Research Database (Denmark)
Johansen, Søren; Nielsen, Morten Ørregaard
In the cointegrated vector autoregression (CVAR) literature, deterministic terms have until now been analyzed on a case-by-case, or as-needed basis. We give a comprehensive unified treatment of deterministic terms in the additive model X(t)= Z(t) + Y(t), where Z(t) belongs to a large class...
Traffic chaotic dynamics modeling and analysis of deterministic network
Wu, Weiqiang; Huang, Ning; Wu, Zhitao
2016-07-01
Network traffic is an important and direct acting factor of network reliability and performance. To understand the behaviors of network traffic, chaotic dynamics models were proposed and helped to analyze nondeterministic network a lot. The previous research thought that the chaotic dynamics behavior was caused by random factors, and the deterministic networks would not exhibit chaotic dynamics behavior because of lacking of random factors. In this paper, we first adopted chaos theory to analyze traffic data collected from a typical deterministic network testbed — avionics full duplex switched Ethernet (AFDX, a typical deterministic network) testbed, and found that the chaotic dynamics behavior also existed in deterministic network. Then in order to explore the chaos generating mechanism, we applied the mean field theory to construct the traffic dynamics equation (TDE) for deterministic network traffic modeling without any network random factors. Through studying the derived TDE, we proposed that chaotic dynamics was one of the nature properties of network traffic, and it also could be looked as the action effect of TDE control parameters. A network simulation was performed and the results verified that the network congestion resulted in the chaotic dynamics for a deterministic network, which was identical with expectation of TDE. Our research will be helpful to analyze the traffic complicated dynamics behavior for deterministic network and contribute to network reliability designing and analysis.
Deterministic operations research models and methods in linear optimization
Rader, David J
2013-01-01
Uniquely blends mathematical theory and algorithm design for understanding and modeling real-world problems Optimization modeling and algorithms are key components to problem-solving across various fields of research, from operations research and mathematics to computer science and engineering. Addressing the importance of the algorithm design process. Deterministic Operations Research focuses on the design of solution methods for both continuous and discrete linear optimization problems. The result is a clear-cut resource for understanding three cornerstones of deterministic operations resear
Deterministic Consistency: A Programming Model for Shared Memory Parallelism
Aviram, Amittai; Ford, Bryan
2009-01-01
The difficulty of developing reliable parallel software is generating interest in deterministic environments, where a given program and input can yield only one possible result. Languages or type systems can enforce determinism in new code, and runtime systems can impose synthetic schedules on legacy parallel code. To parallelize existing serial code, however, we would like a programming model that is naturally deterministic without language restrictions or artificial scheduling. We propose "...
Limiting Shapes for Deterministic Centrally Seeded Growth Models
Fey-den Boer, Anne; Redig, Frank
2007-01-01
We study the rotor router model and two deterministic sandpile models. For the rotor router model in ℤ d , Levine and Peres proved that the limiting shape of the growth cluster is a sphere. For the other two models, only bounds in dimension 2 are known. A unified approach for these models with a
Limiting Shapes for Deterministic Centrally Seeded Growth Models
Fey-den Boer, Anne; Redig, Frank
2007-01-01
We study the rotor router model and two deterministic sandpile models. For the rotor router model in ℤ d , Levine and Peres proved that the limiting shape of the growth cluster is a sphere. For the other two models, only bounds in dimension 2 are known. A unified approach for these models with a
Deterministic treatment of model error in geophysical data assimilation
Carrassi, Alberto
2015-01-01
This chapter describes a novel approach for the treatment of model error in geophysical data assimilation. In this method, model error is treated as a deterministic process fully correlated in time. This allows for the derivation of the evolution equations for the relevant moments of the model error statistics required in data assimilation procedures, along with an approximation suitable for application to large numerical models typical of environmental science. In this contribution we first derive the equations for the model error dynamics in the general case, and then for the particular situation of parametric error. We show how this deterministic description of the model error can be incorporated in sequential and variational data assimilation procedures. A numerical comparison with standard methods is given using low-order dynamical systems, prototypes of atmospheric circulation, and a realistic soil model. The deterministic approach proves to be very competitive with only minor additional computational c...
Deterministic combination of numerical and physical coastal wave models
DEFF Research Database (Denmark)
Zhang, H.W.; Schäffer, Hemming Andreas; Jakobsen, K.P.
2007-01-01
A deterministic combination of numerical and physical models for coastal waves is developed. In the combined model, a Boussinesq model MIKE 21 BW is applied for the numerical wave computations. A piston-type 2D or 3D wavemaker and the associated control system with active wave absorption provides...
MIMO capacity for deterministic channel models: sublinear growth
DEFF Research Database (Denmark)
Bentosela, Francois; Cornean, Horia; Marchetti, Nicola
2013-01-01
This is the second paper by the authors in a series concerned with the development of a deterministic model for the transfer matrix of a MIMO system. In our previous paper, we started from the Maxwell equations and described the generic structure of such a deterministic transfer matrix...... some generic assumptions, we prove that the capacity grows much more slowly than linearly with the number of antennas. These results reinforce previous heuristic results obtained from statistical models of the transfer matrix, which also predict a sublinear behavior....
Constructing stochastic models from deterministic process equations by propensity adjustment
Directory of Open Access Journals (Sweden)
Wu Jialiang
2011-11-01
Full Text Available Abstract Background Gillespie's stochastic simulation algorithm (SSA for chemical reactions admits three kinds of elementary processes, namely, mass action reactions of 0th, 1st or 2nd order. All other types of reaction processes, for instance those containing non-integer kinetic orders or following other types of kinetic laws, are assumed to be convertible to one of the three elementary kinds, so that SSA can validly be applied. However, the conversion to elementary reactions is often difficult, if not impossible. Within deterministic contexts, a strategy of model reduction is often used. Such a reduction simplifies the actual system of reactions by merging or approximating intermediate steps and omitting reactants such as transient complexes. It would be valuable to adopt a similar reduction strategy to stochastic modelling. Indeed, efforts have been devoted to manipulating the chemical master equation (CME in order to achieve a proper propensity function for a reduced stochastic system. However, manipulations of CME are almost always complicated, and successes have been limited to relative simple cases. Results We propose a rather general strategy for converting a deterministic process model into a corresponding stochastic model and characterize the mathematical connections between the two. The deterministic framework is assumed to be a generalized mass action system and the stochastic analogue is in the format of the chemical master equation. The analysis identifies situations: where a direct conversion is valid; where internal noise affecting the system needs to be taken into account; and where the propensity function must be mathematically adjusted. The conversion from deterministic to stochastic models is illustrated with several representative examples, including reversible reactions with feedback controls, Michaelis-Menten enzyme kinetics, a genetic regulatory motif, and stochastic focusing. Conclusions The construction of a stochastic
Nonlinear distortion in wireless systems modeling and simulation with Matlab
Gharaibeh, Khaled M
2011-01-01
This book covers the principles of modeling and simulation of nonlinear distortion in wireless communication systems with MATLAB simulations and techniques In this book, the author describes the principles of modeling and simulation of nonlinear distortion in single and multichannel wireless communication systems using both deterministic and stochastic signals. Models and simulation methods of nonlinear amplifiers explain in detail how to analyze and evaluate the performance of data communication links under nonlinear amplification. The book addresses the analysis of nonlinear systems
Line and lattice networks under deterministic interference models
Goseling, Jasper; Gastpar, Michael; Weber, Jos H.
2011-01-01
Capacity bounds are compared for four different deterministic models of wireless networks, representing four different ways of handling broadcast and superposition in the physical layer. In particular, the transport capacity under a multiple unicast traffic pattern is studied for a 1-D network of re
Nine challenges for deterministic epidemic models
DEFF Research Database (Denmark)
Roberts, Mick G; Andreasen, Viggo; Lloyd, Alun;
2015-01-01
, infections with time-varying infectivity, and those where superinfection is possible. We then consider the need for advances in spatial epidemic models, and draw attention to the lack of models that explore the relationship between communicable and non-communicable diseases. The final two challenges concern...
Discrete Deterministic Modelling of Autonomous Missiles Salvos
Directory of Open Access Journals (Sweden)
Momcilo Milinovic
2014-09-01
Full Text Available The paper deals with mathematical models of sequent salvos battle, of autonomous flight missiles (AFM organized in the groups of combatants. Tactical integration of AFM system distance-controlled weapon is considered by performances of simultaneous approaches on targets, and continual battle models of guerilla and direct fire, are redesigned to the discrete-continual mixed model, for checking missiles sudden, and further salvos, attack effects. Superiority parameters, as well as losses and strengths of full, or the part of salvo battle, for the missiles groups as technology sub-systems combatants’, is expressed by mathematical and simulation examples. Targets engagements capacities of the missiles battle unit, is conducted through designed scenarios and mathematically derived in the research. Model orientated on answers about employment of rapid reaction defending tactics, by distance missiles attacks.Defence Science Journal, Vol. 64, No. 5, September 2014, pp.471-476, DOI:http://dx.doi.org/10.14429/dsj.64.5791
Directory of Open Access Journals (Sweden)
Saul Hazledine
Full Text Available Legume plants form beneficial symbiotic interactions with nitrogen fixing bacteria (called rhizobia, with the rhizobia being accommodated in unique structures on the roots of the host plant. The legume/rhizobial symbiosis is responsible for a significant proportion of the global biologically available nitrogen. The initiation of this symbiosis is governed by a characteristic calcium oscillation within the plant root hair cells and this signal is activated by the rhizobia. Recent analyses on calcium time series data have suggested that stochastic effects have a large role to play in defining the nature of the oscillations. The use of multiple nonlinear time series techniques, however, suggests an alternative interpretation, namely deterministic chaos. We provide an extensive, nonlinear time series analysis on the nature of this calcium oscillation response. We build up evidence through a series of techniques that test for determinism, quantify linear and nonlinear components, and measure the local divergence of the system. Chaos is common in nature and it seems plausible that properties of chaotic dynamics might be exploited by biological systems to control processes within the cell. Systems possessing chaotic control mechanisms are more robust in the sense that the enhanced flexibility allows more rapid response to environmental changes with less energetic costs. The desired behaviour could be most efficiently targeted in this manner, supporting some intriguing speculations about nonlinear mechanisms in biological signaling.
Modeling Deterministic Chaos Using Electronic Circuits
Directory of Open Access Journals (Sweden)
T. Gotthans
2011-06-01
Full Text Available This paper brings a note on systematic circuit synthesis methods for modeling the dynamical systems given by mathematical model. Both classical synthesis and integrator based method is demonstrated via the relatively complicated real physical systems with possible chaotic solution. A variety of the different active building blocks are utilized to make the final circuits as simple as possible while preserving easily measurable voltage-mode state variables. Brief experimental verification, i.e. oscilloscope screenshots, is presented. The observed attractors have some structural stability and good relationship to their numerically integrated counterparts.
Asinari, Pietro
2010-01-01
The homogeneous isotropic Boltzmann equation (HIBE) is a fundamental dynamic model for many applications in thermodynamics, econophysics and sociodynamics. Despite recent hardware improvements, the solution of the Boltzmann equation remains extremely challenging from the computational point of view, in particular by deterministic methods (free of stochastic noise). This work aims to improve a deterministic direct method recently proposed [V.V. Aristov, Kluwer Academic Publishers, 2001] for solving the HIBE with a generic collisional kernel and, in particular, for taking care of the late dynamics of the relaxation towards the equilibrium. Essentially (a) the original problem is reformulated in terms of particle kinetic energy (exact particle number and energy conservation during microscopic collisions) and (b) the computation of the relaxation rates is improved by the DVM-like correction, where DVM stands for Discrete Velocity Model (ensuring that the macroscopic conservation laws are exactly satisfied). Both ...
Evaluating consistency of deterministic streamline tractography in non-linearly warped DTI data
Adluru, Nagesh; Tromp, Do P M; Davidson, Richard J; Zhang, Hui; Alexander, Andrew L
2016-01-01
Tractography is typically performed for each subject using the diffusion tensor imaging (DTI) data in its native subject space rather than in some space common to the entire study cohort. Despite performing tractography on a population average in a normalized space, the latter is considered less favorably at the \\emph{individual} subject level because it requires spatial transformations of DTI data that involve non-linear warping and reorientation of the tensors. Although the commonly used reorientation strategies such as finite strain and preservation of principle direction are expected to result in adequate accuracy for voxel based analyses of DTI measures such as fractional anisotropy (FA), mean diffusivity (MD), the reorientations are not always exact except in the case of rigid transformations. Small imperfections in reorientation at individual voxel level accumulate and could potentially affect the tractography results adversely. This study aims to evaluate and compare deterministic white matter fiber t...
Methods and models in mathematical biology deterministic and stochastic approaches
Müller, Johannes
2015-01-01
This book developed from classes in mathematical biology taught by the authors over several years at the Technische Universität München. The main themes are modeling principles, mathematical principles for the analysis of these models, and model-based analysis of data. The key topics of modern biomathematics are covered: ecology, epidemiology, biochemistry, regulatory networks, neuronal networks, and population genetics. A variety of mathematical methods are introduced, ranging from ordinary and partial differential equations to stochastic graph theory and branching processes. A special emphasis is placed on the interplay between stochastic and deterministic models.
Two-particle correlations via quasi-deterministic analyzer model
Dalton, B J
2001-01-01
We introduce a quasi-deterministic eigenstate transition model of analyzers in which the final eigenstate is selected by initial conditions. We combine this analyzer model with causal spin coupling to calculate both proton-proton and photon-photon correlations, one particle pair at a time. The calculated correlations exceed the Bell limits and show excellent agreement with the measured correlations of [M. Lamehi-Rachti and W. Mittig, Phys. Rev. D 14 (10), 2543 (1976)] and [ A. Aspect, P. Grangier and G. Rogers, Phys. Rev. Lett. 49 91 (1982)] respectively. We discuss why this model exceeds the Bell type limits.
Deterministic multidimensional growth model for small-world networks
Peng, Aoyuan
2011-01-01
We proposed a deterministic multidimensional growth model for small-world networks. The model can characterize the distinguishing properties of many real-life networks with geometric space structure. Our results show the model possesses small-world effect: larger clustering coefficient and smaller characteristic path length. We also obtain some accurate results for its properties including degree distribution, clustering coefficient and network diameter and discuss them. It is also worth noting that we get an accurate analytical expression for calculating the characteristic path length. We verify numerically and experimentally these main features.
Forecasting project schedule performance using probabilistic and deterministic models
Directory of Open Access Journals (Sweden)
S.A. Abdel Azeem
2014-04-01
Full Text Available Earned value management (EVM was originally developed for cost management and has not widely been used for forecasting project duration. In addition, EVM based formulas for cost or schedule forecasting are still deterministic and do not provide any information about the range of possible outcomes and the probability of meeting the project objectives. The objective of this paper is to develop three models to forecast the estimated duration at completion. Two of these models are deterministic; earned value (EV and earned schedule (ES models. The third model is a probabilistic model and developed based on Kalman filter algorithm and earned schedule management. Hence, the accuracies of the EV, ES and Kalman Filter Forecasting Model (KFFM through the different project periods will be assessed and compared with the other forecasting methods such as the Critical Path Method (CPM, which makes the time forecast at activity level by revising the actual reporting data for each activity at a certain data date. A case study project is used to validate the results of the three models. Hence, the best model is selected based on the lowest average percentage of error. The results showed that the KFFM developed in this study provides probabilistic prediction bounds of project duration at completion and can be applied through the different project periods with smaller errors than those observed in EV and ES forecasting models.
Park, Y. C.; Chang, M. H.; Lee, T.-Y.
2007-06-01
A deterministic global optimization method that is applicable to general nonlinear programming problems composed of twice-differentiable objective and constraint functions is proposed. The method hybridizes the branch-and-bound algorithm and a convex cut function (CCF). For a given subregion, the difference of a convex underestimator that does not need an iterative local optimizer to determine the lower bound of the objective function is generated. If the obtained lower bound is located in an infeasible region, then the CCF is generated for constraints to cut this region. The cutting region generated by the CCF forms a hyperellipsoid and serves as the basis of a discarding rule for the selected subregion. However, the convergence rate decreases as the number of cutting regions increases. To accelerate the convergence rate, an inclusion relation between two hyperellipsoids should be applied in order to reduce the number of cutting regions. It is shown that the two-hyperellipsoid inclusion relation is determined by maximizing a quadratic function over a sphere, which is a special case of a trust region subproblem. The proposed method is applied to twelve nonlinear programming test problems and five engineering design problems. Numerical results show that the proposed method converges in a finite calculation time and produces accurate solutions.
Deterministic versus stochastic aspects of superexponential population growth models
Grosjean, Nicolas; Huillet, Thierry
2016-08-01
Deterministic population growth models with power-law rates can exhibit a large variety of growth behaviors, ranging from algebraic, exponential to hyperexponential (finite time explosion). In this setup, selfsimilarity considerations play a key role, together with two time substitutions. Two stochastic versions of such models are investigated, showing a much richer variety of behaviors. One is the Lamperti construction of selfsimilar positive stochastic processes based on the exponentiation of spectrally positive processes, followed by an appropriate time change. The other one is based on stable continuous-state branching processes, given by another Lamperti time substitution applied to stable spectrally positive processes.
On the deterministic and stochastic use of hydrologic models
Farmer, William H.; Vogel, Richard M.
2016-07-01
Environmental simulation models, such as precipitation-runoff watershed models, are increasingly used in a deterministic manner for environmental and water resources design, planning, and management. In operational hydrology, simulated responses are now routinely used to plan, design, and manage a very wide class of water resource systems. However, all such models are calibrated to existing data sets and retain some residual error. This residual, typically unknown in practice, is often ignored, implicitly trusting simulated responses as if they are deterministic quantities. In general, ignoring the residuals will result in simulated responses with distributional properties that do not mimic those of the observed responses. This discrepancy has major implications for the operational use of environmental simulation models as is shown here. Both a simple linear model and a distributed-parameter precipitation-runoff model are used to document the expected bias in the distributional properties of simulated responses when the residuals are ignored. The systematic reintroduction of residuals into simulated responses in a manner that produces stochastic output is shown to improve the distributional properties of the simulated responses. Every effort should be made to understand the distributional behavior of simulation residuals and to use environmental simulation models in a stochastic manner.
On the deterministic and stochastic use of hydrologic models
Farmer, William H.; Vogel, Richard M.
2016-01-01
Environmental simulation models, such as precipitation-runoff watershed models, are increasingly used in a deterministic manner for environmental and water resources design, planning, and management. In operational hydrology, simulated responses are now routinely used to plan, design, and manage a very wide class of water resource systems. However, all such models are calibrated to existing data sets and retain some residual error. This residual, typically unknown in practice, is often ignored, implicitly trusting simulated responses as if they are deterministic quantities. In general, ignoring the residuals will result in simulated responses with distributional properties that do not mimic those of the observed responses. This discrepancy has major implications for the operational use of environmental simulation models as is shown here. Both a simple linear model and a distributed-parameter precipitation-runoff model are used to document the expected bias in the distributional properties of simulated responses when the residuals are ignored. The systematic reintroduction of residuals into simulated responses in a manner that produces stochastic output is shown to improve the distributional properties of the simulated responses. Every effort should be made to understand the distributional behavior of simulation residuals and to use environmental simulation models in a stochastic manner.
Electrocardiogram (ECG) pattern modeling and recognition via deterministic learning
Institute of Scientific and Technical Information of China (English)
Xunde DONG; Cong WANG; Junmin HU; Shanxing OU
2014-01-01
A method for electrocardiogram (ECG) pattern modeling and recognition via deterministic learning theory is presented in this paper. Instead of recognizing ECG signals beat-to-beat, each ECG signal which contains a number of heartbeats is recognized. The method is based entirely on the temporal features (i.e., the dynamics) of ECG patterns, which contains complete information of ECG patterns. A dynamical model is employed to demonstrate the method, which is capable of generating synthetic ECG signals. Based on the dynamical model, the method is shown in the following two phases:the identification (training) phase and the recognition (test) phase. In the identification phase, the dynamics of ECG patterns is accurately modeled and expressed as constant RBF neural weights through the deterministic learning. In the recognition phase, the modeling results are used for ECG pattern recognition. The main feature of the proposed method is that the dynamics of ECG patterns is accurately modeled and is used for ECG pattern recognition. Experimental studies using the Physikalisch-Technische Bundesanstalt (PTB) database are included to demonstrate the effectiveness of the approach.
Mixed deterministic statistical modelling of regional ozone air pollution
Kalenderski, Stoitchko Dimitrov
2011-03-17
We develop a physically motivated statistical model for regional ozone air pollution by separating the ground-level pollutant concentration field into three components, namely: transport, local production and large-scale mean trend mostly dominated by emission rates. The model is novel in the field of environmental spatial statistics in that it is a combined deterministic-statistical model, which gives a new perspective to the modelling of air pollution. The model is presented in a Bayesian hierarchical formalism, and explicitly accounts for advection of pollutants, using the advection equation. We apply the model to a specific case of regional ozone pollution-the Lower Fraser valley of British Columbia, Canada. As a predictive tool, we demonstrate that the model vastly outperforms existing, simpler modelling approaches. Our study highlights the importance of simultaneously considering different aspects of an air pollution problem as well as taking into account the physical bases that govern the processes of interest. © 2011 John Wiley & Sons, Ltd..
Connection between stochastic and deterministic modelling of microbial growth.
Kutalik, Zoltán; Razaz, Moe; Baranyi, József
2005-01-21
We present in this paper various links between individual and population cell growth. Deterministic models of the lag and subsequent growth of a bacterial population and their connection with stochastic models for the lag and subsequent generation times of individual cells are analysed. We derived the individual lag time distribution inherent in population growth models, which shows that the Baranyi model allows a wide range of shapes for individual lag time distribution. We demonstrate that individual cell lag time distributions cannot be retrieved from population growth data. We also present the results of our investigation on the effect of the mean and variance of the individual lag time and the initial cell number on the mean and variance of the population lag time. These relationships are analysed theoretically, and their consequence for predictive microbiology research is discussed.
Rezaee, Hamed; Abdollahi, Farzaneh
2016-12-06
The leaderless consensus problem over a class of high-order nonlinear multiagent systems (MASs) is studied. A robust protocol is proposed which guarantees achieving consensus in the network in the presences of uncertainties in agents models. Achieving consensus in the case of stochastic links failure is studied as well. Based on the concept super-martingales, it is shown that if the probability of the network connectivity is not zero, under some conditions, achieving almost sure consensus in the network can be guaranteed. Despite existing consensus protocols for high-order stochastic networks, the proposed consensus protocol in this paper is robust to uncertain nonlinearities in the agents models, and it can be designed independent of knowledge on the set of feasible topologies (topologies with nonzero probabilities). Numerical examples for a team of single-link flexible joint manipulators with fourth-order models verify the accuracy of the proposed strategy for consensus control of high-order MASs with uncertain nonlinearities.
Sensitivity analysis in a Lassa fever deterministic mathematical model
Abdullahi, Mohammed Baba; Doko, Umar Chado; Mamuda, Mamman
2015-05-01
Lassa virus that causes the Lassa fever is on the list of potential bio-weapons agents. It was recently imported into Germany, the Netherlands, the United Kingdom and the United States as a consequence of the rapid growth of international traffic. A model with five mutually exclusive compartments related to Lassa fever is presented and the basic reproduction number analyzed. A sensitivity analysis of the deterministic model is performed. This is done in order to determine the relative importance of the model parameters to the disease transmission. The result of the sensitivity analysis shows that the most sensitive parameter is the human immigration, followed by human recovery rate, then person to person contact. This suggests that control strategies should target human immigration, effective drugs for treatment and education to reduced person to person contact.
A deterministic combination of numerical and physical models for coastal waves
DEFF Research Database (Denmark)
Zhang, Haiwen
2006-01-01
of numerical and physical modelling hence provides an attractive alternative to the use of either tool on it's own. The goal of this project has been to develop a deterministically combined numerical/physical model where the physical wave tank is enclosed in a much larger computational domain, and the two......Numerical and physical modelling are the two main tools available for predicting the influence of water waves on coastlines and structures placed in the near-shore environment. Numerical models can cover large areas at the correct scale, but are limited in their ability to capture strong...... nonlinearities, wave breaking, splash, mixing, and other such complicated physics. Physical models naturally include the real physics (at the model scale), but are limited by the physical size of the facility and must contend with the fact that different physical effects scale differently. An integrated use...
A Modified Deterministic Model for Reverse Supply Chain in Manufacturing
Directory of Open Access Journals (Sweden)
R. N. Mahapatra
2013-01-01
Full Text Available Technology is becoming pervasive across all facets of our lives today. Technology innovation leading to development of new products and enhancement of features in existing products is happening at a faster pace than ever. It is becoming difficult for the customers to keep up with the deluge of new technology. This trend has resulted in gross increase in use of new materials and decreased customers' interest in relatively older products. This paper deals with a novel model in which the stationary demand is fulfilled by remanufactured products along with newly manufactured products. The current model is based on the assumption that the returned items from the customers can be remanufactured at a fixed rate. The remanufactured products are assumed to be as good as the new ones in terms of features, quality, and worth. A methodology is used for the calculation of optimum level for the newly manufactured items and the optimum level of the remanufactured products simultaneously. The model is formulated depending on the relationship between different parameters. An interpretive-modelling-based approach has been employed to model the reverse logistics variables typically found in supply chains (SCs. For simplicity of calculation a deterministic approach is implemented for the proposed model.
Billings, S. A.
1988-03-01
Time and frequency domain identification methods for nonlinear systems are reviewed. Parametric methods, prediction error methods, structure detection, model validation, and experiment design are discussed. Identification of a liquid level system, a heat exchanger, and a turbocharge automotive diesel engine are illustrated. Rational models are introduced. Spectral analysis for nonlinear systems is treated. Recursive estimation is mentioned.
Research on nonlinear stochastic dynamical price model
Energy Technology Data Exchange (ETDEWEB)
Li Jiaorui [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China); School of Statistics, Xi' an University of Finance and Economics, Xi' an 710061 (China)], E-mail: jiaoruili@mail.nwpu.edu.cn; Xu Wei; Xie Wenxian; Ren Zhengzheng [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China)
2008-09-15
In consideration of many uncertain factors existing in economic system, nonlinear stochastic dynamical price model which is subjected to Gaussian white noise excitation is proposed based on deterministic model. One-dimensional averaged Ito stochastic differential equation for the model is derived by using the stochastic averaging method, and applied to investigate the stability of the trivial solution and the first-passage failure of the stochastic price model. The stochastic price model and the methods presented in this paper are verified by numerical studies.
Deterministic and heuristic models of forecasting spare parts demand
Directory of Open Access Journals (Sweden)
Ivan S. Milojević
2012-04-01
Full Text Available Knowing the demand of spare parts is the basis for successful spare parts inventory management. Inventory management has two aspects. The first one is operational management: acting according to certain models and making decisions in specific situations which could not have been foreseen or have not been encompassed by models. The second aspect is optimization of the model parameters by means of inventory management. Supply items demand (asset demand is the expression of customers' needs in units in the desired time and it is one of the most important parameters in the inventory management. The basic task of the supply system is demand fulfillment. In practice, demand is expressed through requisition or request. Given the conditions in which inventory management is considered, demand can be: - deterministic or stochastic, - stationary or nonstationary, - continuous or discrete, - satisfied or unsatisfied. The application of the maintenance concept is determined by the technological level of development of the assets being maintained. For example, it is hard to imagine that the concept of self-maintenance can be applied to assets developed and put into use 50 or 60 years ago. Even less complex concepts cannot be applied to those vehicles that only have indicators of engine temperature - those that react only when the engine is overheated. This means that the maintenance concepts that can be applied are the traditional preventive maintenance and the corrective maintenance. In order to be applied in a real system, modeling and simulation methods require a completely regulated system and that is not the case with this spare parts supply system. Therefore, this method, which also enables the model development, cannot be applied. Deterministic models of forecasting are almost exclusively related to the concept of preventive maintenance. Maintenance procedures are planned in advance, in accordance with exploitation and time resources. Since the timing
Handbook of EOQ inventory problems stochastic and deterministic models and applications
Choi, Tsan-Ming
2013-01-01
This book explores deterministic and stochastic EOQ-model based problems and applications, presenting technical analyses of single-echelon EOQ model based inventory problems, and applications of the EOQ model for multi-echelon supply chain inventory analysis.
Wang, Mei-Yu; Yan, Feng-Li; Gao, Ting
2016-07-01
We present two deterministic quantum entanglement distribution protocols for a four-photon Dicke polarization entangled state resorting to the frequency and spatial degrees of freedom, which are immune to an arbitrary collective-noise channel. Both of the protocols adopt the X homodyne measurement based on the cross-Kerr nonlinearity to complete the task of the single-photon detection with nearly unit probability in principle. After the four receivers share the photons, they add some local unitary operations to obtain a standard four-photon Dicke polarization entangled state.
Graphics development of DCOR: Deterministic combat model of Oak Ridge
Energy Technology Data Exchange (ETDEWEB)
Hunt, G. [Georgia Inst. of Tech., Atlanta, GA (United States); Azmy, Y.Y. [Oak Ridge National Lab., TN (United States)
1992-10-01
DCOR is a user-friendly computer implementation of a deterministic combat model developed at ORNL. To make the interpretation of the results more intuitive, a conversion of the numerical solution to a graphic animation sequence of battle evolution is desirable. DCOR uses a coarse computational spatial mesh superimposed on the battlefield. This research is aimed at developing robust methods for computing the position of the combative units over the continuum (and also pixeled) battlefield, from DCOR`s discrete-variable solution representing the density of each force type evaluated at gridpoints. Three main problems have been identified and solutions have been devised and implemented in a new visualization module of DCOR. First, there is the problem of distributing the total number of objects, each representing a combative unit of each force type, among the gridpoints at each time level of the animation. This problem is solved by distributing, for each force type, the total number of combative units, one by one, to the gridpoint with the largest calculated number of units. Second, there is the problem of distributing the number of units assigned to each computational gridpoint over the battlefield area attributed to that point. This problem is solved by distributing the units within that area by taking into account the influence of surrounding gridpoints using linear interpolation. Finally, time interpolated solutions must be generated to produce a sufficient number of frames to create a smooth animation sequence. Currently, enough frames may be generated either by direct computation via the PDE solver or by using linear programming techniques to linearly interpolate intermediate frames between calculated frames.
Deterministic Modeling of the High Temperature Test Reactor
Energy Technology Data Exchange (ETDEWEB)
Ortensi, J.; Cogliati, J. J.; Pope, M. A.; Ferrer, R. M.; Ougouag, A. M.
2010-06-01
Idaho National Laboratory (INL) is tasked with the development of reactor physics analysis capability of the Next Generation Nuclear Power (NGNP) project. In order to examine INL’s current prismatic reactor deterministic analysis tools, the project is conducting a benchmark exercise based on modeling the High Temperature Test Reactor (HTTR). This exercise entails the development of a model for the initial criticality, a 19 column thin annular core, and the fully loaded core critical condition with 30 columns. Special emphasis is devoted to the annular core modeling, which shares more characteristics with the NGNP base design. The DRAGON code is used in this study because it offers significant ease and versatility in modeling prismatic designs. Despite some geometric limitations, the code performs quite well compared to other lattice physics codes. DRAGON can generate transport solutions via collision probability (CP), method of characteristics (MOC), and discrete ordinates (Sn). A fine group cross section library based on the SHEM 281 energy structure is used in the DRAGON calculations. HEXPEDITE is the hexagonal z full core solver used in this study and is based on the Green’s Function solution of the transverse integrated equations. In addition, two Monte Carlo (MC) based codes, MCNP5 and PSG2/SERPENT, provide benchmarking capability for the DRAGON and the nodal diffusion solver codes. The results from this study show a consistent bias of 2–3% for the core multiplication factor. This systematic error has also been observed in other HTTR benchmark efforts and is well documented in the literature. The ENDF/B VII graphite and U235 cross sections appear to be the main source of the error. The isothermal temperature coefficients calculated with the fully loaded core configuration agree well with other benchmark participants but are 40% higher than the experimental values. This discrepancy with the measurement stems from the fact that during the experiments the
Stojković, Milan; Kostić, Srđan; Plavšić, Jasna; Prohaska, Stevan
2017-01-01
The authors present a detailed procedure for modelling of mean monthly flow time-series using records of the Great Morava River (Serbia). The proposed procedure overcomes a major challenge of other available methods by disaggregating the time series in order to capture the main properties of the hydrologic process in both long-run and short-run. The main assumption of the conducted research is that a time series of monthly flow rates represents a stochastic process comprised of deterministic, stochastic and random components, the former of which can be further decomposed into a composite trend and two periodic components (short-term or seasonal periodicity and long-term or multi-annual periodicity). In the present paper, the deterministic component of a monthly flow time-series is assessed by spectral analysis, whereas its stochastic component is modelled using cross-correlation transfer functions, artificial neural networks and polynomial regression. The results suggest that the deterministic component can be expressed solely as a function of time, whereas the stochastic component changes as a nonlinear function of climatic factors (rainfall and temperature). For the calibration period, the results of the analysis infers a lower value of Kling-Gupta Efficiency in the case of transfer functions (0.736), whereas artificial neural networks and polynomial regression suggest a significantly better match between the observed and simulated values, 0.841 and 0.891, respectively. It seems that transfer functions fail to capture high monthly flow rates, whereas the model based on polynomial regression reproduces high monthly flows much better because it is able to successfully capture a highly nonlinear relationship between the inputs and the output. The proposed methodology that uses a combination of artificial neural networks, spectral analysis and polynomial regression for deterministic and stochastic components can be applied to forecast monthly or seasonal flow rates.
Energy Technology Data Exchange (ETDEWEB)
Hunt, G. (Georgia Inst. of Tech., Atlanta, GA (United States)); Azmy, Y.Y. (Oak Ridge National Lab., TN (United States))
1992-10-01
DCOR is a user-friendly computer implementation of a deterministic combat model developed at ORNL. To make the interpretation of the results more intuitive, a conversion of the numerical solution to a graphic animation sequence of battle evolution is desirable. DCOR uses a coarse computational spatial mesh superimposed on the battlefield. This research is aimed at developing robust methods for computing the position of the combative units over the continuum (and also pixeled) battlefield, from DCOR's discrete-variable solution representing the density of each force type evaluated at gridpoints. Three main problems have been identified and solutions have been devised and implemented in a new visualization module of DCOR. First, there is the problem of distributing the total number of objects, each representing a combative unit of each force type, among the gridpoints at each time level of the animation. This problem is solved by distributing, for each force type, the total number of combative units, one by one, to the gridpoint with the largest calculated number of units. Second, there is the problem of distributing the number of units assigned to each computational gridpoint over the battlefield area attributed to that point. This problem is solved by distributing the units within that area by taking into account the influence of surrounding gridpoints using linear interpolation. Finally, time interpolated solutions must be generated to produce a sufficient number of frames to create a smooth animation sequence. Currently, enough frames may be generated either by direct computation via the PDE solver or by using linear programming techniques to linearly interpolate intermediate frames between calculated frames.
Energy Technology Data Exchange (ETDEWEB)
Mangiarotti, A. [Physikalisches Insitut, Universitaet Heidelberg, Philosophenweg 12, D-69120 Heidelberg (Germany)]. E-mail: a.mangiarotti@gsi.de; Bueno, C.C. [Instituto de Pesquisas Energeticas e Nucleares, 05508-900 Sao Paulo (Brazil); Departamento de Fisica, Pontificia Universidade Catolica de Sao Paulo, 01303-050 Sao Paulo (Brazil); Fonte, P. [Laboratorio de Instrumentacao e Fisica Experimental de Particulas, 3004-516 Coimbra (Portugal); Instituto Superior de Engenharia de Coimbra, Rua Pedro Nunes, 3030-199 Coimbra (Portugal); Gobbi, A. [Gesellschaft fuer Schwerionenforschung, Planckstr. 1, D-64291 Darmstadt (Germany); Gonzalez-Diaz, D. [LabCaf, Dep. de Fisica de Particulas, Universidade de Santiago de Compostela, 15782 Spain (Spain); Lopes, L. [Laboratorio de Instrumentacao e Fisica Experimental de Particulas, 3004-516 Coimbra (Portugal)
2006-08-15
RPCs offer unique opportunities to investigate basic processes in gaseous electronics. The growth of a single avalanche can be studied in a regime where it reacts to its own field. This induces a saturation in its development, often described in a deterministic scenario by a nonlinear model. Once reinterpreted in a fully stochastic framework, the same feature corresponds to a negative feedback mechanism, which regulates the avalanche development and preserves its timing properties. Fluctuations are hence mostly produced in the initial phase of the growth. A clear evidence of the action of this stabilizing scheme is observed in data collected for single avalanches of fixed length.
Generalized Nonlinear Yule Models
Lansky, Petr; Polito, Federico; Sacerdote, Laura
2016-10-01
With the aim of considering models related to random graphs growth exhibiting persistent memory, we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macroevolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth rates. Among the main results we derive the explicit distribution of the number of in-links of a webpage chosen uniformly at random recognizing the contribution to the asymptotics and the finite time correction. The mean value of the latter distribution is also calculated explicitly in the most general case. Furthermore, in order to show the usefulness of our results, we particularize them in the case of specific birth rates giving rise to a saturating behaviour, a property that is often observed in nature. The further specialization to the non-fractional case allows us to extend the Yule model accounting for a nonlinear growth.
Generalized Nonlinear Yule Models
Lansky, Petr; Polito, Federico; Sacerdote, Laura
2016-11-01
With the aim of considering models related to random graphs growth exhibiting persistent memory, we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macroevolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth rates. Among the main results we derive the explicit distribution of the number of in-links of a webpage chosen uniformly at random recognizing the contribution to the asymptotics and the finite time correction. The mean value of the latter distribution is also calculated explicitly in the most general case. Furthermore, in order to show the usefulness of our results, we particularize them in the case of specific birth rates giving rise to a saturating behaviour, a property that is often observed in nature. The further specialization to the non-fractional case allows us to extend the Yule model accounting for a nonlinear growth.
A Stochastic Nonlinear Water Wave Model for Efficient Uncertainty Quantification
Bigoni, Daniele; Eskilsson, Claes
2014-01-01
A major challenge in next-generation industrial applications is to improve numerical analysis by quantifying uncertainties in predictions. In this work we present a stochastic formulation of a fully nonlinear and dispersive potential flow water wave model for the probabilistic description of the evolution waves. This model is discretized using the Stochastic Collocation Method (SCM), which provides an approximate surrogate of the model. This can be used to accurately and efficiently estimate the probability distribution of the unknown time dependent stochastic solution after the forward propagation of uncertainties. We revisit experimental benchmarks often used for validation of deterministic water wave models. We do this using a fully nonlinear and dispersive model and show how uncertainty in the model input can influence the model output. Based on numerical experiments and assumed uncertainties in boundary data, our analysis reveals that some of the known discrepancies from deterministic simulation in compa...
Deterministic and stochastic trends in the Lee-Carter mortality model
DEFF Research Database (Denmark)
Callot, Laurent; Haldrup, Niels; Kallestrup-Lamb, Malene
2015-01-01
mortality data. We find empirical evidence that this feature of the Lee–Carter model overly restricts the system dynamics and we suggest to separate the deterministic and stochastic time series components at the benefit of improved fit and forecasting performance. In fact, we find that the classical Lee......) factor model where one factor is deterministic and the other factors are stochastic. This feature generalizes to the range of models that extend the Lee–Carter model in various directions.......The Lee and Carter (1992) model assumes that the deterministic and stochastic time series dynamics load with identical weights when describing the development of age-specific mortality rates. Effectively this means that the main characteristics of the model simplify to a random walk model with age...
Deterministic and stochastic trends in the Lee-Carter mortality model
DEFF Research Database (Denmark)
Callot, Laurent; Haldrup, Niels; Kallestrup-Lamb, Malene
that characterizes mortality data. We find empirical evidence that this feature of the Lee-Carter model overly restricts the system dynamics and we suggest to separate the deterministic and stochastic time series components at the benefit of improved fit and forecasting performance. In fact, we find...... as a two (or several)-factor model where one factor is deterministic and the other factors are stochastic. This feature generalizes to the range of models that extend the Lee-Carter model in various directions.......The Lee and Carter (1992) model assumes that the deterministic and stochastic time series dynamics loads with identical weights when describing the development of age specific mortality rates. Effectively this means that the main characteristics of the model simplifies to a random walk model...
A three-variable model of deterministic chaos in the Belousov-Zhabotinsky reaction
Györgyi, László; Field, Richard J.
1992-02-01
CHAOS is exhibited by a wide variety of systems governed by nonlinear dynamic laws1-3. Its most striking feature is an apparent randomness which seems to contradict its deterministic origin. The best-studied chaotic chemical system is the Belousov-Zhabotinsky (BZ) reaction4-6 in a continuous-flow stirred-tank reactor (CSTR). Here we present a simple mechanism for the BZ reaction which allows us to develop a description in terms of a set of differential equations containing only three variables, the minimum number required to generate chaos in a continuous (non-iterative) dynamical system2. In common with experiments, our model shows aperiodicity and transitions between periodicity and chaos near bifurcations between oscillatory and steady-state behaviour, which occur at both low and high CSTR flow rates. While remaining closely related to a real chaotic chemical system, our model is sufficiently simple to allow detailed mathematical analysis. It also reproduces many other features of the BZ reaction better than does the simple Oregonator7 (which cannot produce chaos).
Fraldi, M.; Perrella, G.; Ciervo, M.; Bosia, F.; Pugno, N. M.
2017-09-01
Very recently, a Weibull-based probabilistic strategy has been successfully applied to bundles of wires to determine their overall stress-strain behaviour, also capturing previously unpredicted nonlinear and post-elastic features of hierarchical strands. This approach is based on the so-called ;Equal Load Sharing (ELS); hypothesis by virtue of which, when a wire breaks, the load acting on the strand is homogeneously redistributed among the surviving wires. Despite the overall effectiveness of the method, some discrepancies between theoretical predictions and in silico Finite Element-based simulations or experimental findings might arise when more complex structures are analysed, e.g. helically arranged bundles. To overcome these limitations, an enhanced hybrid approach is proposed in which the probability of rupture is combined with a deterministic mechanical model of a strand constituted by helically-arranged and hierarchically-organized wires. The analytical model is validated comparing its predictions with both Finite Element simulations and experimental tests. The results show that generalized stress-strain responses - incorporating tension/torsion coupling - are naturally found and, once one or more elements break, the competition between geometry and mechanics of the strand microstructure, i.e. the different cross sections and helical angles of the wires in the different hierarchical levels of the strand, determines the no longer homogeneous stress redistribution among the surviving wires whose fate is hence governed by a ;Hierarchical Load Sharing; criterion.
Stability analysis of multi-group deterministic and stochastic epidemic models with vaccination rate
Wang, Zhi-Gang; Gao, Rui-Mei; Fan, Xiao-Ming; Han, Qi-Xing
2014-09-01
We discuss in this paper a deterministic multi-group MSIR epidemic model with a vaccination rate, the basic reproduction number ℛ0, a key parameter in epidemiology, is a threshold which determines the persistence or extinction of the disease. By using Lyapunov function techniques, we show if ℛ0 is greater than 1 and the deterministic model obeys some conditions, then the disease will prevail, the infective persists and the endemic state is asymptotically stable in a feasible region. If ℛ0 is less than or equal to 1, then the infective disappear so the disease dies out. In addition, stochastic noises around the endemic equilibrium will be added to the deterministic MSIR model in order that the deterministic model is extended to a system of stochastic ordinary differential equations. In the stochastic version, we carry out a detailed analysis on the asymptotic behavior of the stochastic model. In addition, regarding the value of ℛ0, when the stochastic system obeys some conditions and ℛ0 is greater than 1, we deduce the stochastic system is stochastically asymptotically stable. Finally, the deterministic and stochastic model dynamics are illustrated through computer simulations.
Spatial versus temporal deterministic wave breakup of nonlinearly coupled light waves.
Salerno, D; Minardi, S; Trull, J; Varanavicius, A; Tamosauskas, G; Valiulis, G; Dubietis, A; Caironi, D; Trillo, S; Piskarskas, A; Di Trapani, P
2003-10-01
We investigate experimentally the competition between spatial and temporal breakup due to modulational instability in chi((2)) nonlinear mixing. The modulation of the wave packets caused by the energy exchange between fundamental and second-harmonic components is found to be the prevailing trigger mechanism which, according to the relative weight of diffraction and dispersion, leads to the appearance of a multisoliton pattern in the low-dimensional spatial or temporal domain.
Szymanowski, Mariusz; Kryza, Maciej
2017-02-01
Our study examines the role of auxiliary variables in the process of spatial modelling and mapping of climatological elements, with air temperature in Poland used as an example. The multivariable algorithms are the most frequently applied for spatialization of air temperature, and their results in many studies are proved to be better in comparison to those obtained by various one-dimensional techniques. In most of the previous studies, two main strategies were used to perform multidimensional spatial interpolation of air temperature. First, it was accepted that all variables significantly correlated with air temperature should be incorporated into the model. Second, it was assumed that the more spatial variation of air temperature was deterministically explained, the better was the quality of spatial interpolation. The main goal of the paper was to examine both above-mentioned assumptions. The analysis was performed using data from 250 meteorological stations and for 69 air temperature cases aggregated on different levels: from daily means to 10-year annual mean. Two cases were considered for detailed analysis. The set of potential auxiliary variables covered 11 environmental predictors of air temperature. Another purpose of the study was to compare the results of interpolation given by various multivariable methods using the same set of explanatory variables. Two regression models: multiple linear (MLR) and geographically weighted (GWR) method, as well as their extensions to the regression-kriging form, MLRK and GWRK, respectively, were examined. Stepwise regression was used to select variables for the individual models and the cross-validation method was used to validate the results with a special attention paid to statistically significant improvement of the model using the mean absolute error (MAE) criterion. The main results of this study led to rejection of both assumptions considered. Usually, including more than two or three of the most significantly
Law of Malus and Photon-Photon Correlations A Quasi-Deterministic Analyzer Model
Dalton, B J
2001-01-01
For polarization experiments involving photon counting we introduce a quasi-deterministic eigenstate transition model of the analyzer process. Distributions accumulated one photon at a time, provide a deterministic explanation for the law of Malus. We combine this analyzer model with causal polarization coupling to calculate photon-photon correlations, one photon pair at a time. The calculated correlations exceed the Bell limits and show excellent agreement with the measured correlations of [ A. Aspect, P. Grangier and G. Rogers, Phys. Rev. Lett. 49 91 (1982)]. We discuss why this model exceeds the Bell type limits.
Numerical Approach to Spatial Deterministic-Stochastic Models Arising in Cell Biology.
Directory of Open Access Journals (Sweden)
James C Schaff
2016-12-01
Full Text Available Hybrid deterministic-stochastic methods provide an efficient alternative to a fully stochastic treatment of models which include components with disparate levels of stochasticity. However, general-purpose hybrid solvers for spatially resolved simulations of reaction-diffusion systems are not widely available. Here we describe fundamentals of a general-purpose spatial hybrid method. The method generates realizations of a spatially inhomogeneous hybrid system by appropriately integrating capabilities of a deterministic partial differential equation solver with a popular particle-based stochastic simulator, Smoldyn. Rigorous validation of the algorithm is detailed, using a simple model of calcium 'sparks' as a testbed. The solver is then applied to a deterministic-stochastic model of spontaneous emergence of cell polarity. The approach is general enough to be implemented within biologist-friendly software frameworks such as Virtual Cell.
Deterministic-statistical model coupling in a DSS for river-basin management
de Kok, Jean-Luc; Booij, Martijn J.
2009-01-01
This paper presents a method for appropriate coupling of deterministic and statistical models. In the decision-support system for the Elbe river, a conceptual rainfall-runoff model is used to obtain the discharge statistics and corresponding average number of flood days, which is a key input
Car Accidents in the Deterministic and Nondeterministic Nagel-Schreckenberg Models
Yang, Xian-Qing; Ma, Yu-Qiang
In this paper, we study further the probability for the occurrence of car accidents in the Nagel-Schreckenberg model. By considering the braking probability, the conditions for car accidents to occur are modified to obtain accurate results. A universal phenomenological theory will also be presented to describe the probability for car accidents to occur in the deterministic and nondeterministic models, respectively.
Deterministic and Advanced Statistical Modeling of Wind-Driven Sea
2015-07-06
CL)k + A^ (5) The renormalization has real and imaginary parts. The imaginary part is ImA(fi;) = -n>,60 (6) Thus, the SnI term is reliably known...is connected with SnI collision term numerical simulation. It is complex non- linear operator having, meanwhile, deep internal symmetry. Several Snl...is unlimited x 10 on co/co Fig.33 Decomposition of the nonlinear term Sni (solid line) for the case by Komen et al. (1984) [R711 into
Directory of Open Access Journals (Sweden)
Kiran Prasad Acharya
2016-01-01
Full Text Available In this work, we prepare and replicate a deterministic slope failure hazard model in small-scale catchments of tertiary sedimentary terrain of Niihama city in western Japan. It is generally difficult to replicate a deterministic model from one catchment to another due to lack of exactly similar geo-mechanical and hydrological parameters. To overcome this problem, discriminant function modelling was done with the deterministic slope failure hazard model and the DEM-based causal factors of slope failure, which yielded an empirical parametric relationship or a discriminant function equation. This parametric relationship was used to predict the slope failure hazard index in a total of 40 target catchments in the study area. From ROC plots, the prediction rate between 0.719–0.814 and 0.704–0.805 was obtained with inventories of September and October slope failures, respectively. This means September slope failures were better predicted than October slope failures by approximately 1%. The results show that the prediction of the slope failure hazard index is possible, even in a small catchment scale, in similar geophysical settings. Moreover, the replication of the deterministic model through discriminant function modelling was found to be successful in predicting typhoon rainfall-induced slope failures with moderate to good accuracy without any use of geo-mechanical and hydrological parameters.
Controlling influenza disease: Comparison between discrete time Markov chain and deterministic model
Novkaniza, F.; Ivana, Aldila, D.
2016-04-01
Mathematical model of respiratory diseases spread with Discrete Time Markov Chain (DTMC) and deterministic approach for constant total population size are analyzed and compared in this article. Intervention of medical treatment and use of medical mask included in to the model as a constant parameter to controlling influenza spreads. Equilibrium points and basic reproductive ratio as the endemic criteria and it level set depend on some variable are given analytically and numerically as a results from deterministic model analysis. Assuming total of human population is constant from deterministic model, number of infected people also analyzed with Discrete Time Markov Chain (DTMC) model. Since Δt → 0, we could assume that total number of infected people might change only from i to i + 1, i - 1, or i. Approximation probability of an outbreak with gambler's ruin problem will be presented. We find that no matter value of basic reproductive ℛ0, either its larger than one or smaller than one, number of infection will always tends to 0 for t → ∞. Some numerical simulation to compare between deterministic and DTMC approach is given to give a better interpretation and a better understanding about the models results.
Monceau, Pascal
2012-12-01
The effects of disorder on the critical behavior of the q-state Potts model in noninteger dimensions are studied by comparison of deterministic and random fractals sharing the same dimensions in the framework of a discrete scale invariance. We carried out intensive Monte Carlo simulations. In the case of a fractal dimension slightly smaller than two d(f) ~/= 1.974636, we give evidence that the disorder structured by discrete scale invariance does not change the first order transition associated with the deterministic case when q = 7. Furthermore the study of the high value q = 14 shows that the transition is a second order one both for deterministic and random scale invariance, but that their behavior belongs to different university classes.
From Ordinary Differential Equations to Structural Causal Models: the deterministic case
Mooij, J.M.; Janzing, D.; Schölkopf, B.; Nicholson, A.; Smyth, P.
2013-01-01
We show how, and under which conditions, the equilibrium states of a first-order Ordinary Differential Equation (ODE) system can be described with a deterministic Structural Causal Model (SCM). Our exposition sheds more light on the concept of causality as expressed within the framework of Structura
On competition in a Stackelberg location-design model with deterministic supplier choice
Hendrix, E.M.T.
2016-01-01
We study a market situation where two firms maximize market capture by deciding on the location in the plane and investing in a competing quality against investment cost. Clients choose one of the suppliers; i.e. deterministic supplier choice. To study this situation, a game theoretic model is formu
Deterministic Models of Inhalational Anthrax in New Zealand White Rabbits
2014-01-01
Computational models describing bacterial kinetics were developed for inhalational anthrax in New Zealand white (NZW) rabbits following inhalation of Ames strain B. anthracis. The data used to parameterize the models included bacterial numbers in the airways, lung tissue, draining lymph nodes, and blood. Initial bacterial numbers were deposited spore dose. The first model was a single exponential ordinary differential equation (ODE) with 3 rate parameters that described mucociliated (physical) clearance, immune clearance (bacterial killing), and bacterial growth. At 36 hours postexposure, the ODE model predicted 1.7×107 bacteria in the rabbit, which agreed well with data from actual experiments (4.0×107 bacteria at 36 hours). Next, building on the single ODE model, a physiological-based biokinetic (PBBK) compartmentalized model was developed in which 1 physiological compartment was the lumen of the airways and the other was the rabbit body (lung tissue, lymph nodes, blood). The 2 compartments were connected with a parameter describing transport of bacteria from the airways into the body. The PBBK model predicted 4.9×107 bacteria in the body at 36 hours, and by 45 hours the model showed all clearance mechanisms were saturated, suggesting the rabbit would quickly succumb to the infection. As with the ODE model, the PBBK model results agreed well with laboratory observations. These data are discussed along with the need for and potential application of the models in risk assessment, drug development, and as a general aid to the experimentalist studying inhalational anthrax. PMID:24527843
Occurrence of HIV eradication for preexposure prophylaxis treatment with a deterministic HIV model
Chang, H.; Moog, C; Astolfi, A
2016-01-01
The authors examine the human immunodeficiency virus (HIV) eradication in this study using a mathematical model and analyse the occurrence of virus eradication during the early stage of infection. To this end they use a deterministic HIV-infection model, modify it to describe the pharmacological dynamics of antiretroviral HIV drugs, and consider the clinical experimental results of preexposure prophylaxis HIV treatment. They also use numerical simulation to model the experimental scenario, th...
Reasoning with probabilistic and deterministic graphical models exact algorithms
Dechter, Rina
2013-01-01
Graphical models (e.g., Bayesian and constraint networks, influence diagrams, and Markov decision processes) have become a central paradigm for knowledge representation and reasoning in both artificial intelligence and computer science in general. These models are used to perform many reasoning tasks, such as scheduling, planning and learning, diagnosis and prediction, design, hardware and software verification, and bioinformatics. These problems can be stated as the formal tasks of constraint satisfaction and satisfiability, combinatorial optimization, and probabilistic inference. It is well
Identification of the FitzHugh-Nagumo Model Dynamics via Deterministic Learning
Dong, Xunde; Wang, Cong
In this paper, a new method is proposed for the identification of the FitzHugh-Nagumo (FHN) model dynamics via deterministic learning. The FHN model is a classic and simple model for studying spiral waves in excitable media, such as the cardiac tissue, biological neural networks. Firstly, the FHN model described by partial differential equations (PDEs) is transformed into a set of ordinary differential equations (ODEs) by using finite difference method. Secondly, the dynamics of the ODEs is identified using the deterministic learning theory. It is shown that, for the spiral waves generated by the FHN model, the dynamics underlying the recurrent trajectory corresponding to any spatial point can be accurately identified by using the proposed approach. Numerical experiments are included to demonstrate the effectiveness of the proposed method.
A deterministic aggregate production planning model considering quality of products
Madadi, Najmeh; Yew Wong, Kuan
2013-06-01
Aggregate Production Planning (APP) is a medium-term planning which is concerned with the lowest-cost method of production planning to meet customers' requirements and to satisfy fluctuating demand over a planning time horizon. APP problem has been studied widely since it was introduced and formulated in 1950s. However, in several conducted studies in the APP area, most of the researchers have concentrated on some common objectives such as minimization of cost, fluctuation in the number of workers, and inventory level. Specifically, maintaining quality at the desirable level as an objective while minimizing cost has not been considered in previous studies. In this study, an attempt has been made to develop a multi-objective mixed integer linear programming model that serves those companies aiming to incur the minimum level of operational cost while maintaining quality at an acceptable level. In order to obtain the solution to the multi-objective model, the Fuzzy Goal Programming approach and max-min operator of Bellman-Zadeh were applied to the model. At the final step, IBM ILOG CPLEX Optimization Studio software was used to obtain the experimental results based on the data collected from an automotive parts manufacturing company. The results show that incorporating quality in the model imposes some costs, however a trade-off should be done between the cost resulting from producing products with higher quality and the cost that the firm may incur due to customer dissatisfaction and sale losses.
Price-Dynamics of Shares and Bohmian Mechanics: Deterministic or Stochastic Model?
Choustova, Olga
2007-02-01
We apply the mathematical formalism of Bohmian mechanics to describe dynamics of shares. The main distinguishing feature of the financial Bohmian model is the possibility to take into account market psychology by describing expectations of traders by the pilot wave. We also discuss some objections (coming from conventional financial mathematics of stochastic processes) against the deterministic Bohmian model. In particular, the objection that such a model contradicts to the efficient market hypothesis which is the cornerstone of the modern market ideology. Another objection is of pure mathematical nature: it is related to the quadratic variation of price trajectories. One possibility to reply to this critique is to consider the stochastic Bohm-Vigier model, instead of the deterministic one. We do this in the present note.
Deterministic Modelling of Carbon Nanotube Near-Infrared Solar Cells
Bellisario, Darin
2015-03-01
With solution-process-ability, scale-able fabrication and purification, and cheap input materials, semiconducting single-walled carbon nanotube (SWNT) networks represent promising materials for near-IR solar cell (SC) applications. This promise has motivated a body of work not only developing solar cells but also exploring alignment/deposition methods and SWNT photovoltaic (PV) physics. Despite this interest, there is to date no quantitative model of SWNT solar cell operation analogous to bulk semiconductor p-n junction PVs, allowing a rigorous understanding of the physical tradeoffs driving experimental observations and informing what research will enable technological progress. In this work we have derived the steady state operation of planar heterojunction SWNT PVs from the fundamental light absorption, exciton transport, and free carrier transport behaviors of single nanotubes. Our method can treat arbitrary distributions of nanotube chiralities, lengths, orientations, defect types and concentration, bundle fraction and size, density, dielectric environment, electrode combinations, etc. We achieve this by treating individual SWNT properties as random variables, and describing the network by the dependent distributions of those properties, yielding coupled stochastic differential equations for light absorption, exciton transport, and free carrier transport. Applying the model to monochiral (6,5) films in aligned and isotropic configurations, we find that there is a strongly optimal film thickness at a given nanotube network density and orientation, reflecting an inherent tradeoff between light absorption (i.e. exciton generation) and diffusion to the electrodes. This optimal shifts lower with increasing density, and is ultra-thin (design.
Small-scale behaviour in deterministic reaction models
Energy Technology Data Exchange (ETDEWEB)
Politi, Paolo [Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, Via Madonna del Piano 10, 50019 Sesto Fiorentino (Italy); Ben-Avraham, Daniel, E-mail: paolo.politi@isc.cnr.i, E-mail: benavraham@clarkson.ed [Physics Department, Clarkson University, Potsdam, NY 13699-5820 (United States)
2010-10-08
In a recent paper published in this journal (2009 J. Phys. A: Math. Theor. 42 495004) we studied a one-dimensional particles system where nearest particles attract with a force inversely proportional to a power {alpha} of their distance and coalesce upon encounter. Numerics yielded a distribution function h(z) for the gap between neighbouring particles, with h(z) {approx} z{sup {beta}({alpha})} for small z and {beta}({alpha}) > {alpha}. We can now prove analytically that in the strict limit of z {yields} 0, {beta} = {alpha} for {alpha} > 0, corresponding to the mean-field result, and we compute the length scale where the mean field breaks down. More generally, in that same limit correlations are negligible for any similar reaction model where attractive forces diverge with vanishing distance. The actual meaning of the measured exponent {beta}({alpha}) remains an open question.
Asinari, P.
2011-03-01
Boltzmann equation is one the most powerful paradigms for explaining transport phenomena in fluids. Since early fifties, it received a lot of attention due to aerodynamic requirements for high altitude vehicles, vacuum technology requirements and nowadays, micro-electro-mechanical systems (MEMs). Because of the intrinsic mathematical complexity of the problem, Boltzmann himself started his work by considering first the case when the distribution function does not depend on space (homogeneous case), but only on time and the magnitude of the molecular velocity (isotropic collisional integral). The interest with regards to the homogeneous isotropic Boltzmann equation goes beyond simple dilute gases. In the so-called econophysics, a Boltzmann type model is sometimes introduced for studying the distribution of wealth in a simple market. Another recent application of the homogeneous isotropic Boltzmann equation is given by opinion formation modeling in quantitative sociology, also called socio-dynamics or sociophysics. The present work [1] aims to improve the deterministic method for solving homogenous isotropic Boltzmann equation proposed by Aristov [2] by two ideas: (a) the homogeneous isotropic problem is reformulated first in terms of particle kinetic energy (this allows one to ensure exact particle number and energy conservation during microscopic collisions) and (b) a DVM-like correction (where DVM stands for Discrete Velocity Model) is adopted for improving the relaxation rates (this allows one to satisfy exactly the conservation laws at macroscopic level, which is particularly important for describing the late dynamics in the relaxation towards the equilibrium).
Expansion or extinction: deterministic and stochastic two-patch models with Allee effects
Kang, Yun
2010-01-01
We investigate the impact of Allee effect and dispersal on the long-term evolution of a population in a patchy environment, focusing on whether a population already established in one patch either successfully invades an adjacent empty patch or undergoes a global in-all-patch extinction. Our study is based on the combination of analytical and numerical results for both a deterministic two-patch model and its stochastic analog. The deterministic model has either two or four attractors. In the presence of weak dispersal, the analysis of the deterministic model shows that a high-density and a low-density populations can coexist at equilibrium in nearby patches, whereas the analysis of the stochastic model indicates that this equilibrium is metastable, thus leading after a large random time to either an in-all-patch expansion or an in-all-patch extinction. Up to some critical dispersal, increasing the intensity of the interactions leads to an increase of both the basin of attraction of the in-all-patch extinction...
Latorre, D.; Mirabella, F.; Chiaraluce, L.; Trippetta, F.; Lomax, A.
2016-11-01
The accuracy of earthquake locations and their correspondence with subsurface geology depends strongly on the accuracy of the available seismic velocity model. Most modern methods to construct a velocity model for earthquake location are based on the inversion of passive source seismological data. Another approach is the integration of high-resolution geological and geophysical data to construct deterministic velocity models in which earthquake locations can be directly correlated to the geological structures. Such models have to be kinematically consistent with independent seismological data in order to provide precise hypocenter solutions. We present the Altotiberina (AT) seismic model, a three-dimensional velocity model for the Upper Tiber Valley region (Northern Apennines, Italy), constructed by combining 300 km of seismic reflection profiles, six deep boreholes (down to 5 km depth), detailed data from geological surveys and direct measurements of P and S wave velocities performed in situ and in laboratory. We assess the robustness of the AT seismic model by locating 11,713 earthquakes with a nonlinear, global-search inversion method and comparing the probabilistic hypocenter solutions to those calculated in three previously published velocity models, constructed by inverting passive seismological data only. Our results demonstrate that the AT seismic model is able to provide higher-quality hypocenter locations than the previous velocity models. Earthquake locations are consistent with the subsurface geological structures and show a high degree of spatial correlation with specific lithostratigraphic units, suggesting a lithological control on the seismic activity evolution.
NONLINEAR STABILITY FOR EADY'S MODEL
Institute of Scientific and Technical Information of China (English)
LIU Yong-ming; QIU Ling-cun
2005-01-01
Poincaré type integral inequality plays an important role in the study of nonlinear stability ( in the sense of Arnold's second theorem) for three-dimensional quasigeostophic flow. The nonlinear stability of Eady's model is one of the most important cases in the application of the method. But the best nonlinear stability criterion obtained so far and the linear stability criterion are not coincident. The two criteria coincide only when the period of the channel is infinite.additional conservation law of momentum and by rigorous estimate of integral inequality. So the new nonlinear stability criterion was obtained, which shows that for Eady 's model in the periodic channel, the linear stable implies the nonlinear stable.
Decision Making Agent Searching for Markov Models in Near-Deterministic World
Matuz, Gabor
2011-01-01
Reinforcement learning has solid foundations, but becomes inefficient in partially observed (non-Markovian) environments. Thus, a learning agent -born with a representation and a policy- might wish to investigate to what extent the Markov property holds. We propose a learning architecture that utilizes combinatorial policy optimization to overcome non-Markovity and to develop efficient behaviors, which are easy to inherit, tests the Markov property of the behavioral states, and corrects against non-Markovity by running a deterministic factored Finite State Model, which can be learned. We illustrate the properties of architecture in the near deterministic Ms. Pac-Man game. We analyze the architecture from the point of view of evolutionary, individual, and social learning.
Deterministic Method for Obtaining Nominal and Uncertainty Models of CD Drives
DEFF Research Database (Denmark)
Vidal, Enrique Sanchez; Stoustrup, Jakob; Andersen, Palle;
2002-01-01
properties. The method provides a systematic way to derive a nominal average model as well as a structures multiplicative input uncertainty model, and it is demonstrated how to apply mu-theory to design a controller based on the models obtained that meets certain robust performance criteria.......In this paper a deterministic method for obtaining the nominal and uncertainty models of the focus loop in a CD-player is presented based on parameter identification and measurements in the focus loop of 12 actual CD drives that differ by having worst-case behaviors with respect to various...
Theory and applications of a deterministic approximation to the coalescent model.
Jewett, Ethan M; Rosenberg, Noah A
2014-05-01
Under the coalescent model, the random number nt of lineages ancestral to a sample is nearly deterministic as a function of time when nt is moderate to large in value, and it is well approximated by its expectation E[nt]. In turn, this expectation is well approximated by simple deterministic functions that are easy to compute. Such deterministic functions have been applied to estimate allele age, effective population size, and genetic diversity, and they have been used to study properties of models of infectious disease dynamics. Although a number of simple approximations of E[nt] have been derived and applied to problems of population-genetic inference, the theoretical accuracy of the resulting approximate formulas and the inferences obtained using these approximations is not known, and the range of problems to which they can be applied is not well understood. Here, we demonstrate general procedures by which the approximation nt≈E[nt] can be used to reduce the computational complexity of coalescent formulas, and we show that the resulting approximations converge to their true values under simple assumptions. Such approximations provide alternatives to exact formulas that are computationally intractable or numerically unstable when the number of sampled lineages is moderate or large. We also extend an existing class of approximations of E[nt] to the case of multiple populations of time-varying size with migration among them. Our results facilitate the use of the deterministic approximation nt≈E[nt] for deriving functionally simple, computationally efficient, and numerically stable approximations of coalescent formulas under complicated demographic scenarios.
Nonlinear models for autoregressive conditional heteroskedasticity
DEFF Research Database (Denmark)
Teräsvirta, Timo
This paper contains a brief survey of nonlinear models of autore- gressive conditional heteroskedasticity. The models in question are parametric nonlinear extensions of the original model by Engle (1982). After presenting the individual models, linearity testing and parameter estimation...... are discussed. Forecasting volatility with nonlinear models is considered. Finally, parametric nonlinear models based on multi- plicative decomposition of the variance receive attention....
Stochastic and deterministic multiscale models for systems biology: an auxin-transport case study
Directory of Open Access Journals (Sweden)
King John R
2010-03-01
Full Text Available Abstract Background Stochastic and asymptotic methods are powerful tools in developing multiscale systems biology models; however, little has been done in this context to compare the efficacy of these methods. The majority of current systems biology modelling research, including that of auxin transport, uses numerical simulations to study the behaviour of large systems of deterministic ordinary differential equations, with little consideration of alternative modelling frameworks. Results In this case study, we solve an auxin-transport model using analytical methods, deterministic numerical simulations and stochastic numerical simulations. Although the three approaches in general predict the same behaviour, the approaches provide different information that we use to gain distinct insights into the modelled biological system. We show in particular that the analytical approach readily provides straightforward mathematical expressions for the concentrations and transport speeds, while the stochastic simulations naturally provide information on the variability of the system. Conclusions Our study provides a constructive comparison which highlights the advantages and disadvantages of each of the considered modelling approaches. This will prove helpful to researchers when weighing up which modelling approach to select. In addition, the paper goes some way to bridging the gap between these approaches, which in the future we hope will lead to integrative hybrid models.
Energy Technology Data Exchange (ETDEWEB)
Charbonnier, D.
2004-12-15
The physical phenomena observed in turbomachines are generally three-dimensional and unsteady. A recent study revealed that a three-dimensional steady simulation can reproduce the time-averaged unsteady phenomena, since the steady flow field equations integrate deterministic stresses. The objective of this work is thus to develop an unsteady deterministic stresses model. The analogy with turbulence makes it possible to write transport equations for these stresses. The equations are implemented in steady flow solver and e model for the energy deterministic fluxes is also developed and implemented. Finally, this work shows that a three-dimensional steady simulation, by taking into account unsteady effects with transport equations of deterministic stresses, increases the computing time by only approximately 30 %, which remains very interesting compared to an unsteady simulation. (author)
Uniform deterministic dictionaries
DEFF Research Database (Denmark)
Ruzic, Milan
2008-01-01
We present a new analysis of the well-known family of multiplicative hash functions, and improved deterministic algorithms for selecting “good” hash functions. The main motivation is realization of deterministic dictionaries with fast lookups and reasonably fast updates. The model of computation...
Directory of Open Access Journals (Sweden)
Lisbet Sneftrup Hansen
2014-07-01
Full Text Available There is a growing requirement to generate more precise model simulations and forecasts of flows in urban drainage systems in both offline and online situations. Data assimilation tools are hence needed to make it possible to include system measurements in distributed, physically-based urban drainage models and reduce a number of unavoidable discrepancies between the model and reality. The latter can be achieved partly by inserting measured water levels from the sewer system into the model. This article describes how deterministic updating of model states in this manner affects a simulation, and then evaluates and documents the performance of this particular updating procedure for flow forecasting. A hypothetical case study and synthetic observations are used to illustrate how the Update method works and affects downstream nodes. A real case study in a 544 ha urban catchment furthermore shows that it is possible to improve the 20-min forecast of water levels in an updated node and the three-hour forecast of flow through a downstream node, compared to simulations without updating. Deterministic water level updating produces better forecasts when implemented in large networks with slow flow dynamics and with measurements from upstream basins that contribute significantly to the flow at the forecast location.
Noaman, B. A.; Korman, C. E.
2009-04-01
In this paper, we present a deterministic approach to calculate terminal current noise characteristics in semiconductor devices in the framework of semiclassical transport based on the spherical harmonics of the Boltzmann Transport Equation. The model relies on the solution of the Boltzmann equation in the frequency domain with special initial and boundary conditions. The terminal current fluctuation is directly related to scattering without the additional Langevin noise term added to the calculation. Simulation results are presented for the terminal current spectral density for a 1-D n+nn+ structure due to elastic-acoustic and intervally scattering.
A deterministic model for the growth of non-conducting electrical tree structures
Dodd, S J
2003-01-01
Electrical treeing is of interest to the electrical generation, transmission and distribution industries as it is one of the causes of insulation failure in electrical machines, switchgear and transformer bushings. In this paper a deterministic electrical tree growth model is described. The model is based on electrostatics and local electron avalanches to model partial discharge activity within the growing tree structure. Damage to the resin surrounding the tree structure is dependent on the local electrostatic energy dissipation by partial discharges within the tree structure and weighted by the magnitudes of the local electric fields in the resin surrounding the tree structure. The model is successful in simulating the formation of branched structures without the need of a random variable, a requirement of previous stochastic models. Instability in the spatial development of partial discharges within the tree structure takes the role of the stochastic element as used in previous models to produce branched t...
A Review of Deterministic Optimization Methods in Engineering and Management
Directory of Open Access Journals (Sweden)
Ming-Hua Lin
2012-01-01
Full Text Available With the increasing reliance on modeling optimization problems in practical applications, a number of theoretical and algorithmic contributions of optimization have been proposed. The approaches developed for treating optimization problems can be classified into deterministic and heuristic. This paper aims to introduce recent advances in deterministic methods for solving signomial programming problems and mixed-integer nonlinear programming problems. A number of important applications in engineering and management are also reviewed to reveal the usefulness of the optimization methods.
Roirand, Q.; Missoum-Benziane, D.; Thionnet, A.; Laiarinandrasana, L.
2017-09-01
Textile composites are composed of 3D complex architecture. To assess the durability of such engineering structures, the failure mechanisms must be highlighted. Examinations of the degradation have been carried out thanks to tomography. The present work addresses a numerical damage model dedicated to the simulation of the crack initiation and propagation at the scale of the warp yarns. For the 3D woven composites under study, loadings in tension and combined tension and bending were considered. Based on an erosion procedure of broken elements, the failure mechanisms have been modelled on 3D periodic cells by finite element calculations. The breakage of one element was determined using a failure criterion at the mesoscopic scale based on the yarn stress at failure. The results were found to be in good agreement with the experimental data for the two kinds of macroscopic loadings. The deterministic approach assumed a homogeneously distributed stress at failure all over the integration points in the meshes of woven composites. A stochastic approach was applied to a simple representative elementary periodic cell. The distribution of the Weibull stress at failure was assigned to the integration points using a Monte Carlo simulation. It was shown that this stochastic approach allowed more realistic failure simulations avoiding the idealised symmetry due to the deterministic modelling. In particular, the stochastic simulations performed have shown several variations of the stress as well as strain at failure and the failure modes of the yarn.
Nonlinear Control of Heartbeat Models
Directory of Open Access Journals (Sweden)
Witt Thanom
2011-02-01
Full Text Available This paper presents a novel application of nonlinear control theory to heartbeat models. Existing heartbeat models are investigated and modified by incorporating the control input as a pacemaker to provide the control channel. A nonlinear feedback linearization technique is applied to force the output of the systems to generate artificial electrocardiogram (ECG signal using discrete data as the reference inputs. The synthetic ECG may serve as a flexible signal source to assess the effectiveness of a diagnostic ECG signal-processing device.
McDonnell, Lisa K; Hume, Patria A; Nolte, Volker
2013-09-01
The aim of this narrative review was to propose a deterministic model based on a review of previous research documenting the evidence for the associations between average kayak velocity and kinematic variables in sprint kayaking. Literature was reviewed after searching electronic databases using key words 'kayak,' 'biomechanics,' 'velocity,' 'kinematics,' and 'performance.' Our kinematic deterministic model for sprint kayaking performance shows that the average kayak velocity is determined by kayak stroke displacement and stroke time. Stroke time had the strongest correlation with 200-m race time (r = 0.86, p < 0.001), and stroke rate (inversely proportional to stroke time) was strongly correlated with average horizontal velocity over two consecutive strokes at race pace (r = -0.83, p < 0.05). Increased stroke rate via decreased absolute water phase time and increased relative water phase time were indicative of more elite performance. There was no significant relationship between stroke displacement and velocity; however, a large decrease in stroke displacement may be detrimental to performance. Individual characteristics may be responsible for a paddlers' ability to achieve and sustain a given stroke rate. Coaches should theoretically focus interventions on increasing stroke rate while maintaining stroke displacement; however this hypothesis should be confirmed with prospective studies.
A Distributed and Deterministic TDMA Algorithm for Write-All-With-Collision Model
Arumugam, Mahesh
2008-01-01
Several self-stabilizing time division multiple access (TDMA) algorithms are proposed for sensor networks. In addition to providing a collision-free communication service, such algorithms enable the transformation of programs written in abstract models considered in distributed computing literature into a model consistent with sensor networks, i.e., write all with collision (WAC) model. Existing TDMA slot assignment algorithms have one or more of the following properties: (i) compute slots using a randomized algorithm, (ii) assume that the topology is known upfront, and/or (iii) assign slots sequentially. If these algorithms are used to transform abstract programs into programs in WAC model then the transformed programs are probabilistically correct, do not allow the addition of new nodes, and/or converge in a sequential fashion. In this paper, we propose a self-stabilizing deterministic TDMA algorithm where a sensor is aware of only its neighbors. We show that the slots are assigned to the sensors in a concu...
[Deterministic and stochastic identification of neurophysiologic systems].
Piatigorskiĭ, B Ia; Kostiukov, A I; Chinarov, V A; Cherkasskiĭ, V L
1984-01-01
The paper deals with deterministic and stochastic identification methods applied to the concrete neurophysiological systems. The deterministic identification was carried out for the system: efferent fibres-muscle. The obtained transition characteristics demonstrated dynamic nonlinearity of the system. Identification of the neuronal model and the "afferent fibres-synapses-neuron" system in mollusc Planorbis corneus was carried out using the stochastic methods. For these purpose the Wiener method of stochastic identification was expanded for the case of pulse trains as input and output signals. The weight of the nonlinear component in the Wiener model and accuracy of the model prediction were quantitatively estimated. The results obtained proves the possibility of using these identification methods for various neurophysiological systems.
Castaneda-Lopez, Homero
A methodology for detecting and locating defects or discontinuities on the outside covering of coated metal underground pipelines subjected to cathodic protection has been addressed. On the basis of wide range AC impedance signals for various frequencies applied to a steel-coated pipeline system and by measuring its corresponding transfer function under several laboratory simulation scenarios, a physical laboratory setup of an underground cathodic-protected, coated pipeline was built. This model included different variables and elements that exist under real conditions, such as soil resistivity, soil chemical composition, defect (holiday) location in the pipeline covering, defect area and geometry, and level of cathodic protection. The AC impedance data obtained under different working conditions were used to fit an electrical transmission line model. This model was then used as a tool to fit the impedance signal for different experimental conditions and to establish trends in the impedance behavior without the necessity of further experimental work. However, due to the chaotic nature of the transfer function response of this system under several conditions, it is believed that non-deterministic models based on pattern recognition algorithms are suitable for field condition analysis. A non-deterministic approach was used for experimental analysis by applying an artificial neural network (ANN) algorithm based on classification analysis capable of studying the pipeline system and differentiating the variables that can change impedance conditions. These variables include level of cathodic protection, location of discontinuities (holidays), and severity of corrosion. This work demonstrated a proof-of-concept for a well-known technique and a novel algorithm capable of classifying impedance data for experimental results to predict the exact location of the active holidays and defects on the buried pipelines. Laboratory findings from this procedure are promising, and
Deterministic Partial Differential Equation Model for Dose Calculation in Electron Radiotherapy
Duclous, Roland; Frank, Martin
2009-01-01
Treatment with high energy ionizing radiation is one of the main methods in modern cancer therapy that is in clinical use. During the last decades, two main approaches to dose calculation were used, Monte Carlo simulations and semi-empirical models based on Fermi-Eyges theory. A third way to dose calculation has only recently attracted attention in the medical physics community. This approach is based on the deterministic kinetic equations of radiative transfer. Starting from these, we derive a macroscopic partial differential equation model for electron transport in tissue. This model involves an angular closure in the phase space. It is exact for the free-streaming and the isotropic regime. We solve it numerically by a newly developed HLLC scheme based on [BerCharDub], that exactly preserves key properties of the analytical solution on the discrete level. Several numerical results for test cases from the medical physics literature are presented.
Directory of Open Access Journals (Sweden)
Claude Gérard
2014-01-01
Full Text Available Recently, a molecular pathway linking inflammation to cell transformation has been discovered. This molecular pathway rests on a positive inflammatory feedback loop between NF-κB, Lin28, Let-7 microRNA and IL6, which leads to an epigenetic switch allowing cell transformation. A transient activation of an inflammatory signal, mediated by the oncoprotein Src, activates NF-κB, which elicits the expression of Lin28. Lin28 decreases the expression of Let-7 microRNA, which results in higher level of IL6 than achieved directly by NF-κB. In turn, IL6 can promote NF-κB activation. Finally, IL6 also elicits the synthesis of STAT3, which is a crucial activator for cell transformation. Here, we propose a computational model to account for the dynamical behavior of this positive inflammatory feedback loop. By means of a deterministic model, we show that an irreversible bistable switch between a transformed and a non-transformed state of the cell is at the core of the dynamical behavior of the positive feedback loop linking inflammation to cell transformation. The model indicates that inhibitors (tumor suppressors or activators (oncogenes of this positive feedback loop regulate the occurrence of the epigenetic switch by modulating the threshold of inflammatory signal (Src needed to promote cell transformation. Both stochastic simulations and deterministic simulations of a heterogeneous cell population suggest that random fluctuations (due to molecular noise or cell-to-cell variability are able to trigger cell transformation. Moreover, the model predicts that oncogenes/tumor suppressors respectively decrease/increase the robustness of the non-transformed state of the cell towards random fluctuations. Finally, the model accounts for the potential effect of competing endogenous RNAs, ceRNAs, on the dynamics of the epigenetic switch. Depending on their microRNA targets, the model predicts that ceRNAs could act as oncogenes or tumor suppressors by regulating
Likelihood-Based Inference in Nonlinear Error-Correction Models
DEFF Research Database (Denmark)
Kristensen, Dennis; Rahbæk, Anders
We consider a class of vector nonlinear error correction models where the transfer function (or loadings) of the stationary relation- ships is nonlinear. This includes in particular the smooth transition models. A general representation theorem is given which establishes the dynamic properties...... of the process in terms of stochastic and deter- ministic trends as well as stationary components. In particular, the behaviour of the cointegrating relations is described in terms of geo- metric ergodicity. Despite the fact that no deterministic terms are included, the process will have both stochastic trends...... and a linear trend in general. Gaussian likelihood-based estimators are considered for the long- run cointegration parameters, and the short-run parameters. Asymp- totic theory is provided for these and it is discussed to what extend asymptotic normality and mixed normaity can be found. A simulation study...
Pest persistence and eradication conditions in a deterministic model for sterile insect release.
Gordillo, Luis F
2015-01-01
The release of sterile insects is an environment friendly pest control method used in integrated pest management programmes. Difference or differential equations based on Knipling's model often provide satisfactory qualitative descriptions of pest populations subject to sterile release at relatively high densities with large mating encounter rates, but fail otherwise. In this paper, I derive and explore numerically deterministic population models that include sterile release together with scarce mating encounters in the particular case of species with long lifespan and multiple matings. The differential equations account separately the effects of mating failure due to sterile male release and the frequency of mating encounters. When insects spatial spread is incorporated through diffusion terms, computations reveal the possibility of steady pest persistence in finite size patches. In the presence of density dependence regulation, it is observed that sterile release might contribute to induce sudden suppression of the pest population.
Nonlinear time series modelling: an introduction
Simon M. Potter
1999-01-01
Recent developments in nonlinear time series modelling are reviewed. Three main types of nonlinear models are discussed: Markov Switching, Threshold Autoregression and Smooth Transition Autoregression. Classical and Bayesian estimation techniques are described for each model. Parametric tests for nonlinearity are reviewed with examples from the three types of models. Finally, forecasting and impulse response analysis is developed.
Glazier, Paul S; Robins, Matthew T
2012-03-01
Although deterministic models may provide a useful starting point for sports biomechanists examining the mechanical aspects of athletic performance, they have inherent weaknesses that limit their proctical application. Specifically, their inability to provide substantive information about coordinative movement patterns or 'technique' suggests that sports biomechanists must explore alternative paradigms and theoretical frameworks if they are to fulfil their main aims of improving performance and reducing injury risk. We believe that dynamical systems theory and its associated analytical tools can provide a useful adjunct to more traditional paradigms in sport biomechanics, such as deterministic modelling, which have only made a limit contribution to the enhancement of knowledge.
Guarnaccia, Claudio; Quartieri, Joseph; Tepedino, Carmine
2017-06-01
One of the most hazardous physical polluting agents, considering their effects on human health, is acoustical noise. Airports are a strong source of acoustical noise, due to the airplanes turbines, to the aero-dynamical noise of transits, to the acceleration or the breaking during the take-off and landing phases of aircrafts, to the road traffic around the airport, etc.. The monitoring and the prediction of the acoustical level emitted by airports can be very useful to assess the impact on human health and activities. In the airports noise scenario, thanks to flights scheduling, the predominant sources may have a periodic behaviour. Thus, a Time Series Analysis approach can be adopted, considering that a general trend and a seasonal behaviour can be highlighted and used to build a predictive model. In this paper, two different approaches are adopted, thus two predictive models are constructed and tested. The first model is based on deterministic decomposition and is built composing the trend, that is the long term behaviour, the seasonality, that is the periodic component, and the random variations. The second model is based on seasonal autoregressive moving average, and it belongs to the stochastic class of models. The two different models are fitted on an acoustical level dataset collected close to the Nice (France) international airport. Results will be encouraging and will show good prediction performances of both the adopted strategies. A residual analysis is performed, in order to quantify the forecasting error features.
Directory of Open Access Journals (Sweden)
Dubitzky Werner
2010-09-01
Full Text Available Abstract Background A gene-regulatory network (GRN refers to DNA segments that interact through their RNA and protein products and thereby govern the rates at which genes are transcribed. Creating accurate dynamic models of GRNs is gaining importance in biomedical research and development. To improve our understanding of continuous deterministic modeling methods employed to construct dynamic GRN models, we have carried out a comprehensive comparative study of three commonly used systems of ordinary differential equations: The S-system (SS, artificial neural networks (ANNs, and the general rate law of transcription (GRLOT method. These were thoroughly evaluated in terms of their ability to replicate the reference models' regulatory structure and dynamic gene expression behavior under varying conditions. Results While the ANN and GRLOT methods appeared to produce robust models even when the model parameters deviated considerably from those of the reference models, SS-based models exhibited a notable loss of performance even when the parameters of the reverse-engineered models corresponded closely to those of the reference models: this is due to the high number of power terms in the SS-method, and the manner in which they are combined. In cross-method reverse-engineering experiments the different characteristics, biases and idiosynchracies of the methods were revealed. Based on limited training data, with only one experimental condition, all methods produced dynamic models that were able to reproduce the training data accurately. However, an accurate reproduction of regulatory network features was only possible with training data originating from multiple experiments under varying conditions. Conclusions The studied GRN modeling methods produced dynamic GRN models exhibiting marked differences in their ability to replicate the reference models' structure and behavior. Our results suggest that care should be taking when a method is chosen for a
Modelling Loudspeaker Non-Linearities
DEFF Research Database (Denmark)
Agerkvist, Finn T.
2007-01-01
This paper investigates different techniques for modelling the non-linear parameters of the electrodynamic loudspeaker. The methods are tested not only for their accuracy within the range of original data, but also for the ability to work reasonable outside that range, and it is demonstrated...... that polynomial expansions are rather poor at this, whereas an inverse polynomial expansion or localized fitting functions such as the gaussian are better suited for modelling the Bl-factor and compliance. For the inductance the sigmoid function is shown to give very good results. Finally the time varying...
Processing Approach of Non-linear Adjustment Models in the Space of Non-linear Models
Institute of Scientific and Technical Information of China (English)
LI Chaokui; ZHU Qing; SONG Chengfang
2003-01-01
This paper investigates the mathematic features of non-linear models and discusses the processing way of non-linear factors which contributes to the non-linearity of a nonlinear model. On the basis of the error definition, this paper puts forward a new adjustment criterion, SGPE.Last, this paper investigates the solution of a non-linear regression model in the non-linear model space and makes the comparison between the estimated values in non-linear model space and those in linear model space.
Nonlinear rheological models for structured interfaces
Sagis, L.M.C.
2010-01-01
The GENERIC formalism is a formulation of nonequilibrium thermodynamics ideally suited to develop nonlinear constitutive equations for the stress–deformation behavior of complex interfaces. Here we develop a GENERIC model for multiphase systems with interfaces displaying nonlinear viscoelastic stres
Solution of deterministic-stochastic epidemic models by dynamical Monte Carlo method
Aièllo, O. E.; Haas, V. J.; daSilva, M. A. A.; Caliri, A.
2000-07-01
This work is concerned with dynamical Monte Carlo (MC) method and its application to models originally formulated in a continuous-deterministic approach. Specifically, a susceptible-infected-removed-susceptible (SIRS) model is used in order to analyze aspects of the dynamical MC algorithm and achieve its applications in epidemic contexts. We first examine two known approaches to the dynamical interpretation of the MC method and follow with the application of one of them in the SIRS model. The working method chosen is based on the Poisson process where hierarchy of events, properly calculated waiting time between events, and independence of the events simulated, are the basic requirements. To verify the consistence of the method, some preliminary MC results are compared against exact steady-state solutions and other general numerical results (provided by Runge-Kutta method): good agreement is found. Finally, a space-dependent extension of the SIRS model is introduced and treated by MC. The results are interpreted under and in accordance with aspects of the herd-immunity concept.
Modelling of nonlinear shoaling based on stochastic evolution equations
DEFF Research Database (Denmark)
Kofoed-Hansen, Henrik; Rasmussen, Jørgen Hvenekær
1998-01-01
A one-dimensional stochastic model is derived to simulate the transformation of wave spectra in shallow water including generation of bound sub- and super-harmonics, near-resonant triad wave interaction and wave breaking. Boussinesq type equations with improved linear dispersion characteristics...... are recast into evolution equations for the complex amplitudes, and serve as the underlying deterministic model. Next, a set of evolution equations for the cumulants is derived. By formally introducing the well-known Gaussian closure hypothesis, nonlinear evolution equations for the power spectrum...... and bispectrum are derived. A simple description of depth-induced wave breaking is incorporated in the model equations, assuming that the total rate of dissipation may be distributed in proportion to the spectral energy density on each discrete frequency. The proposed phase-averaged model is compared...
Directory of Open Access Journals (Sweden)
Rama.S
2017-03-01
Full Text Available Project planning is the important task in many areas like construction, resource allocation and many. A sequence of activities has to be performed to complete one task. Each activity has its unique processing time and all together to identify the critical activities which affect the completion of the project. In this paper the probabilistic and deterministic models to determine the project completion time and also the critical activities are considered. A case study on building construction project has been performed to demonstrate the application of the above said models. The two project scheduling namely PERT and CPM are used to determine numerically the different types of floating times of each activity and hence determined the critical path which plays an important role in the project completion time. Also a linear programing model has been developed to reduce the project completion time which optimize the resource allocation. To apply these techniques numerically the primary data from a housing project company in a metropolitan city has been taken, the network diagram of the activities involved in the building construction project has been drawn and the results are tabulated.
Energy Technology Data Exchange (ETDEWEB)
Boyer, D; Miramontes, O [Departamento de Sistemas Complejos, Instituto de Fisica, Universidad Nacional Autonoma de Mexico, DF 04510 (Mexico); Larralde, H [Instituto de Ciencias Fisicas, Universidad Nacional Autonoma de Mexico, Apartado Postal 48-3, Cuernavaca, 62251 Morelos (Mexico)], E-mail: boyer@fisica.unam.mx, E-mail: octavio@fisica.unam.mx, E-mail: hernan@ce.fis.unam.mx
2009-10-30
Many studies on animal and human movement patterns report the existence of scaling laws and power-law distributions. Whereas a number of random walk models have been proposed to explain observations, in many situations individuals actually rely on mental maps to explore strongly heterogeneous environments. In this work, we study a model of a deterministic walker, visiting sites randomly distributed on the plane and with varying weight or attractiveness. At each step, the walker minimizes a function that depends on the distance to the next unvisited target (cost) and on the weight of that target (gain). If the target weight distribution is a power law, p(k) {approx} k{sup -{beta}}, in some range of the exponent {beta}, the foraging medium induces movements that are similar to Levy flights and are characterized by non-trivial exponents. We explore variations of the choice rule in order to test the robustness of the model and argue that the addition of noise has a limited impact on the dynamics in strongly disordered media.
Boyer, D.; Miramontes, O.; Larralde, H.
2009-10-01
Many studies on animal and human movement patterns report the existence of scaling laws and power-law distributions. Whereas a number of random walk models have been proposed to explain observations, in many situations individuals actually rely on mental maps to explore strongly heterogeneous environments. In this work, we study a model of a deterministic walker, visiting sites randomly distributed on the plane and with varying weight or attractiveness. At each step, the walker minimizes a function that depends on the distance to the next unvisited target (cost) and on the weight of that target (gain). If the target weight distribution is a power law, p(k) ~ k-β, in some range of the exponent β, the foraging medium induces movements that are similar to Lévy flights and are characterized by non-trivial exponents. We explore variations of the choice rule in order to test the robustness of the model and argue that the addition of noise has a limited impact on the dynamics in strongly disordered media.
A data driven nonlinear stochastic model for blood glucose dynamics.
Zhang, Yan; Holt, Tim A; Khovanova, Natalia
2016-03-01
The development of adequate mathematical models for blood glucose dynamics may improve early diagnosis and control of diabetes mellitus (DM). We have developed a stochastic nonlinear second order differential equation to describe the response of blood glucose concentration to food intake using continuous glucose monitoring (CGM) data. A variational Bayesian learning scheme was applied to define the number and values of the system's parameters by iterative optimisation of free energy. The model has the minimal order and number of parameters to successfully describe blood glucose dynamics in people with and without DM. The model accounts for the nonlinearity and stochasticity of the underlying glucose-insulin dynamic process. Being data-driven, it takes full advantage of available CGM data and, at the same time, reflects the intrinsic characteristics of the glucose-insulin system without detailed knowledge of the physiological mechanisms. We have shown that the dynamics of some postprandial blood glucose excursions can be described by a reduced (linear) model, previously seen in the literature. A comprehensive analysis demonstrates that deterministic system parameters belong to different ranges for diabetes and controls. Implications for clinical practice are discussed. This is the first study introducing a continuous data-driven nonlinear stochastic model capable of describing both DM and non-DM profiles.
Adaptive regression for modeling nonlinear relationships
Knafl, George J
2016-01-01
This book presents methods for investigating whether relationships are linear or nonlinear and for adaptively fitting appropriate models when they are nonlinear. Data analysts will learn how to incorporate nonlinearity in one or more predictor variables into regression models for different types of outcome variables. Such nonlinear dependence is often not considered in applied research, yet nonlinear relationships are common and so need to be addressed. A standard linear analysis can produce misleading conclusions, while a nonlinear analysis can provide novel insights into data, not otherwise possible. A variety of examples of the benefits of modeling nonlinear relationships are presented throughout the book. Methods are covered using what are called fractional polynomials based on real-valued power transformations of primary predictor variables combined with model selection based on likelihood cross-validation. The book covers how to formulate and conduct such adaptive fractional polynomial modeling in the s...
Lei, Jinzhi; Yvinec, Romain; Zhuge, Changjing
2012-01-01
This paper considers adiabatic reduction in a model of stochastic gene expression with bursting transcription. We prove that an adiabatic reduction can be performed in a stochastic slow/fast system with a jump Markov process. In the gene expression model, the production of mRNA (the fast variable) is assumed to follow a compound Poisson process (the phenomena called bursting in molecular biology) and the production of protein (the slow variable) is linear as a function of mRNA. When the dynamics of mRNA is assumed to be faster than the protein dynamics (due to a mRNA degradation rate larger than for the protein) we prove that, with the appropriate scaling, the bursting phenomena can be transmitted to the slow variable. We show that the reduced equation is either a stochastic differential equation with a jump Markov process or a deterministic ordinary differential equation depending on the scaling that is appropriate. These results are significant because adiabatic reduction techniques seem to have not been de...
Energy Technology Data Exchange (ETDEWEB)
Farmer, J.C.
1997-10-01
An integrated predictive model is being developed to account for the effects of localized environmental conditions in crevices on the initiation and propagation of pits. A deterministic calculation is used to estimate the accumulation of hydrogen ions (pH suppression) in the crevice solution due to the hydrolysis of dissolved metals. Pit initiation and growth within the crevice is then dealt with by either a probabilistic model, or an equivalent deterministic model. Ultimately, the role of intergranular corrosion will have to be considered. While the strategy presented here is very promising, the integrated model is not yet ready for precise quantitative predictions. Empirical expressions for the rate of penetration based upon experimental crevice corrosion data can be used in the interim period, until the integrated model can be refined. Bounding calculations based upon such empirical expressions can provide important insight into worst-case scenarios.
Deterministic and stochastic bifurcations in the Hindmarsh-Rose neuronal model.
Dtchetgnia Djeundam, S R; Yamapi, R; Kofane, T C; Aziz-Alaoui, M A
2013-09-01
We analyze the bifurcations occurring in the 3D Hindmarsh-Rose neuronal model with and without random signal. When under a sufficient stimulus, the neuron activity takes place; we observe various types of bifurcations that lead to chaotic transitions. Beside the equilibrium solutions and their stability, we also investigate the deterministic bifurcation. It appears that the neuronal activity consists of chaotic transitions between two periodic phases called bursting and spiking solutions. The stochastic bifurcation, defined as a sudden change in character of a stochastic attractor when the bifurcation parameter of the system passes through a critical value, or under certain condition as the collision of a stochastic attractor with a stochastic saddle, occurs when a random Gaussian signal is added. Our study reveals two kinds of stochastic bifurcation: the phenomenological bifurcation (P-bifurcations) and the dynamical bifurcation (D-bifurcations). The asymptotical method is used to analyze phenomenological bifurcation. We find that the neuronal activity of spiking and bursting chaos remains for finite values of the noise intensity.
A deterministic partial differential equation model for dose calculation in electron radiotherapy
Energy Technology Data Exchange (ETDEWEB)
Duclous, R; Dubroca, B [CELIA and IMB Laboratories, Bordeaux University, 33405 Talence (France); Frank, M, E-mail: duclous@celia.u-bordeaux1.f, E-mail: dubroca@celia.u-bordeaux1.f, E-mail: frank@mathcces.rwth-aachen.d [Department of Mathematics and Center for Computational Engineering Science, RWTH Aachen University, Schinkelstr. 2, 52062 Aachen (Germany)
2010-07-07
High-energy ionizing radiation is a prominent modality for the treatment of many cancers. The approaches to electron dose calculation can be categorized into semi-empirical models (e.g. Fermi-Eyges, convolution-superposition) and probabilistic methods (e.g. Monte Carlo). A third approach to dose calculation has only recently attracted attention in the medical physics community. This approach is based on the deterministic kinetic equations of radiative transfer. We derive a macroscopic partial differential equation model for electron transport in tissue. This model involves an angular closure in the phase space. It is exact for the free streaming and the isotropic regime. We solve it numerically by a newly developed HLLC scheme based on Berthon et al (2007 J. Sci. Comput. 31 347-89) that exactly preserves the key properties of the analytical solution on the discrete level. We discuss several test cases taken from the medical physics literature. A test case with an academic Henyey-Greenstein scattering kernel is considered. We compare our model to a benchmark discrete ordinate solution. A simplified model of electron interactions with tissue is employed to compute the dose of an electron beam in a water phantom, and a case of irradiation of the vertebral column. Here our model is compared to the PENELOPE Monte Carlo code. In the academic example, the fluences computed with the new model and a benchmark result differ by less than 1%. The depths at half maximum differ by less than 0.6%. In the two comparisons with Monte Carlo, our model gives qualitatively reasonable dose distributions. Due to the crude interaction model, these so far do not have the accuracy needed in clinical practice. However, the new model has a computational cost that is less than one-tenth of the cost of a Monte Carlo simulation. In addition, simulations can be set up in a similar way as a Monte Carlo simulation. If more detailed effects such as coupled electron-photon transport, bremsstrahlung
A deterministic partial differential equation model for dose calculation in electron radiotherapy
Duclous, R.; Dubroca, B.; Frank, M.
2010-07-01
High-energy ionizing radiation is a prominent modality for the treatment of many cancers. The approaches to electron dose calculation can be categorized into semi-empirical models (e.g. Fermi-Eyges, convolution-superposition) and probabilistic methods (e.g. Monte Carlo). A third approach to dose calculation has only recently attracted attention in the medical physics community. This approach is based on the deterministic kinetic equations of radiative transfer. We derive a macroscopic partial differential equation model for electron transport in tissue. This model involves an angular closure in the phase space. It is exact for the free streaming and the isotropic regime. We solve it numerically by a newly developed HLLC scheme based on Berthon et al (2007 J. Sci. Comput. 31 347-89) that exactly preserves the key properties of the analytical solution on the discrete level. We discuss several test cases taken from the medical physics literature. A test case with an academic Henyey-Greenstein scattering kernel is considered. We compare our model to a benchmark discrete ordinate solution. A simplified model of electron interactions with tissue is employed to compute the dose of an electron beam in a water phantom, and a case of irradiation of the vertebral column. Here our model is compared to the PENELOPE Monte Carlo code. In the academic example, the fluences computed with the new model and a benchmark result differ by less than 1%. The depths at half maximum differ by less than 0.6%. In the two comparisons with Monte Carlo, our model gives qualitatively reasonable dose distributions. Due to the crude interaction model, these so far do not have the accuracy needed in clinical practice. However, the new model has a computational cost that is less than one-tenth of the cost of a Monte Carlo simulation. In addition, simulations can be set up in a similar way as a Monte Carlo simulation. If more detailed effects such as coupled electron-photon transport, bremsstrahlung
Pool, Maria; Carrera, Jesus; Alcolea, Andres
2014-05-01
Inversion of the spatial variability of transmissivity (T) in groundwater models can be handled using either stochastic or deterministic (i.e., geology-based zonation) approaches. While stochastic methods predominate in scientific literature, they have never been formally compared to deterministic approaches, preferred by practitioners, for large aquifer models. We use both approaches to model groundwater flow and solute transport in the Mar del Plata aquifer, where seawater intrusion is a major threat to freshwater resources. The relative performance of the two approaches is evaluated in terms of model fits to head and concentration data (available for nearly a century), plausibility of the estimated T fields and their ability to predict transport. We also address the impact of using T data from large scale (i.e., pumping test) and small scale (i.e., specific capacity) on the calibration of this regional coastal aquifer. We find that stochastic models, based upon conditional estimation and simulation techniques, identify some of the geological features (river deposit channels) and yield better fits to calibration data than the much simpler geology-based deterministic model. However, the latter demonstrates much greater robustness for predicting sea water intrusion and for incorporating concentrations as calibration data. We conclude that qualitative geological information is extremely rich in identifying variability patterns and should be explicitly included in the calibration of stochastic models.
Nonlinear Modelling of Low Frequency Loudspeakers
DEFF Research Database (Denmark)
Olsen, Erling Sandermann
1997-01-01
In the Danish LoDist project on distortion from dynamic low-frequency loudspeakers, a detailed nonlinear model of loudspeakers has been developed. The model has been implemented in a PC program so that it can be used to create signals for listening tests and analysis. Also, different methods...... for describing the nonlinearities have been developed. Different aspects of modelling loudspeaker nonlinearities are discussed, and the program is briefly described....
Nonlinear Modelling of Low Frequency Loudspeakers
DEFF Research Database (Denmark)
Olsen, Erling Sandermann
1997-01-01
In the Danish LoDist project on distortion from dynamic low frequency loudspeakers a detailed nonlinear model of loudspeakers has been developed. The model has been implemented in a PC program so that it can be used to create signals for listening tests and analysis. Also, different methods...... for describing the nonlinearities have been developed. Different aspects of modelling loudspeaker nonlinearities are discussed and the program is briefly demonstrated....
Energy Technology Data Exchange (ETDEWEB)
Scott, B.R.
1995-12-01
Individuals who work at nuclear reactor facilities can be at risk for deterministic effects in the skin from exposure to discrete {Beta}- and {gamma}-emitting ({Beta}{gamma}E) sources (e.g., {Beta}{gamma}E hot particles) on the skin or clothing. Deterministic effects are non-cancer effects that have a threshold and increase in severity as dose increases (e.g., ulcer in skin). Hot {Beta}{gamma}E particles are {sup 60}Co- or nuclear fuel-derived particles with diameters > 10 {mu}m and < 3 mm and contain at least 3.7 kBq (0.1 {mu}Ci) of radioactivity. For such {Beta}{gamma}E sources on the skin, it is the beta component of the dose that is most important. To develop exposure limitation systems that adequately control exposure of workers to discrete {Beta}{gamma}E sources, models are needed for systems that adequately control exposure of workers to discrete {Beta}{gamma}E sources, models are needed for evaluating the risk of deterministic effects of localized {Beta} irradiation of the skin. The purpose of this study was to develop dose-rate and irradiated-area dependent, response-surface models for evaluating risks of significant deterministic effects of localized irradiation of the skin by discrete {Beta}{gamma}E sources and to use modeling results to recommend approaches to limiting occupational exposure to such sources. The significance of the research results as follows: (1) response-surface models are now available for evaluating the risk of specific deterministic effects of localized irradiation of the skin; (2) modeling results have been used to recommend approaches to limiting occupational exposure of workers to {Beta} radiation from {Beta}{gamma}E sources on the skin or on clothing; and (3) the generic irradiated-volume, weighting-factor approach to limiting exposure can be applied to other organs including the eye, the ear, and organs of the respiratory or gastrointestinal tract and can be used for both deterministic and stochastic effects.
Computational Models for Nonlinear Aeroelastic Systems Project
National Aeronautics and Space Administration — Clear Science Corp. and Duke University propose to develop and demonstrate new and efficient computational methods of modeling nonlinear aeroelastic systems. The...
Model Updating Nonlinear System Identification Toolbox Project
National Aeronautics and Space Administration — ZONA Technology (ZONA) proposes to develop an enhanced model updating nonlinear system identification (MUNSID) methodology that utilizes flight data with...
Baldi, Pierre; Rosen-Zvi, Michal
2005-10-01
Machine learning methods that can handle variable-size structured data such as sequences and graphs include Bayesian networks (BNs) and Recursive Neural Networks (RNNs). In both classes of models, the data is modeled using a set of observed and hidden variables associated with the nodes of a directed acyclic graph. In BNs, the conditional relationships between parent and child variables are probabilistic, whereas in RNNs they are deterministic and parameterized by neural networks. Here, we study the formal relationship between both classes of models and show that when the source nodes variables are observed, RNNs can be viewed as limits, both in distribution and probability, of BNs with local conditional distributions that have vanishing covariance matrices and converge to delta functions. Conditions for uniform convergence are also given together with an analysis of the behavior and exactness of Belief Propagation (BP) in 'deterministic' BNs. Implications for the design of mixed architectures and the corresponding inference algorithms are briefly discussed.
Deterministic Mean-Field Ensemble Kalman Filtering
Law, Kody J. H.
2016-05-03
The proof of convergence of the standard ensemble Kalman filter (EnKF) from Le Gland, Monbet, and Tran [Large sample asymptotics for the ensemble Kalman filter, in The Oxford Handbook of Nonlinear Filtering, Oxford University Press, Oxford, UK, 2011, pp. 598--631] is extended to non-Gaussian state-space models. A density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence k between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d<2k. The fidelity of approximation of the true distribution is also established using an extension of the total variation metric to random measures. This is limited by a Gaussian bias term arising from nonlinearity/non-Gaussianity of the model, which arises in both deterministic and standard EnKF. Numerical results support and extend the theory.
Linear and Nonlinear Electrical Models of Neurons for Hopfield Neural Network
Sarwar, Farah; Iqbal, Shaukat; Hussain, Muhammad Waqar
2016-11-01
A novel electrical model of neuron is proposed in this presentation. The suggested neural network model has linear/nonlinear input-output characteristics. This new deterministic model has joint biological properties in excellent agreement with the earlier deterministic neuron model of Hopfield and Tank and to the stochastic neuron model of McCulloch and Pitts. It is an accurate portrayal of differential equation presented by Hopfield and Tank to mimic neurons. Operational amplifiers, resistances, capacitor, and diodes are used to design this system. The presented biological model of neurons remains to be advantageous for simulations. Impulse response is studied and conferred to certify the stability and strength of this innovative model. A simple illustration is mapped to demonstrate the exactness of the intended system. Precisely mapped illustration exhibits 100 % accurate results.
Stochastic and Deterministic Modeling Of Watershed-Scale Suspended Sediment Delivery Timescales
Pizzuto, J. E.; Skalak, K.; Karwan, D. L.
2016-12-01
The influence of storage on the timing of suspended sediment delivery resists prediction. We use sediment budgets to define the probability of storage in fluvial networks and generate a probability density function (pdf) to quantify storage timescales. Storage probability decreases with increasing watershed area, while waiting time pdfs are heavy-tailed power law functions with waiting times from 104 years and exponents from -0.8 to -1.8. When combined with an in-channel drift velocity, deterministic or stochastic (i.e., random walk) suspended sediment routing models can be derived. The fraction of particles transported to a basin outlet without being stored is (1-q)n, where q is the fraction of suspended sediment stored per km and n is the downstream distance; hence storage rather than transport controls travel time when travel distances are large. With power law waiting time pdfs, basin scale travel time pdfs are also power laws. Our routing models also predict how storage filters sediment signals delivered to depositional basins. With typical parameters and 1000 km of transport, a high frequency, 10-year sinusoidal input signal is delayed by 12.5 times its input period, damped by a factor of 380, and output as a power law. A low-frequency, 104-year sinusoidal input signal is delayed by 0.15 times its input period, damped by a factor of 3, and the output signal retains its sinusoidal input form but with a power law "tail". Thus, storage filters high frequency signals, possibly including those from anthropogenic sources, but transmits low frequency signals from tectonics or climate change with greater fidelity. If the waiting time pdf is "stable", and network path lengths are obtained theoretically, a quasi-analytical solution is obtained for travel times through entire networks created by step function input signals. Applications include quantifying lag times for watershed restoration, and unraveling signals recorded in sedimentary basins.
Mathematical modeling and applications in nonlinear dynamics
Merdan, Hüseyin
2016-01-01
The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems. Provides methods for mathematical models with switching, thresholds, and impulses, each of particular importance for discontinuous processes Includes qualitative analysis of behaviors on Tumor-Immune Systems and methods of analysis for DNA, neural networks and epidemiology Introduces...
Effect of nonlinearity in hybrid kinetic Monte Carlo-continuum models.
Balter, Ariel; Lin, Guang; Tartakovsky, Alexandre M
2012-01-01
Recently there has been interest in developing efficient ways to model heterogeneous surface reactions with hybrid computational models that couple a kinetic Monte Carlo (KMC) model for a surface to a finite-difference model for bulk diffusion in a continuous domain. We consider two representative problems that validate a hybrid method and show that this method captures the combined effects of nonlinearity and stochasticity. We first validate a simple deposition-dissolution model with a linear rate showing that the KMC-continuum hybrid agrees with both a fully deterministic model and its analytical solution. We then study a deposition-dissolution model including competitive adsorption, which leads to a nonlinear rate, and show that in this case the KMC-continuum hybrid and fully deterministic simulations do not agree. However, we are able to identify the difference as a natural result of the stochasticity coming from the KMC surface process. Because KMC captures inherent fluctuations, we consider it to be more realistic than a purely deterministic model. Therefore, we consider the KMC-continuum hybrid to be more representative of a real system.
Nonlinear stochastic modeling of river dissolved-oxygen
Energy Technology Data Exchange (ETDEWEB)
Tabios, G.Q. III.
1984-01-01
An important aspect of water quality modeling is forecasting water quality variables for real-time management and control applications to enhance, maintain and sustain desirable water qualities. The major objective of this research is to develop daily time series models for forecasting river dissolved-oxygen (DO). The modeling approach adopted herein combines deterministic and stochastic concepts for determining properties of the DO process based on time series data and dynamic mechanisms governing the said process. This is accomplished by deriving a general DO stochastic model structure based on a modified Streeter-Phelps DO-BOD dynamic model. Then some types of nonlinear models namely, self-exciting threshold autoregressive-moving average (SETARMA), amplitude-dependent autoregressive (ADAR) and bilinear (BL) models, and the class of linear autoregressive-moving average (ARMA) models are adopted for model identification and parameter estimation. Six stream-water quality gaging stations located in the eastern portion of the continental U.S.A. are utilized in this study. Various orders of ARMA, SETARMA, ADAR and BL models are fitted to the data. Results obtained indicated that ADAR and BL models are superior for one-step ahead forecasts, while SETARMA models are better for forecasts of longer lead times. In general, the SETARMA, ADAR and BL models show promise as alternative models for river DO time series modeling and forecasting with unique advantages in each.
Flick, D.; Hoang, H.M.; Alvarez, G.; Laguerre, O.
2012-01-01
Many deterministic models have been developed to describe heat transfer in the cold chain and to predict the thermal and microbial evolution of food products. However, different product items will have different evolutions because of the variability of logistic supply chain, equipment design and operating conditions, etc. The objective of this study is to propose a general methodology to predict the evolution of food products and its variability along a cold chain. This evolution is chara...
Zhen Xu; Y. Jun Xu
2016-01-01
Predicting dissolved oxygen (DO) change at a high frequency in water bodies is useful for water quality management. In this study, we developed a deterministic model that can predict hourly DO change in a water body with high frequency weather parameters. The study was conducted during August 2008–July 2009 in a eutrophic shallow lake in Louisiana, USA. An environment monitoring buoy was deployed to record DO, water temperature and chlorophyll-a concentration at 15-min intervals, and hourly w...
An approach to model reactor core nodalization for deterministic safety analysis
Salim, Mohd Faiz; Samsudin, Mohd Rafie; Mamat @ Ibrahim, Mohd Rizal; Roslan, Ridha; Sadri, Abd Aziz; Farid, Mohd Fairus Abd
2016-01-01
Adopting good nodalization strategy is essential to produce an accurate and high quality input model for Deterministic Safety Analysis (DSA) using System Thermal-Hydraulic (SYS-TH) computer code. The purpose of such analysis is to demonstrate the compliance against regulatory requirements and to verify the behavior of the reactor during normal and accident conditions as it was originally designed. Numerous studies in the past have been devoted to the development of the nodalization strategy for small research reactor (e.g. 250kW) up to the bigger research reactor (e.g. 30MW). As such, this paper aims to discuss the state-of-arts thermal hydraulics channel to be employed in the nodalization for RTP-TRIGA Research Reactor specifically for the reactor core. At present, the required thermal-hydraulic parameters for reactor core, such as core geometrical data (length, coolant flow area, hydraulic diameters, and axial power profile) and material properties (including the UZrH1.6, stainless steel clad, graphite reflector) have been collected, analyzed and consolidated in the Reference Database of RTP using standardized methodology, mainly derived from the available technical documentations. Based on the available information in the database, assumptions made on the nodalization approach and calculations performed will be discussed and presented. The development and identification of the thermal hydraulics channel for the reactor core will be implemented during the SYS-TH calculation using RELAP5-3D® computer code. This activity presented in this paper is part of the development of overall nodalization description for RTP-TRIGA Research Reactor under the IAEA Norwegian Extra-Budgetary Programme (NOKEBP) mentoring project on Expertise Development through the Analysis of Reactor Thermal-Hydraulics for Malaysia, denoted as EARTH-M.
Deterministic modeling of the impact of underground structures on urban groundwater temperature.
Attard, Guillaume; Rossier, Yvan; Winiarski, Thierry; Eisenlohr, Laurent
2016-12-01
Underground structures have a major influence on groundwater temperature and have a major contribution on the anthropogenic heat fluxes into urban aquifers. Groundwater temperature is crucial for resource management as it can provide operational sustainability indicators for groundwater quality and geothermal energy. Here, a three dimensional heat transport modeling approach was conducted to quantify the thermally affected zone (TAZ, i.e. increase in temperature of more than +0.5°C) caused by two common underground structures: (1) an impervious structure and (2) a draining structure. These design techniques consist in (1) ballasting the underground structure in order to resist hydrostatic pressure, or (2) draining the groundwater under the structure in order to remove the hydrostatic pressure. The volume of the TAZ caused by these underground structures was shown to range from 14 to 20 times the volume of the underground structure. Additionally, the cumulative impact of underground structures was assessed under average thermal conditions at the scale of the greater Lyon area (France). The heat island effect caused by underground structures was highlighted in the business center of the city. Increase in temperature of more than +4.5°C were locally put in evidence. The annual heat flow from underground structures to the urban aquifer was computed deterministically and represents 4.5GW·h. Considering these impacts, the TAZ of deep underground structures should be taken into account in the geothermal potential mapping. Finally, the amount of heat energy provided should be used as an indicator of heating potential in these areas.
Ghita, Gabriel M.
Our study aim to design a useful neutron signature characterization device based on 3He detectors, a standard neutron detection methodology used in homeland security applications. Research work involved simulation of the generation, transport, and detection of the leakage radiation from Special Nuclear Materials (SNM). To accomplish research goals, we use a new methodology to fully characterize a standard "1-Ci" Plutonium-Beryllium (Pu-Be) neutron source based on 3-D computational radiation transport methods, employing both deterministic SN and Monte Carlo methodologies. Computational model findings were subsequently validated through experimental measurements. Achieved results allowed us to design, build, and laboratory-test a Nickel composite alloy shield that enables the neutron leakage spectrum from a standard Pu-Be source to be transformed, through neutron scattering interactions in the shield, into a very close approximation of the neutron spectrum leaking from a large, subcritical mass of Weapons Grade Plutonium (WGPu) metal. This source will make possible testing with a nearly exact reproduction of the neutron spectrum from a 6.67 kg WGPu mass equivalent, but without the expense or risk of testing detector components with real materials. Moreover, over thirty moderator materials were studied in order to characterize their neutron energy filtering potential. Specific focus was made to establish the limits of He-3 spectroscopy using ideal filter materials. To demonstrate our methodology, we present the optimally detected spectral differences between SNM materials (Plutonium and Uranium), metal and oxide, using ideal filter materials. Finally, using knowledge gained from previous studies, the design of a He-3 spectroscopy system neutron detector, simulated entirely via computational methods, is proposed to resolve the spectra from SNM neutron sources of high interest. This was accomplished by replacing ideal filters with real materials, and comparing reaction
An approach to model reactor core nodalization for deterministic safety analysis
Energy Technology Data Exchange (ETDEWEB)
Salim, Mohd Faiz, E-mail: mohdfaizs@tnb.com.my; Samsudin, Mohd Rafie, E-mail: rafies@tnb.com.my [Nuclear Energy Department, Regulatory Economics & Planning Division, Tenaga Nasional Berhad (Malaysia); Mamat Ibrahim, Mohd Rizal, E-mail: m-rizal@nuclearmalaysia.gov.my [Prototypes & Plant Development Center, Malaysian Nuclear Agency (Malaysia); Roslan, Ridha, E-mail: ridha@aelb.gov.my; Sadri, Abd Aziz [Nuclear Installation Divisions, Atomic Energy Licensing Board (Malaysia); Farid, Mohd Fairus Abd [Reactor Technology Center, Malaysian Nuclear Agency (Malaysia)
2016-01-22
Adopting good nodalization strategy is essential to produce an accurate and high quality input model for Deterministic Safety Analysis (DSA) using System Thermal-Hydraulic (SYS-TH) computer code. The purpose of such analysis is to demonstrate the compliance against regulatory requirements and to verify the behavior of the reactor during normal and accident conditions as it was originally designed. Numerous studies in the past have been devoted to the development of the nodalization strategy for small research reactor (e.g. 250kW) up to the bigger research reactor (e.g. 30MW). As such, this paper aims to discuss the state-of-arts thermal hydraulics channel to be employed in the nodalization for RTP-TRIGA Research Reactor specifically for the reactor core. At present, the required thermal-hydraulic parameters for reactor core, such as core geometrical data (length, coolant flow area, hydraulic diameters, and axial power profile) and material properties (including the UZrH{sub 1.6}, stainless steel clad, graphite reflector) have been collected, analyzed and consolidated in the Reference Database of RTP using standardized methodology, mainly derived from the available technical documentations. Based on the available information in the database, assumptions made on the nodalization approach and calculations performed will be discussed and presented. The development and identification of the thermal hydraulics channel for the reactor core will be implemented during the SYS-TH calculation using RELAP5-3D{sup ®} computer code. This activity presented in this paper is part of the development of overall nodalization description for RTP-TRIGA Research Reactor under the IAEA Norwegian Extra-Budgetary Programme (NOKEBP) mentoring project on Expertise Development through the Analysis of Reactor Thermal-Hydraulics for Malaysia, denoted as EARTH-M.
Digital simulation and modeling of nonlinear stochastic systems
Energy Technology Data Exchange (ETDEWEB)
Richardson, J M; Rowland, J R
1981-04-01
Digitally generated solutions of nonlinear stochastic systems are not unique but depend critically on the numerical integration algorithm used. Some theoretical and practical implications of this dependence are examined. The Ito-Stratonovich controversy concerning the solution of nonlinear stochastic systems is shown to be more than a theoretical debate on maintaining Markov properties as opposed to utilizing the computational rules of ordinary calculus. The theoretical arguments give rise to practical considerations in the formation and solution of discrete models from continuous stochastic systems. Well-known numerical integration algorithms are shown not only to provide different solutions for the same stochastic system but also to correspond to different stochastic integral definitions. These correspondences are proved by considering first and second moments of solutions that result from different integration algorithms and then comparing the moments to those arising from various stochastic integral definitions. This algorithm-dependence of solutions is in sharp contrast to the deterministic and linear stochastic cases in which unique solutions are determined by any convergent numerical algorithm. Consequences of the relationship between stochastic system solutions and simulation procedures are presented for a nonlinear filtering example. Monte Carlo simulations and statistical tests are applied to the example to illustrate the determining role which computational procedures play in generating solutions.
Digital simulation and modeling of nonlinear stochastic systems
Energy Technology Data Exchange (ETDEWEB)
Richardson, J M; Rowland, J R
1980-01-01
Digitally generated solutions of nonlinear stochastic systems are not unique, but depend critically on the numerical integration algorithm used. Some theoretical and practical implications of this dependence are examined. The Ito-Stratonovich controversy concerning the solution of nonlinear stochastic systems is shown to be more than a theoretical debate on maintaining Markov properties as opposed to utilizing the computational rules of ordinary calculus. The theoretical arguments give rise to practical considerations in the formation and solution of discrete models from continuous stochastic systems. Well-known numerical integration algorithms are shown not only to provide different solutions for the same stochastic system, but also to correspond to different stochastic integral definitions. These correspondences are proved by considering first and second moments of solutions resulting from different integration algorithms and comparing the moments to those arising from various stochastic integral definitions. Monte Carlo simulations and statistical tests are applied to illustrate the determining role that computational procedures play in generating solutions. This algorithm dependence of solutions is in sharp contrast to the deterministic and linear stochastic cases, in which unique solutions are determined by any convergent numerical algorithm. Consequences of this relationship between stochastic system solutions and simulation procedures are presented for a nonlinear filtering example. 2 figures.
Optimal design for nonlinear response models
Fedorov, Valerii V
2013-01-01
Optimal Design for Nonlinear Response Models discusses the theory and applications of model-based experimental design with a strong emphasis on biopharmaceutical studies. The book draws on the authors' many years of experience in academia and the pharmaceutical industry. While the focus is on nonlinear models, the book begins with an explanation of the key ideas, using linear models as examples. Applying the linearization in the parameter space, it then covers nonlinear models and locally optimal designs as well as minimax, optimal on average, and Bayesian designs. The authors also discuss ada
Nonlinear cumulative damage model for multiaxial fatigue
Institute of Scientific and Technical Information of China (English)
SHANG De-guang; SUN Guo-qin; DENG Jing; YAN Chu-liang
2006-01-01
On the basis of the continuum fatigue damage theory,a nonlinear uniaxial fatigue cumulative damage model is first proposed.In order to describe multiaxial fatigue damage characteristics,a nonlinear multiaxial fatigue cumulative damage model is developed based on the critical plane approach,The proposed model can consider the multiaxial fatigue limit,mean hydrostatic pressure and the unseparated characteristic for the damage variables and loading parameters.The recurrence formula of fatigue damage model was derived under multilevel loading,which is used to predict multiaxial fatigue life.The results showed that the proposed nonlinear multiaxial fatigue cumulative damage model is better than Miner's rule.
Completely integrable models of nonlinear optics
Indian Academy of Sciences (India)
Andrey I Maimistov
2001-11-01
The models of the nonlinear optics in which solitons appeared are considered. These models are of paramount importance in studies of nonlinear wave phenomena. The classical examples of phenomena of this kind are the self-focusing, self-induced transparency and parametric interaction of three waves. At present there are a number of theories based on completely integrable systems of equations, which are, both, generations of the original known models and new ones. The modiﬁed Korteweg-de Vries equation, the nonlinear Schrödinger equation, the derivative nonlinear Schrödinger equation, Sine–Gordon equation, the reduced Maxwell–Bloch equation, Hirota equation, the principal chiral ﬁeld equations, and the equations of massive Thirring model are some soliton equations, which are usually to be found in nonlinear optics theory.
Pool, M.; Carrera, J.; Alcolea, A.; Bocanegra, E. M.
2015-12-01
Inversion of the spatial variability of transmissivity (T) in groundwater models can be handled using either stochastic or deterministic (i.e., geology-based zonation) approaches. While stochastic methods predominate in scientific literature, they have never been formally compared to deterministic approaches, preferred by practitioners, for regional aquifer models. We use both approaches to model groundwater flow and solute transport in the Mar del Plata aquifer, where seawater intrusion is a major threat to freshwater resources. The relative performance of the two approaches is evaluated in terms of (i) model fits to head and concentration data (available for nearly a century), (ii) geological plausibility of the estimated T fields, and (iii) their ability to predict transport. We also address the impact of conditioning the estimated fields on T data coming from either pumping tests interpreted with the Theis method or specific capacity values from step-drawdown tests. We find that stochastic models, based upon conditional estimation and simulation techniques, identify some of the geological features (river deposit channels and low transmissivity regions associated to quartzite outcrops) and yield better fits to calibration data than the much simpler geology-based deterministic model, which cannot properly address model structure uncertainty. However, the latter demonstrates much greater robustness for predicting sea water intrusion and for incorporating concentrations as calibration data. We attribute the poor performance, and underestimated uncertainty, of the stochastic simulations to estimation bias introduced by model errors. Qualitative geological information is extremely rich in identifying large-scale variability patterns, which are identified by stochastic models only in data rich areas, and should be explicitly included in the calibration process.
Designing Experiments for Nonlinear Models - An Introduction
Johnson, Rachel T.; Montgomery, Douglas C.
2009-01-01
The article of record as published may be found at http://dx.doi.org/10.1002/qre.1063 We illustrate the construction of Bayesian D-optimal designs for nonlinear models and compare the relative efficiency of standard designs with these designs for several models and prior distributions on the parameters. Through a relative efficiency analysis, we show that standard designs can perform well in situations where the nonlinear model is intrinsically linear. However, if the model is non...
Functional uniform priors for nonlinear modeling.
Bornkamp, Björn
2012-09-01
This article considers the topic of finding prior distributions when a major component of the statistical model depends on a nonlinear function. Using results on how to construct uniform distributions in general metric spaces, we propose a prior distribution that is uniform in the space of functional shapes of the underlying nonlinear function and then back-transform to obtain a prior distribution for the original model parameters. The primary application considered in this article is nonlinear regression, but the idea might be of interest beyond this case. For nonlinear regression the so constructed priors have the advantage that they are parametrization invariant and do not violate the likelihood principle, as opposed to uniform distributions on the parameters or the Jeffrey's prior, respectively. The utility of the proposed priors is demonstrated in the context of design and analysis of nonlinear regression modeling in clinical dose-finding trials, through a real data example and simulation.
Nonlinear extensions of a fractal-multifractal approach for environmental modeling
Energy Technology Data Exchange (ETDEWEB)
Cortis, A.; Puente, C.E.; Sivakumar, B.
2008-10-15
We present the extension of a deterministic fractal geometric procedure aimed at representing the complexity of the spatio-temporal patterns encountered in environmental applications. The original procedure, which is based on transformations of multifractal distributions via fractal functions, is extended through the introduction of nonlinear perturbations to the underlying iterated linear maps. We demonstrate how the nonlinear perturbations generate yet a richer collection of patterns by means of various simulations that include evolutions of patterns based on changes in their parameters and in their statistical and multifractal properties. It is shown that the nonlinear extensions yield structures that closely resemble complex hydrologic temporal data sets, such as rainfall and runoff time series, and width-functions of river networks as a function of distance from the basin outlet. The implications of this nonlinear approach for environmental modeling and prediction are discussed.
Non-linear finite element modeling
DEFF Research Database (Denmark)
Mikkelsen, Lars Pilgaard
The note is written for courses in "Non-linear finite element method". The note has been used by the author teaching non-linear finite element modeling at Civil Engineering at Aalborg University, Computational Mechanics at Aalborg University Esbjerg, Structural Engineering at the University...... on the governing equations and methods of implementing....
A deterministic model for highly contagious diseases: The case of varicella
Acedo, L.; Moraño, J.-A.; Santonja, F.-J.; Villanueva, R.-J.
2016-05-01
The classic nonlinear Kermack-McKendrick model based upon a system of differential equations has been widely applied to model the rise and fall of global pandemic and also seasonal epidemic by introducing a forced harmonic infectivity which would change throughout the year. These methods work well in their respective domains of applicability, and for certain diseases, but they fail when both seasonality and high infectivity are combined. In this paper we consider a Susceptible-Infected-Recovered, or SIR, model with two latent states to model the propagation and evolutionary history of varicella in humans. We show that infectivity can be calculated from real data and we find a nonstandard seasonal variation that cannot be fitted with a single harmonic. Moreover, we show that infectivity for the present strains of the virus has raised following a sigmoid function in a period of several centuries. This could allow the design of vaccination strategies and the study of the epidemiology of varicella and herpes zoster.
Nonlinear Resistivity for Magnetohydrodynamical Models
Lingam, Manasvi; Pfefferlé, David; Comisso, Luca; Bhattacharjee, Amitava
2016-01-01
A nonlinear current-dependent resistivity that accurately accounts for the collisional electron-ion momentum transfer rate is derived. It is shown that the Spitzer resistivity overestimates the resistivity in certain observationally relevant regimes. The nonlinear resistivity computed herein is a strictly decreasing function of the current, in contrast to some notable previous proposals. The relative importance of the new expression with respect to the well-established electron inertia and Hall terms is also examined. The subtle implications of this current-dependent resistivity are discussed in the context of plasma systems and phenomena such as magnetic reconnection.
Immonen, Taina; Gibson, Richard; Leitner, Thomas; Miller, Melanie A; Arts, Eric J; Somersalo, Erkki; Calvetti, Daniela
2012-11-01
We present a new hybrid stochastic-deterministic, spatially distributed computational model to simulate growth competition assays on a relatively immobile monolayer of peripheral blood mononuclear cells (PBMCs), commonly used for determining ex vivo fitness of human immunodeficiency virus type-1 (HIV-1). The novel features of our approach include incorporation of viral diffusion through a deterministic diffusion model while simulating cellular dynamics via a stochastic Markov chain model. The model accounts for multiple infections of target cells, CD4-downregulation, and the delay between the infection of a cell and the production of new virus particles. The minimum threshold level of infection induced by a virus inoculum is determined via a series of dilution experiments, and is used to determine the probability of infection of a susceptible cell as a function of local virus density. We illustrate how this model can be used for estimating the distribution of cells infected by either a single virus type or two competing viruses. Our model captures experimentally observed variation in the fitness difference between two virus strains, and suggests a way to minimize variation and dual infection in experiments.
Deterministic Chaos Model for Self-Organized Adaptive Networks in Atmospheric Flows
Selvam, A M
2003-01-01
The complex spatiotemporal patterns of atmospheric flows resulting from the cooperative existence of fluctuations ranging in size from millimeters to thousands of kilometers are found to exhibit long-range spatial and temporal correlations manifested as the selfsimilar fractal geometry to the global cloud cover pattern and the inverse power law form for the atmospheric eddy energy spectrum. Such long-range spatial and temporal correlations are ubiquitous to extended natural dynamical systems and is a signature of the strange attractor design characterizing deterministic chaos or self-organized criticality. The unified network of global atmospheric circulations is analogous to the neural networks of the human brain.
Nonlinear modeling of thermoacoustically driven energy cascade
Gupta, Prateek; Scalo, Carlo; Lodato, Guido
2016-11-01
We present an investigation of nonlinear energy cascade in thermoacoustically driven high-amplitude oscillations, from the initial weakly nonlinear regime to the shock wave dominated limit cycle. We develop a first principle based quasi-1D model for nonlinear wave propagation in a canonical minimal unit thermoacoustic device inspired by the experimental setup of Biwa et al.. Retaining up to quadratic nonlinear terms in the governing equations, we develop model equations for nonlinear wave propagation in the proximity of differentially heated no-slip boundaries. Furthermore, we discard the effects of acoustic streaming in the present study and focus on nonlinear energy cascade due to high amplitude wave propagation. Our model correctly predicts the observed exponential growth of the thermoacoustically amplified second harmonic, as well as the energy transfer rate to higher harmonics causing wave steepening. Moreover, we note that nonlinear coupling of local pressure with heat transfer reduces thermoacoustic amplification gradually thus causing the system to reach limit cycle exhibiting shock waves. Throughout, we verify the results from the quasi-1D model with fully compressible Navier-Stokes simulations.
Directory of Open Access Journals (Sweden)
A.K. Bhunia
2013-04-01
Full Text Available This paper deals with a deterministic inventory model developed for deteriorating items having two separate storage facilities (owned and rented warehouses due to limited capacity of the existing storage (owned warehouse with linear time dependent demand (increasing over a fixed finite time horizon. The model is formulated with infinite replenishment and the successive replenishment cycle lengths are in arithmetic progression. Partially backlogged shortages are allowed. The stocks of rented warehouse (RW are transported to the owned warehouse (OW in continuous release pattern. For this purpose, the model is formulated as a constrained non-linear mixed integer programming problem. For solving the problem, an advanced genetic algorithm (GA has been developed. This advanced GA is based on ranking selection, elitism, whole arithmetic crossover and non-uniform mutation dependent on the age of the population. Our objective is to determine the optimal replenishment number, lot-size of two-warehouses (OW and RW by maximizing the profit function. The model is illustrated with four numerical examples and sensitivity analyses of the optimal solution are performed with respect to different parameters.
Model Updating Nonlinear System Identification Toolbox Project
National Aeronautics and Space Administration — ZONA Technology proposes to develop an enhanced model updating nonlinear system identification (MUNSID) methodology by adopting the flight data with state-of-the-art...
Comparing coefficients of nested nonlinear probability models
DEFF Research Database (Denmark)
Kohler, Ulrich; Karlson, Kristian Bernt; Holm, Anders
2011-01-01
In a series of recent articles, Karlson, Holm and Breen have developed a method for comparing the estimated coeffcients of two nested nonlinear probability models. This article describes this method and the user-written program khb that implements the method. The KHB-method is a general decomposi......In a series of recent articles, Karlson, Holm and Breen have developed a method for comparing the estimated coeffcients of two nested nonlinear probability models. This article describes this method and the user-written program khb that implements the method. The KHB-method is a general...... decomposition method that is unaffected by the rescaling or attenuation bias that arise in cross-model comparisons in nonlinear models. It recovers the degree to which a control variable, Z, mediates or explains the relationship between X and a latent outcome variable, Y*, underlying the nonlinear probability...
On a Nonlinear Model in Adiabatic Evolutions
Sun, Jie; Lu, Song-Feng
2016-08-01
In this paper, we study a kind of nonlinear model of adiabatic evolution in quantum search problem. As will be seen here, for this problem, there always exists a possibility that this nonlinear model can successfully solve the problem, while the linear model can not. Also in the same setting, when the overlap between the initial state and the final stare is sufficiently large, a simple linear adiabatic evolution can achieve O(1) time efficiency, but infinite time complexity for the nonlinear model of adiabatic evolution is needed. This tells us, it is not always a wise choice to use nonlinear interpolations in adiabatic algorithms. Sometimes, simple linear adiabatic evolutions may be sufficient for using. Supported by the National Natural Science Foundation of China under Grant Nos. 61402188 and 61173050. The first author also gratefully acknowledges the support from the China Postdoctoral Science Foundation under Grant No. 2014M552041
Computational Models for Nonlinear Aeroelastic Systems Project
National Aeronautics and Space Administration — Clear Science Corp. and Duke University propose to develop and demonstrate a new and efficient computational method of modeling nonlinear aeroelastic systems. The...
Non-linear Loudspeaker Unit Modelling
DEFF Research Database (Denmark)
Pedersen, Bo Rohde; Agerkvist, Finn T.
2008-01-01
Simulations of a 6½-inch loudspeaker unit are performed and compared with a displacement measurement. The non-linear loudspeaker model is based on the major nonlinear functions and expanded with time-varying suspension behaviour and flux modulation. The results are presented with FFT plots of three...... frequencies and different displacement levels. The model errors are discussed and analysed including a test with loudspeaker unit where the diaphragm is removed....
Deterministic dynamics of neural activity during absence seizures in rats
Ouyang, Gaoxiang; Li, Xiaoli; Dang, Chuangyin; Richards, Douglas A.
2009-04-01
The study of brain electrical activities in terms of deterministic nonlinear dynamics has recently received much attention. Forbidden ordinal patterns (FOP) is a recently proposed method to investigate the determinism of a dynamical system through the analysis of intrinsic ordinal properties of a nonstationary time series. The advantages of this method in comparison to others include simplicity and low complexity in computation without further model assumptions. In this paper, the FOP of the EEG series of genetic absence epilepsy rats from Strasbourg was examined to demonstrate evidence of deterministic dynamics during epileptic states. Experiments showed that the number of FOP of the EEG series grew significantly from an interictal to an ictal state via a preictal state. These findings indicated that the deterministic dynamics of neural networks increased significantly in the transition from the interictal to the ictal states and also suggested that the FOP measures of the EEG series could be considered as a predictor of absence seizures.
Liao, Wenlin; Dai, Yifan; Xie, Xuhui; Zhou, Lin
2014-07-01
Ion beam figuring (IBF) is established for the final precision figuring of high-performance optical components, where the figuring accuracy is guaranteed by the stability of the removal function and the solution accuracy of the dwell time. In this deterministic method, the figuring process can be represented by a two-dimensional (2D) convolution operation of a constant removal function and the dwell time. However, we have found that the current 2D convolution operation cannot factually describe the IBF process of curved surfaces, which neglects the influences of the projection distortion and the workpiece geometry on the removal function. Consequently, the current 2D convolution algorithm would influence the solution accuracy for the dwell time and reduce the convergence of the figuring process. In this part, based on the material removal characteristics of IBF, a mathematical model of the removal function is developed theoretically and verified experimentally. Research results show that the removal function during IBF of a curved surface is actually a dynamic function in the 2D convolution algorithm. The mathematical modeling of the dynamic removal function provides theoretical foundations for our proposed new algorithm in the next part, and final verification experiments indicate that this algorithm can effectively improve the accuracy of the dwell time solution for the IBF of curved surfaces.
Identifying nonlinear biomechanical models by multicriteria analysis
Srdjevic, Zorica; Cveticanin, Livija
2012-02-01
In this study, the methodology developed by Srdjevic and Cveticanin (International Journal of Industrial Ergonomics 34 (2004) 307-318) for the nonbiased (objective) parameter identification of the linear biomechanical model exposed to vertical vibrations is extended to the identification of n-degree of freedom (DOF) nonlinear biomechanical models. The dynamic performance of the n-DOF nonlinear model is described in terms of response functions in the frequency domain, such as the driving-point mechanical impedance and seat-to-head transmissibility function. For randomly generated parameters of the model, nonlinear equations of motion are solved using the Runge-Kutta method. The appropriate data transformation from the time-to-frequency domain is performed by a discrete Fourier transformation. Squared deviations of the response functions from the target values are used as the model performance evaluation criteria, thus shifting the problem into the multicriteria framework. The objective weights of criteria are obtained by applying the Shannon entropy concept. The suggested methodology is programmed in Pascal and tested on a 4-DOF nonlinear lumped parameter biomechanical model. The identification process over the 2000 generated sets of parameters lasts less than 20 s. The model response obtained with the imbedded identified parameters correlates well with the target values, therefore, justifying the use of the underlying concept and the mathematical instruments and numerical tools applied. It should be noted that the identified nonlinear model has an improved accuracy of the biomechanical response compared to the accuracy of a linear model.
The Mathematics of Psychotherapy: A Nonlinear Model of Change Dynamics.
Schiepek, Gunter; Aas, Benjamin; Viol, Kathrin
2016-07-01
Psychotherapy is a dynamic process produced by a complex system of interacting variables. Even though there are qualitative models of such systems the link between structure and function, between network and network dynamics is still missing. The aim of this study is to realize these links. The proposed model is composed of five state variables (P: problem severity, S: success and therapeutic progress, M: motivation to change, E: emotions, I: insight and new perspectives) interconnected by 16 functions. The shape of each function is modified by four parameters (a: capability to form a trustful working alliance, c: mentalization and emotion regulation, r: behavioral resources and skills, m: self-efficacy and reward expectation). Psychologically, the parameters play the role of competencies or traits, which translate into the concept of control parameters in synergetics. The qualitative model was transferred into five coupled, deterministic, nonlinear difference equations generating the dynamics of each variable as a function of other variables. The mathematical model is able to reproduce important features of psychotherapy processes. Examples of parameter-dependent bifurcation diagrams are given. Beyond the illustrated similarities between simulated and empirical dynamics, the model has to be further developed, systematically tested by simulated experiments, and compared to empirical data.
Nonlinear model predictive control theory and algorithms
Grüne, Lars
2017-01-01
This book offers readers a thorough and rigorous introduction to nonlinear model predictive control (NMPC) for discrete-time and sampled-data systems. NMPC schemes with and without stabilizing terminal constraints are detailed, and intuitive examples illustrate the performance of different NMPC variants. NMPC is interpreted as an approximation of infinite-horizon optimal control so that important properties like closed-loop stability, inverse optimality and suboptimality can be derived in a uniform manner. These results are complemented by discussions of feasibility and robustness. An introduction to nonlinear optimal control algorithms yields essential insights into how the nonlinear optimization routine—the core of any nonlinear model predictive controller—works. Accompanying software in MATLAB® and C++ (downloadable from extras.springer.com/), together with an explanatory appendix in the book itself, enables readers to perform computer experiments exploring the possibilities and limitations of NMPC. T...
Nonlinear optical model for strip plasmonic waveguides
DEFF Research Database (Denmark)
Lysenko, Oleg; Bache, Morten; Lavrinenko, Andrei
2016-01-01
This paper presents a theoretical model of nonlinear optical properties for strip plasmonic waveguides. The particular waveguides geometry that we investigate contains a gold core, adhesion layers, and silicon dioxide cladding. It is shown that the third-order susceptibility of the gold core...... significantly depends on the layer thickness and has the dominant contribution to the effective third-order susceptibility of the long-range plasmon polariton mode. This results in two nonlinear optical effects in plasmonic waveguides, which we experimentally observed and reported in [Opt. Lett. 41, 317 (2016......)]. The first effect is the nonlinear power saturation of the plasmonic mode, and the second effect is the spectral broadening of the plasmonic mode. Both nonlinear plasmonic effects can be used for practical applications and their appropriate model will be important for further developments in communication...
The integrated model for solving the single-period deterministic inventory routing problem
Rahim, Mohd Kamarul Irwan Abdul; Abidin, Rahimi; Iteng, Rosman; Lamsali, Hendrik
2016-08-01
This paper discusses the problem of efficiently managing inventory and routing problems in a two-level supply chain system. Vendor Managed Inventory (VMI) policy is an integrating decisions between a supplier and his customers. We assumed that the demand at each customer is stationary and the warehouse is implementing a VMI. The objective of this paper is to minimize the inventory and the transportation costs of the customers for a two-level supply chain. The problem is to determine the delivery quantities, delivery times and routes to the customers for the single-period deterministic inventory routing problem (SP-DIRP) system. As a result, a linear mixed-integer program is developed for the solutions of the SP-DIRP problem.
Damage detection of structures identified with deterministic-stochastic models using seismic data.
Huang, Ming-Chih; Wang, Yen-Po; Chang, Ming-Lian
2014-01-01
A deterministic-stochastic subspace identification method is adopted and experimentally verified in this study to identify the equivalent single-input-multiple-output system parameters of the discrete-time state equation. The method of damage locating vector (DLV) is then considered for damage detection. A series of shaking table tests using a five-storey steel frame has been conducted. Both single and multiple damage conditions at various locations have been considered. In the system identification analysis, either full or partial observation conditions have been taken into account. It has been shown that the damaged stories can be identified from global responses of the structure to earthquakes if sufficiently observed. In addition to detecting damage(s) with respect to the intact structure, identification of new or extended damages of the as-damaged counterpart has also been studied. This study gives further insights into the scheme in terms of effectiveness, robustness, and limitation for damage localization of frame systems.
Topological approximation of the nonlinear Anderson model
Milovanov, Alexander V.; Iomin, Alexander
2014-06-01
We study the phenomena of Anderson localization in the presence of nonlinear interaction on a lattice. A class of nonlinear Schrödinger models with arbitrary power nonlinearity is analyzed. We conceive the various regimes of behavior, depending on the topology of resonance overlap in phase space, ranging from a fully developed chaos involving Lévy flights to pseudochaotic dynamics at the onset of delocalization. It is demonstrated that the quadratic nonlinearity plays a dynamically very distinguished role in that it is the only type of power nonlinearity permitting an abrupt localization-delocalization transition with unlimited spreading already at the delocalization border. We describe this localization-delocalization transition as a percolation transition on the infinite Cayley tree (Bethe lattice). It is found in the vicinity of the criticality that the spreading of the wave field is subdiffusive in the limit t →+∞. The second moment of the associated probability distribution grows with time as a power law ∝ tα, with the exponent α =1/3 exactly. Also we find for superquadratic nonlinearity that the analog pseudochaotic regime at the edge of chaos is self-controlling in that it has feedback on the topology of the structure on which the transport processes concentrate. Then the system automatically (without tuning of parameters) develops its percolation point. We classify this type of behavior in terms of self-organized criticality dynamics in Hilbert space. For subquadratic nonlinearities, the behavior is shown to be sensitive to the details of definition of the nonlinear term. A transport model is proposed based on modified nonlinearity, using the idea of "stripes" propagating the wave process to large distances. Theoretical investigations, presented here, are the basis for consistency analysis of the different localization-delocalization patterns in systems with many coupled degrees of freedom in association with the asymptotic properties of the
Nonlinear modeling of an aerospace object dynamics
Davydov, I. E.; Davydov, E. I.
2017-01-01
Here are presented the scientific results, obtained by motion modeling of complicated technical systems of aerospace equipment with consideration of nonlinearities. Computerized panel that allows to measure mutual influence of the system's motion and stabilization device with consideration of its real characteristics has been developed. Analysis of motion stability of a system in general has been carried out and time relationships of the system's motion taking in account nonlinearities are presented.
Nonlinear chaotic model for predicting storm surges
Siek, M.; Solomatine, D.P.
This paper addresses the use of the methods of nonlinear dynamics and chaos theory for building a predictive chaotic model from time series. The chaotic model predictions are made by the adaptive local models based on the dynamical neighbors found in the reconstructed phase space of the observables.
On the nonlinear modeling of ring oscillators
Elwakil, Ahmed S.
2009-06-01
We develop higher-order nonlinear models of three-stage and five-stage ring oscillators based on a novel inverter model. The oscillation condition and oscillation frequency are derived and compared to classical linear model analysis. Two important special cases for five-stage ring oscillators are also studied. Numerical simulations are shown. © 2009 World Scientific Publishing Company.
Directory of Open Access Journals (Sweden)
Jun Wu
2016-01-01
Full Text Available Pallet pooling is a basis for the operation of a city joint distribution system. Pallet allocation is a key problem for the success of a pallet pool. This article considers a multi-station, multi-period, and multi-type pallet allocation problem over a pallet pool in a city joint distribution system. First of all, we develop a deterministic model to optimally allocate pallets when managers have perfect knowledge of the information that will be available. By case studies, we show that this model can help managers to make scientific decisions. The influence of transportation capacity on decisions is shown by numerical simulation. And we propose managers should use both demand forecasting and leasing and renting tactics to minimization allocation cost. Then, we propose a multi-scenario model to optimally allocate pallets when some uncertain parameters cannot be estimated through historical data. The application of this multi-scenario model is also illustrated.
Correlations and Non-Linear Probability Models
DEFF Research Database (Denmark)
Breen, Richard; Holm, Anders; Karlson, Kristian Bernt
2014-01-01
the dependent variable of the latent variable model and its predictor variables. We show how this correlation can be derived from the parameters of non-linear probability models, develop tests for the statistical significance of the derived correlation, and illustrate its usefulness in two applications. Under......Although the parameters of logit and probit and other non-linear probability models are often explained and interpreted in relation to the regression coefficients of an underlying linear latent variable model, we argue that they may also be usefully interpreted in terms of the correlations between...... certain circumstances, which we explain, the derived correlation provides a way of overcoming the problems inherent in cross-sample comparisons of the parameters of non-linear probability models....
Modeling of the vibrating beam accelerometer nonlinearities
Romanowski, P. A.; Knop, R. C.
Successful modeling and processing of the output of a quartz Vibrating Beam Accelerometer (VBA), whose errors are inherently nonlinear with respect to input acceleration, are reported. The VBA output, with two signals that are frequencies of vibrating quartz beams, has inherent higher-order terms. In order to avoid vibration rectification errors, the signal output must be sampled at a rapid rate and the output must be reduced using a nonlinear model. The present model, with acceleration as a function of frequency, is derived by a least-squares process where the covariance matrix is obtained from simulated data. The system performance is found to be acceptable to strategic levels, and it is shown that a vibration rectification error of 400 micrograms/sq g can be reduced to 4 micrograms/sq g by using the processor electronics and a nonlinear model.
Nonlinear observer design for a nonlinear string/cable FEM model using contraction theory
DEFF Research Database (Denmark)
Turkyilmaz, Yilmaz; Jouffroy, Jerome; Egeland, Olav
Contraction theory is a recently developed nonlinear analysis tool which may be useful for solving a variety of nonlinear control problems. In this paper, using Contraction theory, a nonlinear observer is designed for a general nonlinear cable/string FEM (Finite Element Method) model. The cable...
Nonlinear observer design for a nonlinear string/cable FEM model using contraction theory
DEFF Research Database (Denmark)
Turkyilmaz, Yilmaz; Jouffroy, Jerome; Egeland, Olav
Contraction theory is a recently developed nonlinear analysis tool which may be useful for solving a variety of nonlinear control problems. In this paper, using Contraction theory, a nonlinear observer is designed for a general nonlinear cable/string FEM (Finite Element Method) model. The cable...
A nonlinear constitutive model for magnetostrictive materials
Institute of Scientific and Technical Information of China (English)
Xin'en Liu; Xiaojing Zheng
2005-01-01
A general nonlinear constitutive model is proposed for magnetostrictive materials, based on the important physical fact that a nonlinear part of the elastic strain produced by a pre-stress is related to the magnetic domain rotation or movement and is responsible for the change of the maximum magnetostrictive strain with the pre-stress. To avoid the complicity of determining the tensor function describing the nonlinear elastic strain part, this paper proposes a simplified model by means of linearizing the nonlinear function.For the convenience of engineering applications, the expressions of the 3-D (bulk), 2-D (film) and 1-D (rod) models are, respectively, given for an isotropic material and their applicable ranges are also discussed. By comparison with the experimental data of a Terfenol-D rod, it is found that the proposed model can accurately predict the magnetostrictive strain curves in low, moderate and high magnetic field regions for various compressive pre-stress levels. The numerical simulation further illustrates that, for either magnetostrictive rods or thin films, the proposed model can effectively describe the effects of the pre-stress or residual stress on the magnetization and magnetostrictive strain curves, while none of the known models can capture all of them. Therefore, the proposed model enjoys higher precision and wider applicability than the previous models, especially in the region of the high field.
A Nonlinear Model of Thermoacoustic Devices
Karpov, Sergey; Prosperetti, Andrea
2002-01-01
This paper presents a nonlinear, time-domain model of thermoacoustic devices based on cross-sectional averaged equations. Heat transfer perpendicular to the device axis - which lies at the core of thermoacoustic effects - is modeled in a novel and more realistic way. Heat conduction in the solid sur
Some Asymptotic Inference in Multinomial Nonlinear Models (a Geometric Approach)
Institute of Scientific and Technical Information of China (English)
WEIBOCHENG
1996-01-01
A geometric framework is proposed for multinomlat nonlinear modelsbased on a modified vemlon of the geometric structure presented by Bates & Watts[4]. We use this geometric framework to study some asymptotic inference in terms ofcurvtures for multlnomial nonlinear models. Our previous results [15] for ordlnary nonlinear regression models are extended to multlnomlal nonlinear models.
Generalized Deterministic Traffic Rules
Fuks, H; Fuks, Henryk; Boccara, Nino
1997-01-01
We study a family of deterministic models for highway traffic flow which generalize cellular automaton rule 184. This family is parametrized by the speed limit $m$ and another parameter $k$ that represents a ``degree of aggressiveness'' in driving, strictly related to the distance between two consecutive cars. We compare two driving strategies with identical maximum throughput: ``conservative'' driving with high speed limit and ``aggressive'' driving with low speed limit. Those two strategies are evaluated in terms of accident probability. We also discuss fundamental diagrams of generalized traffic rules and examine limitations of maximum achievable throughput. Possible modifications of the model are considered.
Damage Detection of Structures Identified with Deterministic-Stochastic Models Using Seismic Data
Directory of Open Access Journals (Sweden)
Ming-Chih Huang
2014-01-01
Full Text Available A deterministic-stochastic subspace identification method is adopted and experimentally verified in this study to identify the equivalent single-input-multiple-output system parameters of the discrete-time state equation. The method of damage locating vector (DLV is then considered for damage detection. A series of shaking table tests using a five-storey steel frame has been conducted. Both single and multiple damage conditions at various locations have been considered. In the system identification analysis, either full or partial observation conditions have been taken into account. It has been shown that the damaged stories can be identified from global responses of the structure to earthquakes if sufficiently observed. In addition to detecting damage(s with respect to the intact structure, identification of new or extended damages of the as-damaged counterpart has also been studied. This study gives further insights into the scheme in terms of effectiveness, robustness, and limitation for damage localization of frame systems.
Li, S.
2002-05-01
Taking advantage of the recent developments in groundwater modeling research and computer, image and graphics processing, and objected oriented programming technologies, Dr. Li and his research group have recently developed a comprehensive software system for unified deterministic and stochastic groundwater modeling. Characterized by a new real-time modeling paradigm and improved computational algorithms, the software simulates 3D unsteady flow and reactive transport in general groundwater formations subject to both systematic and "randomly" varying stresses and geological and chemical heterogeneity. The software system has following distinct features and capabilities: Interactive simulation and real time visualization and animation of flow in response to deterministic as well as stochastic stresses. Interactive, visual, and real time particle tracking, random walk, and reactive plume modeling in both systematically and randomly fluctuating flow. Interactive statistical inference, scattered data interpolation, regression, and ordinary and universal Kriging, conditional and unconditional simulation. Real-time, visual and parallel conditional flow and transport simulations. Interactive water and contaminant mass balance analysis and visual and real-time flux update. Interactive, visual, and real time monitoring of head and flux hydrographs and concentration breakthroughs. Real-time modeling and visualization of aquifer transition from confined to unconfined to partially de-saturated or completely dry and rewetting Simultaneous and embedded subscale models, automatic and real-time regional to local data extraction; Multiple subscale flow and transport models Real-time modeling of steady and transient vertical flow patterns on multiple arbitrarily-shaped cross-sections and simultaneous visualization of aquifer stratigraphy, properties, hydrological features (rivers, lakes, wetlands, wells, drains, surface seeps), and dynamically adjusted surface flooding area
Correlations and Non-Linear Probability Models
DEFF Research Database (Denmark)
Breen, Richard; Holm, Anders; Karlson, Kristian Bernt
2014-01-01
Although the parameters of logit and probit and other non-linear probability models are often explained and interpreted in relation to the regression coefficients of an underlying linear latent variable model, we argue that they may also be usefully interpreted in terms of the correlations betwee...... certain circumstances, which we explain, the derived correlation provides a way of overcoming the problems inherent in cross-sample comparisons of the parameters of non-linear probability models.......Although the parameters of logit and probit and other non-linear probability models are often explained and interpreted in relation to the regression coefficients of an underlying linear latent variable model, we argue that they may also be usefully interpreted in terms of the correlations between...... the dependent variable of the latent variable model and its predictor variables. We show how this correlation can be derived from the parameters of non-linear probability models, develop tests for the statistical significance of the derived correlation, and illustrate its usefulness in two applications. Under...
A nonlinear dynamical system for combustion instability in a pulse model combustor
Takagi, Kazushi; Gotoda, Hiroshi
2016-11-01
We theoretically and numerically study the bifurcation phenomena of nonlinear dynamical system describing combustion instability in a pulse model combustor on the basis of dynamical system theory and complex network theory. The dynamical behavior of pressure fluctuations undergoes a significant transition from steady-state to deterministic chaos via the period-doubling cascade process known as Feigenbaum scenario with decreasing the characteristic flow time. Recurrence plots and recurrence networks analysis we adopted in this study can quantify the significant changes in dynamic behavior of combustion instability that cannot be captured in the bifurcation diagram.
Filtering nonlinear dynamical systems with linear stochastic models
Harlim, J.; Majda, A. J.
2008-06-01
An important emerging scientific issue is the real time filtering through observations of noisy signals for nonlinear dynamical systems as well as the statistical accuracy of spatio-temporal discretizations for filtering such systems. From the practical standpoint, the demand for operationally practical filtering methods escalates as the model resolution is significantly increased. For example, in numerical weather forecasting the current generation of global circulation models with resolution of 35 km has a total of billions of state variables. Numerous ensemble based Kalman filters (Evensen 2003 Ocean Dyn. 53 343-67 Bishop et al 2001 Mon. Weather Rev. 129 420-36 Anderson 2001 Mon. Weather Rev. 129 2884-903 Szunyogh et al 2005 Tellus A 57 528-45 Hunt et al 2007 Physica D 230 112-26) show promising results in addressing this issue; however, all these methods are very sensitive to model resolution, observation frequency, and the nature of the turbulent signals when a practical limited ensemble size (typically less than 100) is used. In this paper, we implement a radical filtering approach to a relatively low (40) dimensional toy model, the L-96 model (Lorenz 1996 Proc. on Predictability (ECMWF, 4-8 September 1995) pp 1-18) in various chaotic regimes in order to address the 'curse of ensemble size' for complex nonlinear systems. Practically, our approach has several desirable features such as extremely high computational efficiency, filter robustness towards variations of ensemble size (we found that the filter is reasonably stable even with a single realization) which makes it feasible for high dimensional problems, and it is independent of any tunable parameters such as the variance inflation coefficient in an ensemble Kalman filter. This radical filtering strategy decouples the problem of filtering a spatially extended nonlinear deterministic system to filtering a Fourier diagonal system of parametrized linear stochastic differential equations (Majda and Grote
Acharya, Ayan; Konar, Amit; Janarthanan, Ramadoss
2008-01-01
Ant Colony Optimization (ACO) is a metaheuristic for solving difficult discrete optimization problems. This paper presents a deterministic model based on differential equation to analyze the dynamics of basic Ant System algorithm. Traditionally, the deposition of pheromone on different parts of the tour of a particular ant is always kept unvarying. Thus the pheromone concentration remains uniform throughout the entire path of an ant. This article introduces an exponentially increasing pheromone deposition approach by artificial ants to improve the performance of basic Ant System algorithm. The idea here is to introduce an additional attracting force to guide the ants towards destination more easily by constructing an artificial potential field identified by increasing pheromone concentration towards the goal. Apart from carrying out analysis of Ant System dynamics with both traditional and the newly proposed deposition rules, the paper presents an exhaustive set of experiments performed to find out suitable p...
Energy Technology Data Exchange (ETDEWEB)
Goreac, Dan, E-mail: Dan.Goreac@u-pem.fr; Kobylanski, Magdalena, E-mail: Magdalena.Kobylanski@u-pem.fr; Martinez, Miguel, E-mail: Miguel.Martinez@u-pem.fr [Université Paris-Est, LAMA (UMR 8050), UPEMLV, UPEC, CNRS (France)
2016-10-15
We study optimal control problems in infinite horizon whxen the dynamics belong to a specific class of piecewise deterministic Markov processes constrained to star-shaped networks (corresponding to a toy traffic model). We adapt the results in Soner (SIAM J Control Optim 24(6):1110–1122, 1986) to prove the regularity of the value function and the dynamic programming principle. Extending the networks and Krylov’s “shaking the coefficients” method, we prove that the value function can be seen as the solution to a linearized optimization problem set on a convenient set of probability measures. The approach relies entirely on viscosity arguments. As a by-product, the dual formulation guarantees that the value function is the pointwise supremum over regular subsolutions of the associated Hamilton–Jacobi integrodifferential system. This ensures that the value function satisfies Perron’s preconization for the (unique) candidate to viscosity solution.
Perturbation analysis of nonlinear matrix population models
Directory of Open Access Journals (Sweden)
Hal Caswell
2008-03-01
Full Text Available Perturbation analysis examines the response of a model to changes in its parameters. It is commonly applied to population growth rates calculated from linear models, but there has been no general approach to the analysis of nonlinear models. Nonlinearities in demographic models may arise due to density-dependence, frequency-dependence (in 2-sex models, feedback through the environment or the economy, and recruitment subsidy due to immigration, or from the scaling inherent in calculations of proportional population structure. This paper uses matrix calculus to derive the sensitivity and elasticity of equilibria, cycles, ratios (e.g. dependency ratios, age averages and variances, temporal averages and variances, life expectancies, and population growth rates, for both age-classified and stage-classified models. Examples are presented, applying the results to both human and non-human populations.
Nonlinear control of the Salnikov model reaction
DEFF Research Database (Denmark)
Recke, Bodil; Jørgensen, Sten Bay
1999-01-01
This paper explores different nonlinear control schemes, applied to a simple model reaction. The model is the Salnikov model, consisting of two ordinary differential equations. The control strategies investigated are I/O-linearisation, Exact linearisation, exact linearisation combined with LQR...... and Control Lyapunov Functions (CLF's). The results show that based on the lowest possible cost function and shortest settling time, the exact linearisation performs marginally better than the other methods....
Nonlinear System Identification and Behavioral Modeling
Huq, Kazi Mohammed Saidul; Kabir, A F M Sultanul
2010-01-01
The problem of determining a mathematical model for an unknown system by observing its input-output data pair is generally referred to as system identification. A behavioral model reproduces the required behavior of the original analyzed system, such as there is a one-to-one correspondence between the behavior of the original system and the simulated system. This paper presents nonlinear system identification and behavioral modeling using a work assignment.
Nonlinearity detection in hyperspectral images using a polynomial post-nonlinear mixing model.
Altmann, Yoann; Dobigeon, Nicolas; Tourneret, Jean-Yves
2013-04-01
This paper studies a nonlinear mixing model for hyperspectral image unmixing and nonlinearity detection. The proposed model assumes that the pixel reflectances are nonlinear functions of pure spectral components contaminated by an additive white Gaussian noise. These nonlinear functions are approximated by polynomials leading to a polynomial post-nonlinear mixing model. We have shown in a previous paper that the parameters involved in the resulting model can be estimated using least squares methods. A generalized likelihood ratio test based on the estimator of the nonlinearity parameter is proposed to decide whether a pixel of the image results from the commonly used linear mixing model or from a more general nonlinear mixing model. To compute the test statistic associated with the nonlinearity detection, we propose to approximate the variance of the estimated nonlinearity parameter by its constrained Cramér-Rao bound. The performance of the detection strategy is evaluated via simulations conducted on synthetic and real data. More precisely, synthetic data have been generated according to the standard linear mixing model and three nonlinear models from the literature. The real data investigated in this study are extracted from the Cuprite image, which shows that some minerals seem to be nonlinearly mixed in this image. Finally, it is interesting to note that the estimated abundance maps obtained with the post-nonlinear mixing model are in good agreement with results obtained in previous studies.
Nonlinear GARCH model and 1 / f noise
Kononovicius, A.; Ruseckas, J.
2015-06-01
Auto-regressive conditionally heteroskedastic (ARCH) family models are still used, by practitioners in business and economic policy making, as a conditional volatility forecasting models. Furthermore ARCH models still are attracting an interest of the researchers. In this contribution we consider the well known GARCH(1,1) process and its nonlinear modifications, reminiscent of NGARCH model. We investigate the possibility to reproduce power law statistics, probability density function and power spectral density, using ARCH family models. For this purpose we derive stochastic differential equations from the GARCH processes in consideration. We find the obtained equations to be similar to a general class of stochastic differential equations known to reproduce power law statistics. We show that linear GARCH(1,1) process has power law distribution, but its power spectral density is Brownian noise-like. However, the nonlinear modifications exhibit both power law distribution and power spectral density of the 1 /fβ form, including 1 / f noise.
Dynamical effects of overparametrization in nonlinear models
Aguirre, Luis Antonio; Billings, S. A.
1995-01-01
This paper is concemed with dynamical reconstruction for nonlinear systems. The effects of the driving function and of the complexity of a given representation on the bifurcation patter are investigated. It is shown that the use of different driving functions to excite the system may yield models with different bifurcation patterns. The complexity of the reconstructions considered is quantified by the embedding dimension and the number of estimated parameters. In this respect it appears that models which reproduce the original bifurcation behaviour are of limited complexity and that excessively complex models tend to induce ghost bifurcations and spurious dynamical regimes. Moreover, some results suggest that the effects of overparametrization on the global dynamical behaviour of a nonlinear model may be more deleterious than the presence of moderate noise levels. In order to precisely quantify the complexity of the reconstructions, global polynomials are used although the results are believed to apply to a much wider class of representations including neural networks.
Prakash, J; Srinivasan, K
2009-07-01
In this paper, the authors have represented the nonlinear system as a family of local linear state space models, local PID controllers have been designed on the basis of linear models, and the weighted sum of the output from the local PID controllers (Nonlinear PID controller) has been used to control the nonlinear process. Further, Nonlinear Model Predictive Controller using the family of local linear state space models (F-NMPC) has been developed. The effectiveness of the proposed control schemes has been demonstrated on a CSTR process, which exhibits dynamic nonlinearity.
Directory of Open Access Journals (Sweden)
Zhen Xu
2016-01-01
Full Text Available Predicting dissolved oxygen (DO change at a high frequency in water bodies is useful for water quality management. In this study, we developed a deterministic model that can predict hourly DO change in a water body with high frequency weather parameters. The study was conducted during August 2008–July 2009 in a eutrophic shallow lake in Louisiana, USA. An environment monitoring buoy was deployed to record DO, water temperature and chlorophyll-a concentration at 15-min intervals, and hourly weather data including air temperature, precipitation, wind speed, relative humidity, and solar radiation were gathered from a nearby weather station. These data formed a foundation for developing a DO model that predicts rapid change of source and sink components including photosynthesis, re-aeration, respiration, and oxygen consumption by sediments. We then applied the model to a studied shallow lake that is widely representative of lake water conditions in the subtropical southern United States. Overall, the model successfully simulated high-time fluctuation of DO in the studied lake, showing good predictability for extreme algal bloom events. However, a knowledge gap still exists in accurately quantifying oxygen source produced by photosynthesis in high frequency DO modeling.
Simplified Model of Nonlinear Landau Damping
Energy Technology Data Exchange (ETDEWEB)
N. A. Yampolsky and N. J. Fisch
2009-07-16
The nonlinear interaction of a plasma wave with resonant electrons results in a plateau in the electron distribution function close to the phase velocity of the plasma wave. As a result, Landau damping of the plasma wave vanishes and the resonant frequency of the plasma wave downshifts. However, this simple picture is invalid when the external driving force changes the plasma wave fast enough so that the plateau cannot be fully developed. A new model to describe amplification of the plasma wave including the saturation of Landau damping and the nonlinear frequency shift is proposed. The proposed model takes into account the change of the plasma wave amplitude and describes saturation of the Landau damping rate in terms of a single fluid equation, which simplifies the description of the inherently kinetic nature of Landau damping. A proposed fluid model, incorporating these simplifications, is verified numerically using a kinetic Vlasov code.
On Projection-Based Model Reduction of Biochemical Networks Part I: The Deterministic Case
Sootla, Aivar; Anderson, James
2014-01-01
This paper addresses the problem of model reduction for dynamical system models that describe biochemical reaction networks. Inherent in such models are properties such as stability, positivity and network structure. Ideally these properties should be preserved by model reduction procedures, although traditional projection based approaches struggle to do this. We propose a projection based model reduction algorithm which uses generalised block diagonal Gramians to preserve structure and posit...
STEW A Nonlinear Data Modeling Computer Program
Chen, H
2000-01-01
A nonlinear data modeling computer program, STEW, employing the Levenberg-Marquardt algorithm, has been developed to model the experimental sup 2 sup 3 sup 9 Pu(n,f) and sup 2 sup 3 sup 5 U(n,f) cross sections. This report presents results of the modeling of the sup 2 sup 3 sup 9 Pu(n,f) and sup 2 sup 3 sup 5 U(n,f) cross-section data. The calculation of the fission transmission coefficient is based on the double-humped-fission-barrier model of Bjornholm and Lynn. Incident neutron energies of up to 5 MeV are considered.
STEW: A Nonlinear Data Modeling Computer Program
Energy Technology Data Exchange (ETDEWEB)
Chen, H.
2000-03-04
A nonlinear data modeling computer program, STEW, employing the Levenberg-Marquardt algorithm, has been developed to model the experimental {sup 239}Pu(n,f) and {sup 235}U(n,f) cross sections. This report presents results of the modeling of the {sup 239}Pu(n,f) and {sup 235}U(n,f) cross-section data. The calculation of the fission transmission coefficient is based on the double-humped-fission-barrier model of Bjornholm and Lynn. Incident neutron energies of up to 5 MeV are considered.
Directory of Open Access Journals (Sweden)
Yuichi eYamashita
2011-04-01
Full Text Available How the brain learns and generates temporal sequences is a fundamental issue in neuroscience. The production of birdsongs, a process which involves complex learned sequences, provides researchers with an excellent biological model for this topic. The Bengalese finch in particular learns a highly complex song with syntactical structure. The nucleus HVC (HVC, a premotor nucleus within the avian song system, plays a key role in generating the temporal structures of their songs. From lesion studies, the nucleus interfacialis (NIf projecting to the HVC is considered one of the essential regions that contribute to the complexity of their songs. However, the types of interaction between the HVC and the NIf that can produce complex syntactical songs remain unclear. In order to investigate the function of interactions between the HVC and NIf, we have proposed a neural network model based on previous biological evidence. The HVC is modeled by a recurrent neural network (RNN that learns to generate temporal patterns of songs. The NIf is modeled as a mechanism that provides auditory feedback to the HVC and generates random noise that feeds into the HVC. The model showed that complex syntactical songs can be replicated by simple interactions between deterministic dynamics of the RNN and random noise. In the current study, the plausibility of the model is tested by the comparison between the changes in the songs of actual birds induced by pharmacological inhibition of the NIf and the changes in the songs produced by the model resulting from modification of parameters representing NIf functions. The efficacy of the model demonstrates that the changes of songs induced by pharmacological inhibition of the NIf can be interpreted as a trade-off between the effects of noise and the effects of feedback on the dynamics of the RNN of the HVC. These facts suggest that the current model provides a convincing hypothesis for the functional role of NIf-HVC interaction.
Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models
Daunizeau, J.; Friston, K. J.; Kiebel, S. J.
2009-11-01
In this paper, we describe a general variational Bayesian approach for approximate inference on nonlinear stochastic dynamic models. This scheme extends established approximate inference on hidden-states to cover: (i) nonlinear evolution and observation functions, (ii) unknown parameters and (precision) hyperparameters and (iii) model comparison and prediction under uncertainty. Model identification or inversion entails the estimation of the marginal likelihood or evidence of a model. This difficult integration problem can be finessed by optimising a free-energy bound on the evidence using results from variational calculus. This yields a deterministic update scheme that optimises an approximation to the posterior density on the unknown model variables. We derive such a variational Bayesian scheme in the context of nonlinear stochastic dynamic hierarchical models, for both model identification and time-series prediction. The computational complexity of the scheme is comparable to that of an extended Kalman filter, which is critical when inverting high dimensional models or long time-series. Using Monte-Carlo simulations, we assess the estimation efficiency of this variational Bayesian approach using three stochastic variants of chaotic dynamic systems. We also demonstrate the model comparison capabilities of the method, its self-consistency and its predictive power.
Astroza, Rodrigo; Ebrahimian, Hamed; Li, Yong; Conte, Joel P.
2017-09-01
A methodology is proposed to update mechanics-based nonlinear finite element (FE) models of civil structures subjected to unknown input excitation. The approach allows to jointly estimate unknown time-invariant model parameters of a nonlinear FE model of the structure and the unknown time histories of input excitations using spatially-sparse output response measurements recorded during an earthquake event. The unscented Kalman filter, which circumvents the computation of FE response sensitivities with respect to the unknown model parameters and unknown input excitations by using a deterministic sampling approach, is employed as the estimation tool. The use of measurement data obtained from arrays of heterogeneous sensors, including accelerometers, displacement sensors, and strain gauges is investigated. Based on the estimated FE model parameters and input excitations, the updated nonlinear FE model can be interrogated to detect, localize, classify, and assess damage in the structure. Numerically simulated response data of a three-dimensional 4-story 2-by-1 bay steel frame structure with six unknown model parameters subjected to unknown bi-directional horizontal seismic excitation, and a three-dimensional 5-story 2-by-1 bay reinforced concrete frame structure with nine unknown model parameters subjected to unknown bi-directional horizontal seismic excitation are used to illustrate and validate the proposed methodology. The results of the validation studies show the excellent performance and robustness of the proposed algorithm to jointly estimate unknown FE model parameters and unknown input excitations.
Simple nonlinear models suggest variable star universality
Lindner, John F; Kia, Behnam; Hippke, Michael; Learned, John G; Ditto, William L
2015-01-01
Dramatically improved data from observatories like the CoRoT and Kepler spacecraft have recently facilitated nonlinear time series analysis and phenomenological modeling of variable stars, including the search for strange (aka fractal) or chaotic dynamics. We recently argued [Lindner et al., Phys. Rev. Lett. 114 (2015) 054101] that the Kepler data includes "golden" stars, whose luminosities vary quasiperiodically with two frequencies nearly in the golden ratio, and whose secondary frequencies exhibit power-law scaling with exponent near -1.5, suggesting strange nonchaotic dynamics and singular spectra. Here we use a series of phenomenological models to make plausible the connection between golden stars and fractal spectra. We thereby suggest that at least some features of variable star dynamics reflect universal nonlinear phenomena common to even simple systems.
Thermoviscous Model Equations in Nonlinear Acoustics
DEFF Research Database (Denmark)
Rasmussen, Anders Rønne
Four nonlinear acoustical wave equations that apply to both perfect gasses and arbitrary fluids with a quadratic equation of state are studied. Shock and rarefaction wave solutions to the equations are studied. In order to assess the accuracy of the wave equations, their solutions are compared...... to solutions of the basic equations from which the wave equations are derived. A straightforward weakly nonlinear equation is the most accurate for shock modeling. A higher order wave equation is the most accurate for modeling of smooth disturbances. Investigations of the linear stability properties...... of solutions to the wave equations, reveal that the solutions may become unstable. Such instabilities are not found in the basic equations. Interacting shocks and standing shocks are investigated....
Modified Nonlinear Model of Arcsin-Electrodynamics
Kruglov, S. I.
2016-07-01
A new modified model of nonlinear arcsin-electrodynamics with two parameters is proposed and analyzed. We obtain the corrections to the Coulomb law. The effect of vacuum birefringence takes place when the external constant magnetic field is present. We calculate indices of refraction for two perpendicular polarizations of electromagnetic waves and estimate bounds on the parameter γ from the BMV and PVLAS experiments. It is shown that the electric field of a point-like charge is finite at the origin. We calculate the finite static electric energy of point-like particles and demonstrate that the electron mass can have the pure electromagnetic nature. The symmetrical Belinfante energy-momentum tensor and dilatation current are found. We show that the dilatation symmetry and dual symmetry are broken in the model suggested. We have investigated the gauge covariant quantization of the nonlinear electrodynamics fields as well as the gauge fixing approach based on Dirac's brackets.
Energy Technology Data Exchange (ETDEWEB)
Barus, R. P. P., E-mail: rismawan.ppb@gmail.com [Engineering Physics, Faculty of Industrial Technology, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung and Centre for Material and Technical Product, Jalan Sangkuriang No. 14 Bandung (Indonesia); Tjokronegoro, H. A.; Leksono, E. [Engineering Physics, Faculty of Industrial Technology, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung (Indonesia); Ismunandar [Chemistry Study, Faculty of Mathematics and Science, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung (Indonesia)
2014-09-25
Fuel cells are promising new energy conversion devices that are friendly to the environment. A set of control systems are required in order to operate a fuel cell based power plant system optimally. For the purpose of control system design, an accurate fuel cell stack model in describing the dynamics of the real system is needed. Currently, linear model are widely used for fuel cell stack control purposes, but it has limitations in narrow operation range. While nonlinear models lead to nonlinear control implemnetation whos more complex and hard computing. In this research, nonlinear cancellation technique will be used to transform a nonlinear model into a linear form while maintaining the nonlinear characteristics. The transformation is done by replacing the input of the original model by a certain virtual input that has nonlinear relationship with the original input. Then the equality of the two models is tested by running a series of simulation. Input variation of H2, O2 and H2O as well as disturbance input I (current load) are studied by simulation. The error of comparison between the proposed model and the original nonlinear model are less than 1 %. Thus we can conclude that nonlinear cancellation technique can be used to represent fuel cell nonlinear model in a simple linear form while maintaining the nonlinear characteristics and therefore retain the wide operation range.
Clustering With Side Information: From a Probabilistic Model to a Deterministic Algorithm
Khashabi, Daniel; Wieting, John; Liu, Jeffrey Yufei; Liang, Feng
2015-01-01
In this paper, we propose a model-based clustering method (TVClust) that robustly incorporates noisy side information as soft-constraints and aims to seek a consensus between side information and the observed data. Our method is based on a nonparametric Bayesian hierarchical model that combines the probabilistic model for the data instance and the one for the side-information. An efficient Gibbs sampling algorithm is proposed for posterior inference. Using the small-variance asymptotics of ou...
Nonlinear chaotic model for predicting storm surges
Directory of Open Access Journals (Sweden)
M. Siek
2010-09-01
Full Text Available This paper addresses the use of the methods of nonlinear dynamics and chaos theory for building a predictive chaotic model from time series. The chaotic model predictions are made by the adaptive local models based on the dynamical neighbors found in the reconstructed phase space of the observables. We implemented the univariate and multivariate chaotic models with direct and multi-steps prediction techniques and optimized these models using an exhaustive search method. The built models were tested for predicting storm surge dynamics for different stormy conditions in the North Sea, and are compared to neural network models. The results show that the chaotic models can generally provide reliable and accurate short-term storm surge predictions.
The Nonlinear Magnetosphere: Expressions in MHD and in Kinetic Models
Hesse, Michael; Birn, Joachim
2011-01-01
Like most plasma systems, the magnetosphere of the Earth is governed by nonlinear dynamic evolution equations. The impact of nonlinearities ranges from large scales, where overall dynamics features are exhibiting nonlinear behavior, to small scale, kinetic, processes, where nonlinear behavior governs, among others, energy conversion and dissipation. In this talk we present a select set of examples of such behavior, with a specific emphasis on how nonlinear effects manifest themselves in MHD and in kinetic models of magnetospheric plasma dynamics.
MCRG Flow for the nonlinear Sigma Model
Koerner, Daniel; Wipf, Andreas
2013-01-01
A study of the renormalization group flow in the three-dimensional nonlinear O(N) sigma model using Monte Carlo Renormalization Group (MCRG) techniques is presented. To achieve this, we combine an improved blockspin transformation with the canonical demon method to determine the flow diagram for a number of different truncations. Systematic errors of the approach are highlighted. Results are discussed with hindsight on the fixed point structure of the model and the corresponding critical exponents. Special emphasis is drawn on the existence of a nontrivial ultraviolet fixed point as required for theories modeling the asymptotic safety scenario of quantum gravity.
Forecasting with nonlinear time series models
DEFF Research Database (Denmark)
Kock, Anders Bredahl; Teräsvirta, Timo
and two versions of a simple artificial neural network model. Techniques for generating multi-period forecasts from nonlinear models recursively are considered, and the direct (non-recursive) method for this purpose is mentioned as well. Forecasting with com- plex dynamic systems, albeit less frequently...... applied to economic fore- casting problems, is briefly highlighted. A number of large published studies comparing macroeconomic forecasts obtained using different time series models are discussed, and the paper also contains a small simulation study comparing recursive and direct forecasts in a partic...
Nonlinear Modelling of Low Frequency Loudspeakers
DEFF Research Database (Denmark)
Olsen, Erling Sandermann; Christensen, Knud Bank
1996-01-01
A central part of the Danish LoDist project has been the derivation of an extended equivalent circuit and a corresponding set of differential equations suitable for the simulation of high-fidelity woofers under large and very large (clipping) signal conditions. A model including suspension creep ...... and eddy current losses seems to be sufficient, but all the parameters of the model vary with the position of the diaphragm. The model and the associated set of nonlinear differential equations and the solution of the equations are discussed....
NONLINEAR MODEL PREDICTIVE CONTROL OF CHEMICAL PROCESSES
Directory of Open Access Journals (Sweden)
R. G. SILVA
1999-03-01
Full Text Available A new algorithm for model predictive control is presented. The algorithm utilizes a simultaneous solution and optimization strategy to solve the model's differential equations. The equations are discretized by equidistant collocation, and along with the algebraic model equations are included as constraints in a nonlinear programming (NLP problem. This algorithm is compared with the algorithm that uses orthogonal collocation on finite elements. The equidistant collocation algorithm results in simpler equations, providing a decrease in computation time for the control moves. Simulation results are presented and show a satisfactory performance of this algorithm.
Nonlinear Inertia Classification Model and Application
Directory of Open Access Journals (Sweden)
Mei Wang
2014-01-01
Full Text Available Classification model of support vector machine (SVM overcomes the problem of a big number of samples. But the kernel parameter and the punishment factor have great influence on the quality of SVM model. Particle swarm optimization (PSO is an evolutionary search algorithm based on the swarm intelligence, which is suitable for parameter optimization. Accordingly, a nonlinear inertia convergence classification model (NICCM is proposed after the nonlinear inertia convergence (NICPSO is developed in this paper. The velocity of NICPSO is firstly defined as the weighted velocity of the inertia PSO, and the inertia factor is selected to be a nonlinear function. NICPSO is used to optimize the kernel parameter and a punishment factor of SVM. Then, NICCM classifier is trained by using the optical punishment factor and the optical kernel parameter that comes from the optimal particle. Finally, NICCM is applied to the classification of the normal state and fault states of online power cable. It is experimentally proved that the iteration number for the proposed NICPSO to reach the optimal position decreases from 15 to 5 compared with PSO; the training duration is decreased by 0.0052 s and the recognition precision is increased by 4.12% compared with SVM.
Model reduction of systems with localized nonlinearities.
Energy Technology Data Exchange (ETDEWEB)
Segalman, Daniel Joseph
2006-03-01
An LDRD funded approach to development of reduced order models for systems with local nonlinearities is presented. This method is particularly useful for problems of structural dynamics, but has potential application in other fields. The key elements of this approach are (1) employment of eigen modes of a reference linear system, (2) incorporation of basis functions with an appropriate discontinuity at the location of the nonlinearity. Galerkin solution using the above combination of basis functions appears to capture the dynamics of the system with a small basis set. For problems involving small amplitude dynamics, the addition of discontinuous (joint) modes appears to capture the nonlinear mechanics correctly while preserving the modal form of the predictions. For problems involving large amplitude dynamics of realistic joint models (macro-slip), the use of appropriate joint modes along with sufficient basis eigen modes to capture the frequencies of the system greatly enhances convergence, though the modal nature the result is lost. Also observed is that when joint modes are used in conjunction with a small number of elastic eigen modes in problems of macro-slip of realistic joint models, the resulting predictions are very similar to those of the full solution when seen through a low pass filter. This has significance both in terms of greatly reducing the number of degrees of freedom of the problem and in terms of facilitating the use of much larger time steps.
Deterministic Graphical Games Revisited
DEFF Research Database (Denmark)
Andersson, Daniel; Hansen, Kristoffer Arnsfelt; Miltersen, Peter Bro
2008-01-01
We revisit the deterministic graphical games of Washburn. A deterministic graphical game can be described as a simple stochastic game (a notion due to Anne Condon), except that we allow arbitrary real payoffs but disallow moves of chance. We study the complexity of solving deterministic graphical...... games and obtain an almost-linear time comparison-based algorithm for computing an equilibrium of such a game. The existence of a linear time comparison-based algorithm remains an open problem....
S.I. Birbil (Ilker); J.B.G. Frenk (Hans); Z.P. Bayindir (Pelin)
2004-01-01
textabstractWe present a thorough analysis of the economic order quantity model with shortages under a general inventory cost rate function and concave production costs. By using some standard results from convex analysis, we show that the model exhibits a composite concave-convex structure.
Directory of Open Access Journals (Sweden)
Anand Joshi
2013-01-01
Full Text Available This paper presents use of semiempirical method for seismic hazard zonation. The seismotectonically important region of Uttarakhand Himalaya has been considered in this work. Ruptures along the lineaments in the area identified from tectonic map are modeled deterministically using semi empirical approach given by Midorikawa (1993. This approach makes use of attenuation relation of peak ground acceleration for simulating strong ground motion at any site. Strong motion data collected over a span of three years in this region have been used to develop attenuation relation of peak ground acceleration of limited magnitude and distance applicability. The developed attenuation relation is used in the semi empirical method to predict peak ground acceleration from the modeled rupture planes in the area. A set of values of peak ground acceleration from possible ruptures in the area at the point of investigation is further used to compute probability of exceedance of peak ground acceleration of values 100 and 200 gals. The prepared map shows that regions like Tehri, Chamoli, Almora, Srinagar, Devprayag, Bageshwar, and Pauri fall in a zone of 10% probability of exceedence of peak ground acceleration of value 200 gals.
Energy Technology Data Exchange (ETDEWEB)
Stephens, Michael B. (Geological Survey of Sweden, Uppsala (Sweden)); Simeonov, Assen (Swedish Nuclear Fuel and Waste Management Co., Stockholm (Sweden)); Isaksson, Hans (GeoVista AB, Luleaa (Sweden))
2008-12-15
The Swedish Nuclear Fuel and Waste Management Company is in the process of completing site descriptive modelling at two locations in Sweden, with the objective to site a deep geological repository for spent nuclear fuel. At Forsmark, the results of the stage 2.2 geological modelling formed the input for downstream users. Since complementary ground and borehole geological and geophysical data, acquired after model stage 2.2, were not planned to be included in the deterministic rock domain, fracture domain and deformation zone models supplied to the users, it was deemed necessary to evaluate the implications of these stage 2.3 data for the stage 2.2 deterministic geological models and, if possible, to make use of these data to verify the models. This report presents the results of the analysis of the complementary stage 2.3 geological and geophysical data. Model verification from borehole data has been implemented in the form of a prediction-outcome test. The stage 2.3 geological and geophysical data at Forsmark mostly provide information on the bedrock outside the target volume. Additional high-resolution ground magnetic data and the data from the boreholes KFM02B, KFM11A, KFM12A and HFM33 to HFM37 can be included in this category. Other data complement older information of identical character, both inside and outside this volume. These include the character and kinematics of deformation zones and fracture mineralogy. In general terms, it can be stated that all these new data either confirm the geological modelling work completed during stage 2.2 or are in good agreement with the data that were used in this work. In particular, although the new high-resolution ground magnetic data modify slightly the position and trace length of some stage 2.2 deformation zones at the ground surface, no new or modified deformation zones with a trace length longer than 3,000 m at the ground surface have emerged. It is also apparent that the revision of fracture orientation data
Evaluation of model fit in nonlinear multilevel structural equation modeling
Directory of Open Access Journals (Sweden)
Karin eSchermelleh-Engel
2014-03-01
Full Text Available Evaluating model fit in nonlinear multilevel structural equation models (MSEM presents a challenge as no adequate test statistic is available. Nevertheless, using a product indicator approach a likelihood ratio test for linear models is provided which may also be useful for nonlinear MSEM. The main problem with nonlinear models is that product variables are nonnormally distributed. Although robust test statistics have been developed for linear SEM to ensure valid results under the condition of nonnormality, they were not yet investigated for nonlinear MSEM. In a Monte Carlo study, the performance of the robust likelihood ratio test was investigated for models with single-level latent interaction effects using the unconstrained product indicator approach. As overall model fit evaluation has a potential limitation in detecting the lack of fit at a single level even for linear models, level-specific model fit evaluation was also investigated using partially saturated models. Four population models were considered: a model with interaction effects at both levels, an interaction effect at the within-group level, an interaction effect at the between-group level, and a model with no interaction effects at both levels. For these models the number of groups, predictor correlation, and model misspecification was varied. The results indicate that the robust test statistic performed sufficiently well. Advantages of level-specific model fit evaluation for the detection of model misfit are demonstrated.
Evaluation of model fit in nonlinear multilevel structural equation modeling.
Schermelleh-Engel, Karin; Kerwer, Martin; Klein, Andreas G
2014-01-01
Evaluating model fit in nonlinear multilevel structural equation models (MSEM) presents a challenge as no adequate test statistic is available. Nevertheless, using a product indicator approach a likelihood ratio test for linear models is provided which may also be useful for nonlinear MSEM. The main problem with nonlinear models is that product variables are non-normally distributed. Although robust test statistics have been developed for linear SEM to ensure valid results under the condition of non-normality, they have not yet been investigated for nonlinear MSEM. In a Monte Carlo study, the performance of the robust likelihood ratio test was investigated for models with single-level latent interaction effects using the unconstrained product indicator approach. As overall model fit evaluation has a potential limitation in detecting the lack of fit at a single level even for linear models, level-specific model fit evaluation was also investigated using partially saturated models. Four population models were considered: a model with interaction effects at both levels, an interaction effect at the within-group level, an interaction effect at the between-group level, and a model with no interaction effects at both levels. For these models the number of groups, predictor correlation, and model misspecification was varied. The results indicate that the robust test statistic performed sufficiently well. Advantages of level-specific model fit evaluation for the detection of model misfit are demonstrated.
Hoshyaripour, G.; Brasseur, G.; Andrade, M. F.; Gavidia-Calderón, M.; Bouarar, I.; Ynoue, R. Y.
2016-11-01
Two state-of-the-art models (deterministic: Weather Research and Forecast model with Chemistry (WRF-Chem) and statistic: Artificial Neural Networks: (ANN)) are implemented to predict the ground-level ozone concentration in São Paulo (SP), Brazil. Two domains are set up for WRF-Chem simulations: a coarse domain (with 50 km horizontal resolution) including whole South America (D1) and a nested domain (with horizontal resolution of 10 km) including South Eastern Brazil (D2). To evaluate the spatial distribution of the chemical species, model results are compared to the Measurements of Pollution in The Troposphere (MOPITT) data, showing that the model satisfactorily predicts the CO concentrations in both D1 and D2. The model also reproduces the measurements made at three air quality monitoring stations in SP with the correlation coefficients of 0.74, 0.70, and 0.77 for O3 and 0.51, 0.48, and 0.57 for NOx. The input selection for ANN model is carried out using Forward Selection (FS) method. FS-ANN is then trained and validated using the data from two air quality monitoring stations, showing correlation coefficients of 0.84 and 0.75 for daily mean and 0.64 and 0.67 for daily peak ozone during the test stage. Then, both WRF-Chem and FS-ANN are deployed to forecast the daily mean and peak concentrations of ozone in two stations during 5-20 August 2012. Results show that WRF-Chem preforms better in predicting mean and peak ozone concentrations as well as in conducting mechanistic and sensitivity analysis. FS-ANN is only advantageous in predicting mean daily ozone concentrations considering its significantly lower computational costs and ease of development and implementation, compared to that of WRF-Chem.
Deterministic Compilation of Temporal Safety Properties in Explicit State Model Checking
National Aeronautics and Space Administration — The translation of temporal logic specifications constitutes an essen- tial step in model checking and a major influence on the efficiency of formal verification via...
Directory of Open Access Journals (Sweden)
Marek Bodnar
Full Text Available Angiogenesis modelling is an important tool to understand the underlying mechanisms yielding tumour growth. Nevertheless, there is usually a gap between models and experimental data. We propose a model based on the intrinsic microscopic reactions defining the angiogenesis process to link experimental data with previous macroscopic models. The microscopic characterisation can describe the macroscopic behaviour of the tumour, which stability analysis reveals a set of predicted tumour states involving different morphologies. Additionally, the microscopic description also gives a framework to study the intrinsic stochasticity of the reactive system through the resulting Langevin equation. To follow the goal of the paper, we use available experimental information on the Lewis lung carcinoma to infer meaningful parameters for the model that are able to describe the different stages of the tumour growth. Finally we explore the predictive capabilities of the fitted model by showing that fluctuations are determinant for the survival of the tumour during the first week and that available treatments can give raise to new stable tumour dormant states with a reduced vascular network.
Mergili, Martin; Marchesini, Ivan; Rossi, Mauro; Guzzetti, Fausto; Fellin, Wolfgang
2013-04-01
Various deterministic slope stability models, based on the assumption of an infinite slope with a plane, slope-parallel failure plane, have been proposed in the literature. These models are commonly implemented in a GIS environment and are mostly used to model shallow landslides. Other models consider the three-dimensional geometry of possible slope failures and assume an ellipsoidal sliding surface. Such models are best suited to investigate deep-seated landslides. The latter models rely on complex neighbourhood relationships and are difficult to implement in a GIS environment. Here, we present a GIS-based landslide modelling tool that considers the three-dimensional geometry of the sliding surfaces and is capable of dealing with shallow and deep-seated failures. The model is developed in the GRASS GIS software as the C-based raster module r.rotstab, and adopts a modification of the three-dimensional sliding surface model proposed by Hovland and revised and extended by Xie and co-workers. Given a Digital Elevation Model and a set of thematic layers, the model evaluates slope stability for a large number of randomly selected potential slip surfaces, ellipsoidal in shape. Truncated ellipsoids can be used to model the presence of shallow weak layers in the soil or the bedrock. Any single raster cell may be intersected by multiple sliding surfaces, each associated with a computed safety factor. For each grid cell, the lowest value of the safety factor and the depth of the associated slip surface are stored. This information can be used to obtain a spatial overview of the potentially unstable regions in the study area. In addition, a landslide susceptibility index in the range 0 - 1 is calculated. The index relates the number of unstable slip surfaces to the total number of slip surfaces simulated for each pixel. We tested the model in the Collazzone area, Umbria, Central Italy, which is susceptible to landslides of different types. The presence of both shallow
Energy Technology Data Exchange (ETDEWEB)
Farmer, J. C., LLNL
1997-07-01
An integrated predictive model is being developed to account for the effects of localized environmental conditions in crevices on pit initiation and propagation. A deterministic calculation is used to estimate the accumulation of hydrogen ions in the crevice solution due to equilibrium hydrolysis reactions of dissolved metal. Pit initiation and growth within the crevice is dealt with by either a stochastic probability model, or an equivalent deterministic model. While the strategy presented here is very promising, the integrated model is not yet ready for accurate quantitative predictions. Empirical expressions for the rate of penetration based upon experimental crevice corrosion data should be used in the interim period, until the integrated model can be refined. Both approaches are discussed.
Observations and modeling of deterministic properties of human heart rate variability
Indian Academy of Sciences (India)
J J Zebrowski; R Baranowski
2005-04-01
Simple models show that in Type-I intermittency a characteristic U-shaped probability distribution is obtained for the laminar phase length. The laminar phase length distribution characteristic for Type-I intermittency may be obtained in human heart rate variability data for some cases of pathology. The heart and its regulatory systems are presumed to be both noisy and non-stationary. Although the effect of additive noise on the laminar phase distribution in Type-I intermittency is well-known, the effect of neither multiplicative noise nor non-stationarity have been studied. We first discuss the properties of two classes of models of Type-I intermittency: (a) the control parameter of the logistic map is changed dichotomously from a value within the intermittency range to just below the bifurcation point and back; (b) the control parameter is changed randomly within the same parameter range as in the model class (a). We show that the properties of both models are different from those obtained for Type-I intermittency in the presence of additive noise. The two models help to explain some of the features seen in the intermittency in human heart rate variability.
Nonlinear trading models through Sharpe Ratio maximization.
Choey, M; Weigend, A S
1997-08-01
While many trading strategies are based on price prediction, traders in financial markets are typically interested in optimizing risk-adjusted performance such as the Sharpe Ratio, rather than the price predictions themselves. This paper introduces an approach which generates a nonlinear strategy that explicitly maximizes the Sharpe Ratio. It is expressed as a neural network model whose output is the position size between a risky and a risk-free asset. The iterative parameter update rules are derived and compared to alternative approaches. The resulting trading strategy is evaluated and analyzed on both computer-generated data and real world data (DAX, the daily German equity index). Trading based on Sharpe Ratio maximization compares favorably to both profit optimization and probability matching (through cross-entropy optimization). The results show that the goal of optimizing out-of-sample risk-adjusted profit can indeed be achieved with this nonlinear approach.
Nonlinear Model of non-Debye Relaxation
Zon, Boris A
2010-01-01
We present a simple nonlinear relaxation equation which contains the Debye equation as a particular case. The suggested relaxation equation results in power-law decay of fluctuations. This equation contains a parameter defining the frequency dependence of the dielectric permittivity similarly to the well-known one-parameter phenomenological equations of Cole-Cole, Davidson-Cole and Kohlrausch-Williams-Watts. Unlike these models, the obtained dielectric permittivity (i) obeys to the Kramers-Kronig relation; (ii) has proper behaviour at large frequency; (iii) its imaginary part, conductivity, shows a power-law frequency dependence \\sigma ~ \\omega^n where n1 is also observed in several experiments. The nonlinear equation proposed may be useful in various fields of relaxation theory.
Zieher, T.; Rutzinger, M.; Bremer, M.; Meissl, G.; Geitner, C.
2014-12-01
The potentially stabilizing effects of forest cover in respect of slope stability have been the subject of many studies in the recent past. Hence, the effects of trees are also considered in many deterministic landslide susceptibility models. TRIGRS 2.0 (Transient Rainfall Infiltration and Grid-Based Regional Slope-Stability; USGS) is a dynamic, physically-based model designed to estimate shallow landslide susceptibility in space and time. In the original version the effects of forest cover are not considered. As for further studies in Vorarlberg (Austria) TRIGRS 2.0 is intended to be applied in selected catchments that are densely forested, the effects of trees on slope stability were implemented in the model. Besides hydrological impacts such as interception or transpiration by tree canopies and stems, root cohesion directly influences the stability of slopes especially in case of shallow landslides while the additional weight superimposed by trees is of minor relevance. Detailed data on tree positions and further attributes such as tree height and diameter at breast height were derived throughout the study area (52 km²) from high-resolution airborne laser scanning data. Different scenarios were computed for spruce (Picea abies) in the study area. Root cohesion was estimated area-wide based on published correlations between root reinforcement and distance to tree stems depending on the stem diameter at breast height. In order to account for decreasing root cohesion with depth an exponential distribution was assumed and implemented in the model. Preliminary modelling results show that forest cover can have positive effects on slope stability yet strongly depending on tree age and stand structure. This work has been conducted within C3S-ISLS, which is funded by the Austrian Climate and Energy Fund, 5th ACRP Program.
Toward a Deterministic Model of Planetary Formation VII: Eccentricity Distribution of Gas Giants
Ida, S; Nagasawa, M
2013-01-01
The ubiquity of planets and diversity of planetary systems reveal planet formation encompass many complex and competing processes. In this series of papers, we develop and upgrade a population synthesis model as a tool to identify the dominant physical effects and to calibrate the range of physical conditions. Recent planet searches leads to the discovery of many multiple-planet systems. Any theoretical models of their origins must take into account dynamical interaction between emerging protoplanets. Here, we introduce a prescription to approximate the close encounters between multiple planets. We apply this method to simulate the growth, migration, and dynamical interaction of planetary systems. Our models show that in relatively massive disks, several gas giants and rocky/icy planets emerge, migrate, and undergo dynamical instability. Secular perturbation between planets leads to orbital crossings, eccentricity excitation, and planetary ejection. In disks with modest masses, two or less gas giants form wit...
DEFF Research Database (Denmark)
Hansen, Lisbeth S.; Borup, Morten; Møller, A.;
2011-01-01
the performance of the updating procedure for flow forecasting. Measured water levels in combination with rain gauge input are used as basis for the evaluation. When compared to simulations without updating, the results show that it is possible to obtain an improvement in the 20 minute forecast of the water level...... to eliminate some of the unavoidable discrepancies between model and reality. The latter can partly be achieved by using the commercial tool MOUSE UPDATE, which is capable of inserting measured water levels from the system into the distributed, physically based MOUSE model. This study evaluates and documents...
Directory of Open Access Journals (Sweden)
Wu Kun-Shan
2002-01-01
Full Text Available In this paper, an EOQ inventory model is depleted not only by time varying demand but also by Weibull distribution deterioration, in which the inventory is permitted to start with shortages and end without shortages. A theory is developed to obtain the optimal solution of the problem; it is then illustrated with the aid of several numerical examples. Moreover, we also assume that the holding cost is a continuous, non-negative and non-decreasing function of time in order to extend the EOQ model. Finally, sensitivity of the optimal solution to changes in the values of different system parameters is also studied.
Height-Deterministic Pushdown Automata
DEFF Research Database (Denmark)
Nowotka, Dirk; Srba, Jiri
2007-01-01
of regular languages and still closed under boolean language operations, are considered. Several of such language classes have been described in the literature. Here, we suggest a natural and intuitive model that subsumes all the formalisms proposed so far by employing height-deterministic pushdown automata...
Residual models for nonlinear partial differential equations
Directory of Open Access Journals (Sweden)
Garry Pantelis
2005-11-01
Full Text Available Residual terms that appear in nonlinear PDEs that are constructed to generate filtered representations of the variables of the fully resolved system are examined by way of a consistency condition. It is shown that certain commonly used empirical gradient models for the residuals fail the test of consistency and therefore cannot be validated as approximations in any reliable sense. An alternate method is presented for computing the residuals. These residual models are independent of free or artificial parameters and there direct link with the functional form of the system of PDEs which describe the fully resolved system are established.
An Efficient Deterministic Approach to Model-based Prediction Uncertainty Estimation
2012-09-01
always choose the end- points to determine the RUL bounds, however, in this case the UT does this automatically with the added benefit of be- ing able to...approaches for model-based prognostics. In Proceedings of the 2012 ieee aerospace conference. Edwards, D., Orchard , M. E., Tang, L., Goebel, K., & Vacht
Verification of Overall Safety Factors In Deterministic Design Of Model Tested Breakwaters
DEFF Research Database (Denmark)
Burcharth, H. F.
2001-01-01
The paper deals with concepts of safety implementation in design. An overall safety factor concept is evaluated on the basis of a reliability analysis of a model tested rubble mound breakwater with monolithic super structure. Also discussed are design load identification and failure mode limit st...
Model I - V curves and figures of merit of underdamped deterministic Josephson ratchets
Goldobin, E.; Menditto, R.; Koelle, D.; Kleiner, R.
2016-09-01
We propose simple models for the current-voltage characteristics of typical Josephson ratchets. We consider the case of a ratchet working against a constant applied counter force and derive analytical expressions for the key characteristics of such a ratchet: rectification curve, stopping force, input and output powers, and rectification efficiency. Optimization of the ratchet performance is discussed.
Ding, Shaojie; Qian, Min; Qian, Hong; Zhang, Xuejuan
2016-12-01
The stochastic Hodgkin-Huxley model is one of the best-known examples of piecewise deterministic Markov processes (PDMPs), in which the electrical potential across a cell membrane, V(t), is coupled with a mesoscopic Markov jump process representing the stochastic opening and closing of ion channels embedded in the membrane. The rates of the channel kinetics, in turn, are voltage-dependent. Due to this interdependence, an accurate and efficient sampling of the time evolution of the hybrid stochastic systems has been challenging. The current exact simulation methods require solving a voltage-dependent hitting time problem for multiple path-dependent intensity functions with random thresholds. This paper proposes a simulation algorithm that approximates an alternative representation of the exact solution by fitting the log-survival function of the inter-jump dwell time, H(t), with a piecewise linear one. The latter uses interpolation points that are chosen according to the time evolution of the H(t), as the numerical solution to the coupled ordinary differential equations of V(t) and H(t). This computational method can be applied to all PDMPs. Pathwise convergence of the approximated sample trajectories to the exact solution is proven, and error estimates are provided. Comparison with a previous algorithm that is based on piecewise constant approximation is also presented.
Liao, Wenlin; Dai, Yifan; Xie, Xuhui; Zhou, Lin
2014-07-01
Ion beam figuring (IBF) is established for the final precision figuring of optical components. In this deterministic method, the figuring process is represented by a two-dimensional (2D) convolution operation of a constant removal function and the dwell time, where the figuring precision is guaranteed by the stability of the removal function as well as the solution accuracy of the dwell time. However, the current 2D convolution equation cannot factually reflect the IBF process of curved surfaces, which neglects the influence of the projection distortion and the workpiece geometry. Consequently, the current convolution algorithm for the IBF process would influence the solution accuracy for the dwell time and reduce the convergence of the figuring process. In this part, we propose an improved algorithm based on the mathematical modeling of the dynamic removal function in Part A, which provides a more accurate dwell time for IBF of a curved surface. Additionally, simulation analysis and figuring experiments are carried out to verify the feasibility of our proposed algorithm. The final experimental results indicate that the figuring precision and efficiency can be simultaneously improved by this method.
Ding, Shaojie; Qian, Min; Qian, Hong; Zhang, Xuejuan
2016-12-28
The stochastic Hodgkin-Huxley model is one of the best-known examples of piecewise deterministic Markov processes (PDMPs), in which the electrical potential across a cell membrane, V(t), is coupled with a mesoscopic Markov jump process representing the stochastic opening and closing of ion channels embedded in the membrane. The rates of the channel kinetics, in turn, are voltage-dependent. Due to this interdependence, an accurate and efficient sampling of the time evolution of the hybrid stochastic systems has been challenging. The current exact simulation methods require solving a voltage-dependent hitting time problem for multiple path-dependent intensity functions with random thresholds. This paper proposes a simulation algorithm that approximates an alternative representation of the exact solution by fitting the log-survival function of the inter-jump dwell time, H(t), with a piecewise linear one. The latter uses interpolation points that are chosen according to the time evolution of the H(t), as the numerical solution to the coupled ordinary differential equations of V(t) and H(t). This computational method can be applied to all PDMPs. Pathwise convergence of the approximated sample trajectories to the exact solution is proven, and error estimates are provided. Comparison with a previous algorithm that is based on piecewise constant approximation is also presented.
Deterministically patterned biomimetic human iPSC-derived hepatic model via rapid 3D bioprinting.
Ma, Xuanyi; Qu, Xin; Zhu, Wei; Li, Yi-Shuan; Yuan, Suli; Zhang, Hong; Liu, Justin; Wang, Pengrui; Lai, Cheuk Sun Edwin; Zanella, Fabian; Feng, Gen-Sheng; Sheikh, Farah; Chien, Shu; Chen, Shaochen
2016-02-23
The functional maturation and preservation of hepatic cells derived from human induced pluripotent stem cells (hiPSCs) are essential to personalized in vitro drug screening and disease study. Major liver functions are tightly linked to the 3D assembly of hepatocytes, with the supporting cell types from both endodermal and mesodermal origins in a hexagonal lobule unit. Although there are many reports on functional 2D cell differentiation, few studies have demonstrated the in vitro maturation of hiPSC-derived hepatic progenitor cells (hiPSC-HPCs) in a 3D environment that depicts the physiologically relevant cell combination and microarchitecture. The application of rapid, digital 3D bioprinting to tissue engineering has allowed 3D patterning of multiple cell types in a predefined biomimetic manner. Here we present a 3D hydrogel-based triculture model that embeds hiPSC-HPCs with human umbilical vein endothelial cells and adipose-derived stem cells in a microscale hexagonal architecture. In comparison with 2D monolayer culture and a 3D HPC-only model, our 3D triculture model shows both phenotypic and functional enhancements in the hiPSC-HPCs over weeks of in vitro culture. Specifically, we find improved morphological organization, higher liver-specific gene expression levels, increased metabolic product secretion, and enhanced cytochrome P450 induction. The application of bioprinting technology in tissue engineering enables the development of a 3D biomimetic liver model that recapitulates the native liver module architecture and could be used for various applications such as early drug screening and disease modeling.
Energy Technology Data Exchange (ETDEWEB)
Shouri, P.V.; Sreejith, P.S. [Division of Mechanical Engineering, School of Engineering, Cochin University of Science and Technology (CUSAT), Cochin 682 022, Kerala (India)
2008-06-15
In the present scenario of energy demand overtaking energy supply, top priority is given for energy conservation programs and policies. As a result, most existing systems are redesigned or modified with a view for improving energy efficiency. Often these modifications can have an impact on process system configuration, thereby affecting process system reliability. The paper presents a model for valuation of process systems incorporating reliability that can be used to determine the change in process system value resulting from system modification. The model also determines the break even system availability and presents an algorithm for allocation of component reliabilities of the modified system based on the break even system availability. The developed equations are applied to a steam power plant to study the effect of various operating parameters on system value. (author)
A Reference-Dependent Regret Model for Deterministic Trade-off Studies
Energy Technology Data Exchange (ETDEWEB)
Kujawski, Edouard
2005-02-25
Today's typical multi-criteria decision analysis is based on classical expected utility theory that assumes a mythical ''Rational Individual'' immune to psychological influences such as anticipated regret. It is therefore in conflict with rational individuals who trade-off some benefits and forgo the alternative with the highest total classical utility for a more balanced alternative in order to reduce their levels of anticipated regret. This paper focuses on decision making under certainty. It presents a reference-dependent regret model (RDRM) in which the level of regret that an individual experiences depends on the absolute values rather than the differences of the utilities of the chosen and forgone alternatives. The RDRM best choice may differ from the conventional linear additive utility model, the analytic hierarchy process, and the regret theory of Bell and Loomes and Sugden. Examples are presented that indicate that RDRM is the better predictive descriptor for decision making under certainty. RDRM satisfies transitivity of the alternatives under pairwise comparisons and models rank reversal consistent with observed reasonable choices under dynamic or distinct situations. Like regret theory, the RDRM utilities of all the alternatives under consideration are interrelated. For complex trade-off studies regret is incorporated as an element of a cost-utility-regret analysis that characterizes each alternative in terms of its monetary cost, an aggregate performance utility, and a regret value. This provides decision makers adequate information to compare the alternatives and depending on their values they may trade-off some performance and/or cost to avoid high levels of regret. The result is a well-balanced alternative often preferred by reasonable decision makers to the optimal choice of classical multi-attribute utility analysis. The model can readily be extended to incorporate rejoicing to suit decision makers who seek it. The
Energy Technology Data Exchange (ETDEWEB)
JOSEPH C. FARMER AND R. DANIEL MCCRIGHT
1997-10-01
A key component of the Engineered Barrier System (EBS) being designed for containment of spent-fuel and high-level waste at the proposed geological repository at Yucca Mountain, Nevada is a two-layer canister. In this particular design, the inner barrier is made of a corrosion resistant material (CRM) such as Alloy 625 or C-22, while the outer barrier is made of a corrosion-allowance material (CAM) such as carbon steel or Monel 400. An integrated predictive model is being developed to account for the effects of localized environmental conditions in the CRM-CAM crevice on the initiation and propagation of pits through the CRM.
Controlling chaos in ecology: from deterministic to individual-based models.
Solé, R V; Gamarra, J G; Ginovart, M; López, D
1999-11-01
The possibility of chaos control in biological systems has been stimulated by recent advances in the study of heart and brain tissue dynamics. More recently, some authors have conjectured that such a method might be applied to population dynamics and even play a nontrivial evolutionary role in ecology. In this paper we explore this idea by means of both mathematical and individual-based simulation models. Because of the intrinsic noise linked to individual behavior, controlling a noisy system becomes more difficult but, as shown here, it is a feasible task allowed to be experimentally tested.
Deterministic Walks with Choice
Energy Technology Data Exchange (ETDEWEB)
Beeler, Katy E.; Berenhaut, Kenneth S.; Cooper, Joshua N.; Hunter, Meagan N.; Barr, Peter S.
2014-01-10
This paper studies deterministic movement over toroidal grids, integrating local information, bounded memory and choice at individual nodes. The research is motivated by recent work on deterministic random walks, and applications in multi-agent systems. Several results regarding passing tokens through toroidal grids are discussed, as well as some open questions.
Model of anisotropic nonlinearity in self-defocusing photorefractive media.
Barsi, C; Fleischer, J W
2015-09-21
We develop a phenomenological model of anisotropy in self-defocusing photorefractive crystals. In addition to an independent term due to nonlinear susceptibility, we introduce a nonlinear, non-separable correction to the spectral diffraction operator. The model successfully describes the crossover between photovoltaic and photorefractive responses and the spatially dispersive shock wave behavior of a nonlinearly spreading Gaussian input beam. It should prove useful for characterizing internal charge dynamics in complex materials and for accurate image reconstruction through nonlinear media.
Modeling of the ORNL PCA Benchmark Using SCALE6.0 Hybrid Deterministic-Stochastic Methodology
Directory of Open Access Journals (Sweden)
Mario Matijević
2013-01-01
Full Text Available Revised guidelines with the support of computational benchmarks are needed for the regulation of the allowed neutron irradiation to reactor structures during power plant lifetime. Currently, US NRC Regulatory Guide 1.190 is the effective guideline for reactor dosimetry calculations. A well known international shielding database SINBAD contains large selection of models for benchmarking neutron transport methods. In this paper a PCA benchmark has been chosen from SINBAD for qualification of our methodology for pressure vessel neutron fluence calculations, as required by the Regulatory Guide 1.190. The SCALE6.0 code package, developed at Oak Ridge National Laboratory, was used for modeling of the PCA benchmark. The CSAS6 criticality sequence of the SCALE6.0 code package, which includes KENO-VI Monte Carlo code, as well as MAVRIC/Monaco hybrid shielding sequence, was utilized for calculation of equivalent fission fluxes. The shielding analysis was performed using multigroup shielding library v7_200n47g derived from general purpose ENDF/B-VII.0 library. As a source of response functions for reaction rate calculations with MAVRIC we used international reactor dosimetry libraries (IRDF-2002 and IRDF-90.v2 and appropriate cross-sections from transport library v7_200n47g. The comparison of calculational results and benchmark data showed a good agreement of the calculated and measured equivalent fission fluxes.
Mulugeta, Lealem; Walton, Marlei; Nelson, Emily; Myers, Jerry
2015-01-01
Human missions beyond low earth orbit to destinations, such as to Mars and asteroids will expose astronauts to novel operational conditions that may pose health risks that are currently not well understood and perhaps unanticipated. In addition, there are limited clinical and research data to inform development and implementation of health risk countermeasures for these missions. Consequently, NASA's Digital Astronaut Project (DAP) is working to develop and implement computational models and simulations (M&S) to help predict and assess spaceflight health and performance risks, and enhance countermeasure development. In order to effectively accomplish these goals, the DAP evaluates its models and simulations via a rigorous verification, validation and credibility assessment process to ensure that the computational tools are sufficiently reliable to both inform research intended to mitigate potential risk as well as guide countermeasure development. In doing so, DAP works closely with end-users, such as space life science researchers, to establish appropriate M&S credibility thresholds. We will present and demonstrate the process the DAP uses to vet computational M&S for space biomedical analysis using real M&S examples. We will also provide recommendations on how the larger space biomedical community can employ these concepts to enhance the credibility of their M&S codes.
Energy Technology Data Exchange (ETDEWEB)
Grace, Matthew; Lowry, Thomas Stephen; Arnold, Bill Walter; James, Scott Carlton; Gray, Genetha Anne; Ahlmann, Michael
2008-08-01
Uncertainty in site characterization arises from a lack of data and knowledge about a site and includes uncertainty in the boundary conditions, uncertainty in the characteristics, location, and behavior of major features within an investigation area (e.g., major faults as barriers or conduits), uncertainty in the geologic structure, as well as differences in numerical implementation (e.g., 2-D versus 3-D, finite difference versus finite element, grid resolution, deterministic versus stochastic, etc.). Since the true condition at a site can never be known, selection of the best conceptual model is very difficult. In addition, limiting the understanding to a single conceptualization too early in the process, or before data can support that conceptualization, may lead to confidence in a characterization that is unwarranted as well as to data collection efforts and field investigations that are misdirected and/or redundant. Using a series of numerical modeling experiments, this project examined the application and use of information criteria within the site characterization process. The numerical experiments are based on models of varying complexity that were developed to represent one of two synthetically developed groundwater sites; (1) a fully hypothetical site that represented a complex, multi-layer, multi-faulted site, and (2) a site that was based on the Horonobe site in northern Japan. Each of the synthetic sites were modeled in detail to provide increasingly informative 'field' data over successive iterations to the representing numerical models. The representing numerical models were calibrated to the synthetic site data and then ranked and compared using several different information criteria approaches. Results show, that for the early phases of site characterization, low-parameterized models ranked highest while more complex models generally ranked lowest. In addition, predictive capabilities were also better with the low-parameterized models. For
Model updating of nonlinear structures from measured FRFs
Canbaloğlu, Güvenç; Özgüven, H. Nevzat
2016-12-01
There are always certain discrepancies between modal and response data of a structure obtained from its mathematical model and experimentally measured ones. Therefore it is a general practice to update the theoretical model by using experimental measurements in order to have a more accurate model. Most of the model updating methods used in structural dynamics are for linear systems. However, in real life applications most of the structures have nonlinearities, which restrict us applying model updating techniques available for linear structures, unless they work in linear range. Well-established frequency response function (FRF) based model updating methods would easily be extended to a nonlinear system if the FRFs of the underlying linear system (linear FRFs) could be experimentally measured. When frictional type of nonlinearity co-exists with other types of nonlinearities, it is not possible to obtain linear FRFs experimentally by using low level forcing. In this study a method (named as Pseudo Receptance Difference (PRD) method) is presented to obtain linear FRFs of a nonlinear structure having multiple nonlinearities including friction type of nonlinearity. PRD method, calculates linear FRFs of a nonlinear structure by using FRFs measured at various forcing levels, and simultaneously identifies all nonlinearities in the system. Then, any model updating method can be used to update the linear part of the mathematical model. In this present work, PRD method is used to predict the linear FRFs from measured nonlinear FRFs, and the inverse eigensensitivity method is employed to update the linear finite element (FE) model of the nonlinear structure. The proposed method is validated with different case studies using nonlinear lumped single-degree of freedom system, as well as a continuous system. Finally, a real nonlinear T-beam test structure is used to show the application and the accuracy of the proposed method. The accuracy of the updated nonlinear model of the
Deterministic chaos and noise in three in vitro hippocampal models of epilepsy.
Slutzky, M W; Cvitanović, P; Mogul, D J
2001-01-01
Recent reports have suggested that chaos control techniques may be useful for electrically manipulating epileptiform bursting behavior in neuronal ensembles. Because the dynamics of spontaneous in vitro bursting had not been well determined previously, analysis of this behavior in the rat hippocampus was performed. Epileptiform bursting was induced in transverse rat hippocampal slices using three experimental methods. Slices were bathed in artificial cerebrospinal fluid containing: (1) elevated potassium ([K+]o= 10.5 mM), (2) zero magnesium, or (3) the GABAA-receptor antagonists bicuculline (20 microM) and picrotoxin (250 microM). The existence of chaos and determinism was assessed using two different analytical techniques: unstable periodic orbit (UPO) analysis and a new technique for estimating Lyapunov exponents. Significance of these results was assessed by comparing the calculations for each experiment with corresponding randomized surrogate data. UPOs of multiple periods were highly prevalent in experiments from all three epilepsy models: 73% of all experiments contained at least one statistically significant period-1 or period-2 orbit. However, the expansion rate analysis did not provide any evidence of determinism in the data. This suggests that the system may be globally stochastic but contains local pockets of determinism. Thus, manipulation of bursting behavior using chaos control algorithms may yet hold promise for reverting or preventing epileptic seizures.
From spiking neuron models to linear-nonlinear models.
Directory of Open Access Journals (Sweden)
Srdjan Ostojic
Full Text Available Neurons transform time-varying inputs into action potentials emitted stochastically at a time dependent rate. The mapping from current input to output firing rate is often represented with the help of phenomenological models such as the linear-nonlinear (LN cascade, in which the output firing rate is estimated by applying to the input successively a linear temporal filter and a static non-linear transformation. These simplified models leave out the biophysical details of action potential generation. It is not a priori clear to which extent the input-output mapping of biophysically more realistic, spiking neuron models can be reduced to a simple linear-nonlinear cascade. Here we investigate this question for the leaky integrate-and-fire (LIF, exponential integrate-and-fire (EIF and conductance-based Wang-Buzsáki models in presence of background synaptic activity. We exploit available analytic results for these models to determine the corresponding linear filter and static non-linearity in a parameter-free form. We show that the obtained functions are identical to the linear filter and static non-linearity determined using standard reverse correlation analysis. We then quantitatively compare the output of the corresponding linear-nonlinear cascade with numerical simulations of spiking neurons, systematically varying the parameters of input signal and background noise. We find that the LN cascade provides accurate estimates of the firing rates of spiking neurons in most of parameter space. For the EIF and Wang-Buzsáki models, we show that the LN cascade can be reduced to a firing rate model, the timescale of which we determine analytically. Finally we introduce an adaptive timescale rate model in which the timescale of the linear filter depends on the instantaneous firing rate. This model leads to highly accurate estimates of instantaneous firing rates.
Fallacies of composition in nonlinear marketing models
Bischi, Gian Italo; Cerboni Baiardi, Lorenzo
2015-01-01
In this paper we consider some nonlinear discrete-time dynamic models proposed in the literature to represent marketing competition, and we use these models to critically discuss the statement, often made in economic literature, that identical agents behave identically and quasi-identical ones behave in a similar way. We show, through examples and some general mathematical statements, that the one-dimensional model of a representative agent, whose dynamics summarize the common behavior of identical interacting agents, may be misleading. In order to discuss these topics some simple methods for the study of local stability and bifurcations are employed, as well as numerical examples where some results taken from the literature on chaos synchronization are applied to two-dimensional marketing models that exhibit riddling, blowout and other global phenomena related to the existence of measure-theoretic attractors.
Nonlinear regime-switching state-space (RSSS) models.
Chow, Sy-Miin; Zhang, Guangjian
2013-10-01
Nonlinear dynamic factor analysis models extend standard linear dynamic factor analysis models by allowing time series processes to be nonlinear at the latent level (e.g., involving interaction between two latent processes). In practice, it is often of interest to identify the phases--namely, latent "regimes" or classes--during which a system is characterized by distinctly different dynamics. We propose a new class of models, termed nonlinear regime-switching state-space (RSSS) models, which subsumes regime-switching nonlinear dynamic factor analysis models as a special case. In nonlinear RSSS models, the change processes within regimes, represented using a state-space model, are allowed to be nonlinear. An estimation procedure obtained by combining the extended Kalman filter and the Kim filter is proposed as a way to estimate nonlinear RSSS models. We illustrate the utility of nonlinear RSSS models by fitting a nonlinear dynamic factor analysis model with regime-specific cross-regression parameters to a set of experience sampling affect data. The parallels between nonlinear RSSS models and other well-known discrete change models in the literature are discussed briefly.
Priano, L; Saccomandi, F; Mauro, A; Guiot, C
2010-01-01
Sleep is a dynamic process aimed at obtaining the required neurophysiological states at certain times, according to circadian and homeostatic needs and despite external or internal interfering stimuli. In this context, peculiar transient synchronized EEG patterns (TSEP) are supposed to play the main role in the building up of EEG synchronization and in the flexible adaptation against perturbations Our study aimed at disclosing and quantifying attractor driven, hidden periodicity or, conversely, chaotic oscillation patterns in the series of these TSEP related to sleep stage transitions and sleep maintenance. At first we devised a multistep algorithm, able to capture TSEP from EEG during sleep in 10 healthy volunteers. The time series of TSEP were then analyzed according to the Recurrence Plot (RP). TSEP series showed to form a pseudo-periodic series which becomes progressively denser and more stable until steady slow wave NREM sleep is reached, but looses stability just before REM sleep starts. This suggests that deterministic oscillatory patterns maybe adequate descriptors of the balance between homeostatic needs for NREM sleep and REM sleep pressure, supported by different cortical neuronal populations interactions.
Model Reduction of Nonlinear Fire Dynamics Models
Lattimer, Alan Martin
2016-01-01
Due to the complexity, multi-scale, and multi-physics nature of the mathematical models for fires, current numerical models require too much computational effort to be useful in design and real-time decision making, especially when dealing with fires over large domains. To reduce the computational time while retaining the complexity of the domain and physics, our research has focused on several reduced-order modeling techniques. Our contributions are improving wildland fire reduced-order mod...
Modeling of unusual nonlinear behaviors in superconducting microstrip transmission lines
Energy Technology Data Exchange (ETDEWEB)
Javadzadeh, S. Mohammad Hassan, E-mail: smh_javadzadeh@ee.sharif.edu [School of Electrical Engineering, Sharif University of Technology, P.O. Box 11365-9363, Tehran (Iran, Islamic Republic of); Farzaneh, Forouhar; Fardmanesh, Mehdi [School of Electrical Engineering, Sharif University of Technology, P.O. Box 11365-9363, Tehran (Iran, Islamic Republic of)
2013-03-15
Highlights: ► Avoiding of considering just quadratic or modulus nonlinearity. ► Proposing a nonlinear model to predict unusual nonlinear behaviors at low temperatures. ► Description of temperature dependency of nonlinear behaviors in superconducting lines. ► Analytical formulation for each parameter in our proposed model. ► Obtaining very good results which shows this model can predict unusual nonlinear behavior. -- Abstract: There are unusual nonlinear behaviors in superconducting materials, especially at low temperatures. This paper describes the procedure to reliably predict this nonlinearity in superconducting microstrip transmission lines (SMTLs). An accurate nonlinear distributed circuit model, based on simultaneously considering of both quadratic and modulus nonlinearity dependences, is proposed. All parameters of the equivalent circuit can be calculated analytically using proposed closed-form expressions. A numerical method based on Harmonic Balance approach is used to predict nonlinear phenomena like intermodulation distortions and third harmonic generations. Nonlinear analyses of the SMTLs at the different temperatures and the input powers have been presented. This proposed model can describe the unusual behaviors of the nonlinearity at low temperatures, which are frequently observed in the SMTLs.
Model Reduction for Nonlinear Systems by Incremental Balanced Truncation
Besselink, Bart; van de Wouw, Nathan; Scherpen, Jacquelien M. A.; Nijmeijer, Henk
2014-01-01
In this paper, the method of incremental balanced truncation is introduced as a tool for model reduction of nonlinear systems. Incremental balanced truncation provides an extension of balanced truncation for linear systems towards the nonlinear case and differs from existing nonlinear balancing tech
Model Reduction for Nonlinear Systems by Incremental Balanced Truncation
Besselink, Bart; van de Wouw, Nathan; Scherpen, Jacquelien M. A.; Nijmeijer, Henk
2014-01-01
In this paper, the method of incremental balanced truncation is introduced as a tool for model reduction of nonlinear systems. Incremental balanced truncation provides an extension of balanced truncation for linear systems towards the nonlinear case and differs from existing nonlinear balancing tech
A nonlinear RDF model for waves propagating in shallow water
Institute of Scientific and Technical Information of China (English)
王厚杰; 杨作升; 李瑞杰; 张军
2001-01-01
In this paper, a composite explicit nonlinear dispersion relation is presented with reference to Stokes 2nd order dispersion relation and the empirical relation of Hedges. The explicit dispersion relation has such advantages that it can smoothly match the Stokes relation in deep and intermediate water and Hedgs’s relation in shallow water. As an explicit formula, it separates the nonlinear term from the linear dispersion relation. Therefore it is convenient to obtain the numerical solution of nonlinear dispersion relation. The present formula is combined with the modified mild-slope equation including nonlinear effect to make a Refraction-Diffraction (RDF) model for wave propagating in shallow water. This nonlinear model is verified over a complicated topography with two submerged elliptical shoals resting on a slope beach. The computation results compared with those obtained from linear model show that at present the nonlinear RDF model can predict the nonlinear characteristics and the combined refracti
Nonlinear structural finite element model updating and uncertainty quantification
Ebrahimian, Hamed; Astroza, Rodrigo; Conte, Joel P.
2015-04-01
This paper presents a framework for nonlinear finite element (FE) model updating, in which state-of-the-art nonlinear structural FE modeling and analysis techniques are combined with the maximum likelihood estimation method (MLE) to estimate time-invariant parameters governing the nonlinear hysteretic material constitutive models used in the FE model of the structure. The estimation uncertainties are evaluated based on the Cramer-Rao lower bound (CRLB) theorem. A proof-of-concept example, consisting of a cantilever steel column representing a bridge pier, is provided to verify the proposed nonlinear FE model updating framework.
Nonlinear system modeling based on experimental data
Energy Technology Data Exchange (ETDEWEB)
PAEZ,THOMAS L.; HUNTER,NORMAN F.
2000-02-02
The canonical variate analysis technique is used in this investigation, along with a data transformation algorithm, to identify a system in a transform space. The transformation algorithm involves the preprocessing of measured excitation/response data with a zero-memory-nonlinear transform, specifically, the Rosenblatt transform. This transform approximately maps the measured excitation and response data from its own space into the space of uncorrelated, standard normal random variates. Following this transform, it is appropriate to model the excitation/response relation as linear since Gaussian inputs excite Gaussian responses in linear structures. The linear model is identified in the transform space using the canonical variate analysis approach, and system responses in the original space are predicted using inverse Rosenblatt transformation. An example is presented.
Modified nonlinear model of arcsin-electrodynamics
Kruglov, S I
2015-01-01
A new modified model of nonlinear arcsin-electrodynamics with two parameters is proposed and analyzed. We obtain the corrections to the Coulomb law. The effect of vacuum birefringence takes place when the external constant magnetic field is present. We calculate indices of refraction for two perpendicular polarizations of electromagnetic waves and estimate bounds on the parameter $\\gamma$ from the BMV and PVLAS experiments. It is shown that the electric field of a point-like charge is finite at the origin. We calculate the finite static electric energy of point-like particles and demonstrate that the electron mass can have the pure electromagnetic nature. The symmetrical Belinfante energy-momentum tensor and dilatation current are found. We show that the dilatation symmetry and dual symmetry are broken in the model suggested.
Nonlinear time reversal of classical waves: experiment and model.
Frazier, Matthew; Taddese, Biniyam; Xiao, Bo; Antonsen, Thomas; Ott, Edward; Anlage, Steven M
2013-12-01
We consider time reversal of electromagnetic waves in a closed, wave-chaotic system containing a discrete, passive, harmonic-generating nonlinearity. An experimental system is constructed as a time-reversal mirror, in which excitations generated by the nonlinearity are gathered, time-reversed, transmitted, and directed exclusively to the location of the nonlinearity. Here we show that such nonlinear objects can be purely passive (as opposed to the active nonlinearities used in previous work), and we develop a higher data rate exclusive communication system based on nonlinear time reversal. A model of the experimental system is developed, using a star-graph network of transmission lines, with one of the lines terminated by a model diode. The model simulates time reversal of linear and nonlinear signals, demonstrates features seen in the experimental system, and supports our interpretation of the experimental results.
Nonlinear dynamical model of an automotive dual mass flywheel
Directory of Open Access Journals (Sweden)
Lei Chen
2015-06-01
Full Text Available The hysteresis, stick–slip, and rotational speed-dependent characteristics in a basic dual mass flywheel are obtained from a static and a dynamic experiments. Based on the experimental results, a nonlinear model of the transferred torque in this dual mass flywheel is developed, with the overlying form of nonlinear elastic torque and frictional torque. The nonlinearities of stiffness are investigated, deriving a nonlinear model to describe the rotational speed-dependent stiffness. In addition, Bouc–Wen model is used to model the hysteretic frictional torque. Thus, the nonlinear 2-degree-of-freedom system of this dual mass flywheel is set up. Then, the Levenberg–Marquardt method is adopted for the parameter estimation of the frictional torque. Finally, taking the nonlinear stiffness in this model into account, the parameters of Bouc–Wen model are estimated based on the dynamic test data.
Recovering map static nonlinearities from chaotic data using dynamical models
Aguirre, Luis Antonio
1997-02-01
This paper is concerned with the estimation from chaotic data of maps with static nonlinearities. A number of issues concerning model construction such as structure selection, over-parametrization and model validation are discussed in the light of the shape of the static non-linearities reproduced by the estimated maps. A new interpretation of term clusters and cluster coefficients of polynomial models is provided based on this approach. The paper discusses model limitations and some useful principles to select the structure of nonlinear maps. Some of the ideas have been tested using several nonlinear systems including a boost voltage regulator map and a set of real data from a chaotic circuit.
Variational modelling of nonlinear water waves
Kalogirou, Anna; Bokhove, Onno
2015-11-01
Mathematical modelling of water waves is demonstrated by investigating variational methods. A potential flow water wave model is derived using variational techniques and extented to include explicit time-dependence, leading to non-autonomous dynamics. As a first example, we consider the problem of a soliton splash in a long wave channel with a contraction at its end, resulting after a sluice gate is removed at a finite time. The removal of the sluice gate is included in the variational principle through a time-dependent gravitational potential. A second example involving non-autonomous dynamics concerns the motion of a free surface in a vertical Hele-Shaw cell. Explicit time-dependence now enters the model through a linear damping term due to the effect of wall friction and a term representing the motion of an artificially driven wave pump. In both cases, the model is solved numerically using a Galerkin FEM and the numerical results are compared to wave structures observed in experiments. The water wave model is also adapted to accommodate nonlinear ship dynamics. The novelty is this case is the coupling between the water wave dynamics, the ship dynamics and water line dynamics on the ship. For simplicity, we consider a simple ship structure consisting of V-shaped cross-sections.
Nonlinear Eddy Viscosity Models applied to Wind Turbine Wakes
DEFF Research Database (Denmark)
Laan, van der, Paul Maarten; Sørensen, Niels N.; Réthoré, Pierre-Elouan;
2013-01-01
The linear k−ε eddy viscosity model and modified versions of two existing nonlinear eddy viscosity models are applied to single wind turbine wake simulations using a Reynolds Averaged Navier-Stokes code. Results are compared with field wake measurements. The nonlinear models give better results...
A simple numerical model of a geometrically nonlinear Timoshenko beam
Keijdener, C.; Metrikine, A.
2015-01-01
In the original problem for which this model was developed, onedimensional flexible objects interact through a non-linear contact model. Due to the non-linear nature of the contact model, a numerical time-domain approach was adopted. One of the goals was to see if the coupling between axial and tran
Directory of Open Access Journals (Sweden)
Manna S.K.
2005-01-01
Full Text Available This paper develops an infinite time-horizon deterministic economic order quantity (EOQ inventory model with deterioration based on discounted cash flows (DCF approach where demand rate is assumed to be non-linear over time. The effects of inflation and time-value of money are also taken into account under a trade-credit policy of type "α/T1 net T". The results are illustrated with a numerical example. Sensitivity analysis of the optimal solution with respect to the parameters of the system is carried out.
Smith, Dianna M; Pearce, Jamie R; Harland, Kirk
2011-03-01
Models created to estimate neighbourhood level health outcomes and behaviours can be difficult to validate as prevalence is often unknown at the local level. This paper tests the reliability of a spatial microsimulation model, using a deterministic reweighting method, to predict smoking prevalence in small areas across New Zealand. The difference in the prevalence of smoking between those estimated by the model and those calculated from census data is less than 20% in 1745 out of 1760 areas. The accuracy of these results provides users with greater confidence to utilize similar approaches in countries where local-level smoking prevalence is unknown.
Directory of Open Access Journals (Sweden)
Roy T.
2007-01-01
Full Text Available A finite time-horizon deterministic inventory model is developed, taking the demand rate at any instant to be a function of the on-hand inventory (stock-level at that instant. Shortages in inventory are allowed. The effects of inflation and time value of money are considered. Two separate inflation rates: namely, the internal (company and the external (general economy are introduced. A numerical example of the model is discussed. A sensitivity analysis of the optimal solution with respect to the parameters of the model is examined.
Energy Technology Data Exchange (ETDEWEB)
Biondo, Elliott D [ORNL; Ibrahim, Ahmad M [ORNL; Mosher, Scott W [ORNL; Grove, Robert E [ORNL
2015-01-01
Detailed radiation transport calculations are necessary for many aspects of the design of fusion energy systems (FES) such as ensuring occupational safety, assessing the activation of system components for waste disposal, and maintaining cryogenic temperatures within superconducting magnets. Hybrid Monte Carlo (MC)/deterministic techniques are necessary for this analysis because FES are large, heavily shielded, and contain streaming paths that can only be resolved with MC. The tremendous complexity of FES necessitates the use of CAD geometry for design and analysis. Previous ITER analysis has required the translation of CAD geometry to MCNP5 form in order to use the AutomateD VAriaNce reducTion Generator (ADVANTG) for hybrid MC/deterministic transport. In this work, ADVANTG was modified to support CAD geometry, allowing hybrid (MC)/deterministic transport to be done automatically and eliminating the need for this translation step. This was done by adding a new ray tracing routine to ADVANTG for CAD geometries using the Direct Accelerated Geometry Monte Carlo (DAGMC) software library. This new capability is demonstrated with a prompt dose rate calculation for an ITER computational benchmark problem using both the Consistent Adjoint Driven Importance Sampling (CADIS) method an the Forward Weighted (FW)-CADIS method. The variance reduction parameters produced by ADVANTG are shown to be the same using CAD geometry and standard MCNP5 geometry. Significant speedups were observed for both neutrons (as high as a factor of 7.1) and photons (as high as a factor of 59.6).
Non-Linear Sigma Model on Conifolds
Parthasarathy, R
2002-01-01
Explicit solutions to the conifold equations with complex dimension $n=3,4$ in terms of {\\it{complex coordinates (fields)}} are employed to construct the Ricci-flat K\\"{a}hler metrics on these manifolds. The K\\"{a}hler 2-forms are found to be closed. The complex realization of these conifold metrics are used in the construction of 2-dimensional non-linear sigma model with the conifolds as target spaces. The action for the sigma model is shown to be bounded from below. By a suitable choice of the 'integration constants', arising in the solution of Ricci flatness requirement, the metric and the equations of motion are found to be {\\it{non-singular}}. As the target space is Ricci flat, the perturbative 1-loop counter terms being absent, the model becomes topological. The inherent U(1) fibre over the base of the conifolds is shown to correspond to a gauge connection in the sigma model. The same procedure is employed to construct the metric for the resolved conifold, in terms of complex coordinates and the action ...
Deterministic nature of the underlying dynamics of surface wind fluctuations
Directory of Open Access Journals (Sweden)
R. C. Sreelekshmi
2012-10-01
Full Text Available Modelling the fluctuations of the Earth's surface wind has a significant role in understanding the dynamics of atmosphere besides its impact on various fields ranging from agriculture to structural engineering. Most of the studies on the modelling and prediction of wind speed and power reported in the literature are based on statistical methods or the probabilistic distribution of the wind speed data. In this paper we investigate the suitability of a deterministic model to represent the wind speed fluctuations by employing tools of nonlinear dynamics. We have carried out a detailed nonlinear time series analysis of the daily mean wind speed data measured at Thiruvananthapuram (8.483° N,76.950° E from 2000 to 2010. The results of the analysis strongly suggest that the underlying dynamics is deterministic, low-dimensional and chaotic suggesting the possibility of accurate short-term prediction. As most of the chaotic systems are confined to laboratories, this is another example of a naturally occurring time series showing chaotic behaviour.
Deterministic nature of the underlying dynamics of surface wind fluctuations
Sreelekshmi, R. C.; Asokan, K.; Satheesh Kumar, K.
2012-10-01
Modelling the fluctuations of the Earth's surface wind has a significant role in understanding the dynamics of atmosphere besides its impact on various fields ranging from agriculture to structural engineering. Most of the studies on the modelling and prediction of wind speed and power reported in the literature are based on statistical methods or the probabilistic distribution of the wind speed data. In this paper we investigate the suitability of a deterministic model to represent the wind speed fluctuations by employing tools of nonlinear dynamics. We have carried out a detailed nonlinear time series analysis of the daily mean wind speed data measured at Thiruvananthapuram (8.483° N,76.950° E) from 2000 to 2010. The results of the analysis strongly suggest that the underlying dynamics is deterministic, low-dimensional and chaotic suggesting the possibility of accurate short-term prediction. As most of the chaotic systems are confined to laboratories, this is another example of a naturally occurring time series showing chaotic behaviour.
Explicit Nonlinear Model Predictive Control Theory and Applications
Grancharova, Alexandra
2012-01-01
Nonlinear Model Predictive Control (NMPC) has become the accepted methodology to solve complex control problems related to process industries. The main motivation behind explicit NMPC is that an explicit state feedback law avoids the need for executing a numerical optimization algorithm in real time. The benefits of an explicit solution, in addition to the efficient on-line computations, include also verifiability of the implementation and the possibility to design embedded control systems with low software and hardware complexity. This book considers the multi-parametric Nonlinear Programming (mp-NLP) approaches to explicit approximate NMPC of constrained nonlinear systems, developed by the authors, as well as their applications to various NMPC problem formulations and several case studies. The following types of nonlinear systems are considered, resulting in different NMPC problem formulations: Ø Nonlinear systems described by first-principles models and nonlinear systems described by black-box models; �...
Highly Nonlinear Ising Model and Social Segregation
Sumour, M A; Shabat, M M
2011-01-01
The usual interaction energy of the random field Ising model in statistical physics is modified by complementing the random field by added to the energy of the usual Ising model a nonlinear term S^n were S is the sum of the neighbor spins, and n=0,1,3,5,7,9,11. Within the Schelling model of urban segregation, this modification corresponds to housing prices depending on the immediate neighborhood. Simulations at different temperatures, lattice size, magnetic field, number of neighbors and different time intervals showed that results for all n are similar, expect for n=3 in violation of the universality principle and the law of corresponding states. In order to find the critical temperatures, for large n we no longer start with all spins parallel but instead with a random configuration, in order to facilitate spin flips. However, in all cases we have a Curie temperature with phase separation or long-range segregation only below this Curie temperature, and it is approximated by a simple formula: Tc is proportion...
Asymmetric and common absorption of shocks in nonlinear autoregressive models
Dijk, Dick van; Franses, Philip Hans; Boswijk, Peter
2000-01-01
textabstractA key feature of many nonlinear time series models is that they allow for the possibility that the model structure experiences changes, depending on for example the state of the economy or of the financial market. A common property of these models is that it generally is not possible to fully understand the structure of the model by considering the estimated values of the model parameters only. Put differently, it often is difficult to interpret a specific nonlinear model. To shed...
Fuzzy Modeling for Uncertainty Nonlinear Systems with Fuzzy Equations
Directory of Open Access Journals (Sweden)
Raheleh Jafari
2017-01-01
Full Text Available The uncertain nonlinear systems can be modeled with fuzzy equations by incorporating the fuzzy set theory. In this paper, the fuzzy equations are applied as the models for the uncertain nonlinear systems. The nonlinear modeling process is to find the coefficients of the fuzzy equations. We use the neural networks to approximate the coefficients of the fuzzy equations. The approximation theory for crisp models is extended into the fuzzy equation model. The upper bounds of the modeling errors are estimated. Numerical experiments along with comparisons demonstrate the excellent behavior of the proposed method.
A NEW SOLUTION MODEL OF NONLINEAR DYNAMIC LEAST SQUARE ADJUSTMENT
Institute of Scientific and Technical Information of China (English)
陶华学; 郭金运
2000-01-01
The nonlinear least square adjustment is a head object studied in technology fields. The paper studies on the non-derivative solution to the nonlinear dynamic least square adjustment and puts forward a new algorithm model and its solution model. The method has little calculation load and is simple. This opens up a theoretical method to solve the linear dynamic least square adjustment.
Lattice Boltzmann model for nonlinear convection-diffusion equations.
Shi, Baochang; Guo, Zhaoli
2009-01-01
A lattice Boltzmann model for convection-diffusion equation with nonlinear convection and isotropic-diffusion terms is proposed through selecting equilibrium distribution function properly. The model can be applied to the common real and complex-valued nonlinear evolutionary equations, such as the nonlinear Schrödinger equation, complex Ginzburg-Landau equation, Burgers-Fisher equation, nonlinear heat conduction equation, and sine-Gordon equation, by using a real and complex-valued distribution function and relaxation time. Detailed simulations of these equations are performed, and it is found that the numerical results agree well with the analytical solutions and the numerical solutions reported in previous studies.
Nonlinear lower hybrid modeling in tokamak plasmas
Energy Technology Data Exchange (ETDEWEB)
Napoli, F.; Schettini, G. [Università Roma Tre, Dipartimento di Ingegneria, Roma (Italy); Castaldo, C.; Cesario, R. [Associazione EURATOM/ENEA sulla Fusione, Centro Ricerche Frascati (Italy)
2014-02-12
We present here new results concerning the nonlinear mechanism underlying the observed spectral broadening produced by parametric instabilities occurring at the edge of tokamak plasmas in present day LHCD (lower hybrid current drive) experiments. Low frequency (LF) ion-sound evanescent modes (quasi-modes) are the main parametric decay channel which drives a nonlinear mode coupling of lower hybrid (LH) waves. The spectrum of the LF fluctuations is calculated here considering the beating of the launched LH wave at the radiofrequency (RF) operating line frequency (pump wave) with the noisy background of the RF power generator. This spectrum is calculated in the frame of the kinetic theory, following a perturbative approach. Numerical solutions of the nonlinear LH wave equation show the evolution of the nonlinear mode coupling in condition of a finite depletion of the pump power. The role of the presence of heavy ions in a Deuterium plasma in mitigating the nonlinear effects is analyzed.
Deterministic and stochastic control of chimera states in delayed feedback oscillator
Energy Technology Data Exchange (ETDEWEB)
Semenov, V. [Department of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov (Russian Federation); Zakharova, A.; Schöll, E. [Institut für Theoretische Physik, TU Berlin, Hardenbergstraße 36, 10623 Berlin (Germany); Maistrenko, Y. [Institute of Mathematics and Center for Medical and Biotechnical Research, NAS of Ukraine, Tereschenkivska Str. 3, 01601 Kyiv (Ukraine)
2016-06-08
Chimera states, characterized by the coexistence of regular and chaotic dynamics, are found in a nonlinear oscillator model with negative time-delayed feedback. The control of these chimera states by external periodic forcing is demonstrated by numerical simulations. Both deterministic and stochastic external periodic forcing are considered. It is shown that multi-cluster chimeras can be achieved by adjusting the external forcing frequency to appropriate resonance conditions. The constructive role of noise in the formation of a chimera states is shown.
A Modal Model to Simulate Typical Structural Dynamic Nonlinearity
Energy Technology Data Exchange (ETDEWEB)
Pacini, Benjamin Robert [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Mayes, Randall L. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Roettgen, Daniel R [Univ. of Wisconsin, Madison, WI (United States)
2015-10-01
Some initial investigations have been published which simulate nonlinear response with almost traditional modal models: instead of connecting the modal mass to ground through the traditional spring and damper, a nonlinear Iwan element was added. This assumes that the mode shapes do not change with amplitude and there are no interactions between modal degrees of freedom. This work expands on these previous studies. An impact experiment is performed on a structure which exhibits typical structural dynamic nonlinear response, i.e. weak frequency dependence and strong damping dependence on the amplitude of vibration. Use of low level modal test results in combination with high level impacts are processed using various combinations of modal filtering, the Hilbert Transform and band-pass filtering to develop response data that are then fit with various nonlinear elements to create a nonlinear pseudo-modal model. Simulations of forced response are compared with high level experimental data for various nonlinear element assumptions.
First principles modeling of nonlinear incidence rates in seasonal epidemics.
Directory of Open Access Journals (Sweden)
José M Ponciano
2011-02-01
Full Text Available In this paper we used a general stochastic processes framework to derive from first principles the incidence rate function that characterizes epidemic models. We investigate a particular case, the Liu-Hethcote-van den Driessche's (LHD incidence rate function, which results from modeling the number of successful transmission encounters as a pure birth process. This derivation also takes into account heterogeneity in the population with regard to the per individual transmission probability. We adjusted a deterministic SIRS model with both the classical and the LHD incidence rate functions to time series of the number of children infected with syncytial respiratory virus in Banjul, Gambia and Turku, Finland. We also adjusted a deterministic SEIR model with both incidence rate functions to the famous measles data sets from the UK cities of London and Birmingham. Two lines of evidence supported our conclusion that the model with the LHD incidence rate may very well be a better description of the seasonal epidemic processes studied here. First, our model was repeatedly selected as best according to two different information criteria and two different likelihood formulations. The second line of evidence is qualitative in nature: contrary to what the SIRS model with classical incidence rate predicts, the solution of the deterministic SIRS model with LHD incidence rate will reach either the disease free equilibrium or the endemic equilibrium depending on the initial conditions. These findings along with computer intensive simulations of the models' Poincaré map with environmental stochasticity contributed to attain a clear separation of the roles of the environmental forcing and the mechanics of the disease transmission in shaping seasonal epidemics dynamics.
First principles modeling of nonlinear incidence rates in seasonal epidemics.
Ponciano, José M; Capistrán, Marcos A
2011-02-01
In this paper we used a general stochastic processes framework to derive from first principles the incidence rate function that characterizes epidemic models. We investigate a particular case, the Liu-Hethcote-van den Driessche's (LHD) incidence rate function, which results from modeling the number of successful transmission encounters as a pure birth process. This derivation also takes into account heterogeneity in the population with regard to the per individual transmission probability. We adjusted a deterministic SIRS model with both the classical and the LHD incidence rate functions to time series of the number of children infected with syncytial respiratory virus in Banjul, Gambia and Turku, Finland. We also adjusted a deterministic SEIR model with both incidence rate functions to the famous measles data sets from the UK cities of London and Birmingham. Two lines of evidence supported our conclusion that the model with the LHD incidence rate may very well be a better description of the seasonal epidemic processes studied here. First, our model was repeatedly selected as best according to two different information criteria and two different likelihood formulations. The second line of evidence is qualitative in nature: contrary to what the SIRS model with classical incidence rate predicts, the solution of the deterministic SIRS model with LHD incidence rate will reach either the disease free equilibrium or the endemic equilibrium depending on the initial conditions. These findings along with computer intensive simulations of the models' Poincaré map with environmental stochasticity contributed to attain a clear separation of the roles of the environmental forcing and the mechanics of the disease transmission in shaping seasonal epidemics dynamics.
ASYMPTOTIC EFFICIENT ESTIMATION IN SEMIPARAMETRIC NONLINEAR REGRESSION MODELS
Institute of Scientific and Technical Information of China (English)
ZhuZhongyi; WeiBocheng
1999-01-01
In this paper, the estimation method based on the “generalized profile likelihood” for the conditionally parametric models in the paper given by Severini and Wong (1992) is extendedto fixed design semiparametrie nonlinear regression models. For these semiparametrie nonlinear regression models,the resulting estimator of parametric component of the model is shown to beasymptotically efficient and the strong convergence rate of nonparametric component is investigated. Many results (for example Chen (1988) ,Gao & Zhao (1993), Rice (1986) et al. ) are extended to fixed design semiparametric nonlinear regression models.
Control design approaches for nonlinear systems using multiple models
Institute of Scientific and Technical Information of China (English)
Junyong ZHAI; Shumin FEI; Feipeng DA
2007-01-01
It is difficult to realize control for some complex nonlinear systems operated in different operating regions.Based on developing local models for different operating regions of the process, a novel algorithm using multiple models is proposed. It utilizes dynamic model bank to establish multiple local models, and their membership functions are defined according to respective regions. Then the nonlinear system is approximated to a weighted combination of the local models.The stability of the nonlinear system is proven. Finally, simulations are given to demonstrate the validity of the proposed method.
TESTING FOR VARYING DISPERSION IN DISCRETE EXPONENTIAL FAMILY NONLINEAR MODELS
Institute of Scientific and Technical Information of China (English)
LinJinguan; WeiBocheng; ZhangNansong
2003-01-01
It is necessary to test for varying dispersion in generalized nonlinear models. Wei ,et al(1998) developed a likelihood ratio test,a score test and their adjustments to test for varying dispersion in continuous exponential family nonlinear models. This type of problem in the framework of general discrete exponential family nonlinear models is discussed. Two types of varying dispersion, which are random coefficients model and random effects model, are proposed,and corresponding score test statistics are constructed and expressed in simple ,easy to use ,matrix formulas.
Nonlinear flow model for well production in an underground formation
Directory of Open Access Journals (Sweden)
J. C. Guo
2013-05-01
Full Text Available Fluid flow in underground formations is a nonlinear process. In this article we modelled the nonlinear transient flow behaviour of well production in an underground formation. Based on Darcy's law and material balance equations, we used quadratic pressure gradients to deduce diffusion equations and discuss the origins of nonlinear flow issues. By introducing an effective-well-radius approach that considers skin factor, we established a nonlinear flow model for both gas and liquid (oil or water. The liquid flow model was solved using a semi-analytical method, while the gas flow model was solved using numerical simulations because the diffusion equation of gas flow is a stealth function of pressure. For liquid flow, a series of standard log-log type curves of pressure transients were plotted and nonlinear transient flow characteristics were analyzed. Qualitative and quantitative analyses were used to compare the solutions of the linear and nonlinear models. The effect of nonlinearity upon pressure transients should not be ignored. For gas flow, pressure transients were simulated and compared with oil flow under the same formation and well conditions, resulting in the conclusion that, under the same volume rate production, oil wells demand larger pressure drops than gas wells. Comparisons between theoretical data and field data show that nonlinear models will describe fluid flow in underground formations realistically and accurately.
Model reduction of nonlinear systems subject to input disturbances
Ndoye, Ibrahima
2017-07-10
The method of convex optimization is used as a tool for model reduction of a class of nonlinear systems in the presence of disturbances. It is shown that under some conditions the nonlinear disturbed system can be approximated by a reduced order nonlinear system with similar disturbance-output properties to the original plant. The proposed model reduction strategy preserves the nonlinearity and the input disturbance nature of the model. It guarantees a sufficiently small error between the outputs of the original and the reduced-order systems, and also maintains the properties of input-to-state stability. The matrices of the reduced order system are given in terms of a set of linear matrix inequalities (LMIs). The paper concludes with a demonstration of the proposed approach on model reduction of a nonlinear electronic circuit with additive disturbances.
Nonlinear and Non Normal Regression Models in Physiological Research
1984-01-01
Applications of nonlinear and non normal regression models are in increasing order for appropriate interpretation of complex phenomenon of biomedical sciences. This paper reviews critically some applications of these models physiological research.
Rojas, Santiago Rojas; Naether, Uta; Xavier, Guilherme B; Nolte, Stefan; Szameit, Alexander; Vicencio, Rodrigo A; Lima, Gustavo; Delgado, Aldo
2014-01-01
We study the polarization properties of elliptical femtosecond-laser-written waveguides arrays. A new analytical model is presented to explain the asymmetry of the spatial transverse profiles of linearly polarized modes in these waveguides. This asymmetry produces a polarization dependent coupling coeffcient, between adjacent waveguides, which strongly affects the propagation of light in a lattice. Our analysis explains how this effect can be exploited to tune the final intensity distribution of light propagated through the array. Then, we show how a compact, balanced, and deterministic polarizing beam splitter can be constructed in integrated circuits.
Nonlinear Dynamic Model Explains The Solar Dynamic
Kuman, Maria
Nonlinear mathematical model in torus representation describes the solar dynamic. Its graphic presentation shows that without perturbing force the orbits of the planets would be circles; only perturbing force could elongate the circular orbits into ellipses. Since the Hubble telescope found that the planetary orbits of other stars in the Milky Way are also ellipses, powerful perturbing force must be present in our galaxy. Such perturbing force is the Sagittarius Dwarf Galaxy with its heavy Black Hole and leftover stars, which we see orbiting around the center of our galaxy. Since observations of NASA's SDO found that magnetic fields rule the solar activity, we can expect when the planets align and their magnetic moments sum up, the already perturbed stars to reverse their magnetic parity (represented graphically as periodic looping through the hole of the torus). We predict that planets aligned on both sides of the Sun, when their magnetic moments sum-up, would induce more flares in the turbulent equatorial zone, which would bulge. When planets align only on one side of the Sun, the strong magnetic gradient of their asymmetric pull would flip the magnetic poles of the Sun. The Sun would elongate pole-to-pole, emit some energy through the poles, and the solar activity would cease. Similar reshaping and emission was observed in stars called magnetars and experimentally observed in super-liquid fast-spinning Helium nanodroplets. We are certain that NASA's SDO will confirm our predictions.
Institute of Scientific and Technical Information of China (English)
SHAO Yuanzhi; ZHONG Weirong; HE Zhenhui
2005-01-01
We report the nonequilibrium dynamical phase transition (NDPT) appearing in a kinetic Ising spin system (ISS) subject to the joint application of a deterministic external field and the stochastic mutually correlated noises simultaneously. A time-dependent Ginzburg-Landau stochastic differential equation, including an oscillating modulation and the correlated multiplicative and additive white noises, was addressed and the numerical solution to the relevant Fokker-Planck equation was presented on the basis of an average-period approach of driven field. The correlated white noises and the deterministic modulation induce a kind of dynamic symmetry-breaking order, analogous to the stochastic resonance in trend, in the kinetic ISS, and the reentrant transition has been observed between the dynamic disorder and order phases when the intensities of multiplicative and additive noises were changing. The dependencies of a dynamic order parameter Q upon the intensities of additive noise A and multiplicative noise M, the correlation λ between two noises, and the amplitude of applied external field h were investigated quantitatively and visualized vividly. Here a brief discussion is given to outline the underlying mechanism of the NDPT in a kinetic ISS driven by an external force and correlated noises.
Deterministic Discrepancy Minimization
Bansal, N.; Spencer, J.
2013-01-01
We derandomize a recent algorithmic approach due to Bansal (Foundations of Computer Science, FOCS, pp. 3–10, 2010) to efficiently compute low discrepancy colorings for several problems, for which only existential results were previously known. In particular, we give an efficient deterministic algori
Spurious deterministic seasonality
Ph.H.B.F. Franses (Philip Hans); S. Hylleberg; H.S. Lee (Hahn)
1995-01-01
textabstractIt is sometimes assumed that the R2 of a regression of a first-order differenced time series on seasonal dummy variables reflects the amount of seasonal fluctuations that can be explained by deterministic variation in the series. In this paper we show that neglecting the presence of seas
Nonlinear State Space Modeling and System Identification for Electrohydraulic Control
Directory of Open Access Journals (Sweden)
Jun Yan
2013-01-01
Full Text Available The paper deals with nonlinear modeling and identification of an electrohydraulic control system for improving its tracking performance. We build the nonlinear state space model for analyzing the highly nonlinear system and then develop a Hammerstein-Wiener (H-W model which consists of a static input nonlinear block with two-segment polynomial nonlinearities, a linear time-invariant dynamic block, and a static output nonlinear block with single polynomial nonlinearity to describe it. We simplify the H-W model into a linear-in-parameters structure by using the key term separation principle and then use a modified recursive least square method with iterative estimation of internal variables to identify all the unknown parameters simultaneously. It is found that the proposed H-W model approximates the actual system better than the independent Hammerstein, Wiener, and ARX models. The prediction error of the H-W model is about 13%, 54%, and 58% less than the Hammerstein, Wiener, and ARX models, respectively.
Modelling and Estimation of Hammerstein System with Preload Nonlinearity
Directory of Open Access Journals (Sweden)
Khaled ELLEUCH
2010-12-01
Full Text Available This paper deals with modelling and parameter identification of nonlinear systems described by Hammerstein model having asymmetric static nonlinearities known as preload nonlinearity characteristic. The simultaneous use of both an easy decomposition technique and the generalized orthonormal bases leads to a particular form of Hammerstein model containing a minimal parameters number. The employ of orthonormal bases for the description of the linear dynamic block conducts to a linear regressor model, so that least squares techniques can be used for the parameter estimation. Singular Values Decomposition (SVD technique has been applied to separate the coupled parameters. To demonstrate the feasibility of the identification method, an illustrative example is included.
Applications of Nonlinear Dynamics Model and Design of Complex Systems
In, Visarath; Palacios, Antonio
2009-01-01
This edited book is aimed at interdisciplinary, device-oriented, applications of nonlinear science theory and methods in complex systems. In particular, applications directed to nonlinear phenomena with space and time characteristics. Examples include: complex networks of magnetic sensor systems, coupled nano-mechanical oscillators, nano-detectors, microscale devices, stochastic resonance in multi-dimensional chaotic systems, biosensors, and stochastic signal quantization. "applications of nonlinear dynamics: model and design of complex systems" brings together the work of scientists and engineers that are applying ideas and methods from nonlinear dynamics to design and fabricate complex systems.
Extended models of nonlinear waves in liquid with gas bubbles
Kudryashov, Nikolay A
2016-01-01
In this work we generalize the models for nonlinear waves in a gas--liquid mixture taking into account an interphase heat transfer, a surface tension and a weak liquid compressibility simultaneously at the derivation of the equations for nonlinear waves. We also take into consideration high order terms with respect to the small parameter. Two new nonlinear differential equations are derived for long weakly nonlinear waves in a liquid with gas bubbles by the reductive perturbation method considering both high order terms with respect to the small parameter and the above mentioned physical properties. One of these equations is the perturbation of the Burgers equation and corresponds to main influence of dissipation on nonlinear waves propagation. The other equation is the perturbation of the Burgers--Korteweg--de Vries equation and corresponds to main influence of dispersion on nonlinear waves propagation.
Nonlinear Mixed-Effects Models for Repairable Systems Reliability
Institute of Scientific and Technical Information of China (English)
TAN Fu-rong; JIANG Zhi-bin; KUO Way; Suk Joo BAE
2007-01-01
Mixed-effects models, also called random-effects models, are a regression type of analysis which enables the analyst to not only describe the trend over time within each subject, but also to describe the variation among different subjects. Nonlinear mixed-effects models provide a powerful and flexible tool for handling the unbalanced count data. In this paper, nonlinear mixed-effects models are used to analyze the failure data from a repairable system with multiple copies. By using this type of models, statistical inferences about the population and all copies can be made when accounting for copy-to-copy variance. Results of fitting nonlinear mixed-effects models to nine failure-data sets show that the nonlinear mixed-effects models provide a useful tool for analyzing the failure data from multi-copy repairable systems.
A Boussinesq model with alleviated nonlinearity and dispersion
Institute of Scientific and Technical Information of China (English)
ZHANG Dian-xin; TAO Jian-hua
2008-01-01
The classical Boussinesq equation is a weakly nonlinear and weakly dispersive equation, which has been widely applied to simulate wave propagation in off-coast shallow waters. A new form of the Boussinesq model for an uneven bottoms is derived in this paper. In the new model, nonlinearity is reduced without increasing the order of the highest derivative in the differential equations. Dispersion relationship of the model is improved to the order of Pade (2,2) by adjusting a parameter in the model based on the long wave approximation. Analysis of the linear dispersion, linear shoaling and nonlinearity of the present model shows that the performances in terms of nonlinearity, dispersion and shoaling of this model are improved. Numerical results obtained with the present model are in agreement with experimental data.
Directory of Open Access Journals (Sweden)
YouHua Chen
2014-06-01
Full Text Available In the present report, the coexistence of Prisoners' Dilemma game players (cooperators and defectors were explored in an individual-based framework with the consideration of the impacts of deterministic and stochastic waiting time (WT for triggering mortality and/or colonization events. For the type of deterministic waiting time, the time step for triggering a mortality and/or colonization event is fixed. For the type of stochastic waiting time, whether a mortality and/or colonization event should be triggered for each time step of a simulation is randomly determined by a given acceptance probability (the event takes place when a variate drawn from a uniform distribution [0,1] is smaller than the acceptance probability. The two strategies of modeling waiting time are considered simultaneously and applied to both quantities (mortality: WTm, colonization: WTc. As such, when WT (WTm and/or WTc is an integral >=1, it indicated a deterministically triggering strategy. In contrast, when 1>WT>0, it indicated a stochastically triggering strategy and the WT value itself is used as the acceptance probability. The parameter space between the waiting time for mortality (WTm-[0.1,40] and colonization (WTc-[0.1,40] was traversed to explore the coexistence and non-coexistence regions. The role of defense award was evaluated. My results showed that, one non-coexistence region is identified consistently, located at the area where 1>=WTm>=0.3 and 40>=WTc>=0.1. As a consequence, it was found that the coexistence of cooperators and defectors in the community is largely dependent on the waiting time of mortality events, regardless of the defense or cooperation rewards. When the mortality events happen in terms of stochastic waiting time (1>=WTm>=0.3, extinction of either cooperators or defectors or both could be very likely, leading to the emergence of non-coexistence scenarios. However, when the mortality events occur in forms of relatively long deterministic
Employment of CB models for non-linear dynamic analysis
Klein, M. R. M.; Deloo, P.; Fournier-Sicre, A.
1990-01-01
The non-linear dynamic analysis of large structures is always very time, effort and CPU consuming. Whenever possible the reduction of the size of the mathematical model involved is of main importance to speed up the computational procedures. Such reduction can be performed for the part of the structure which perform linearly. Most of the time, the classical Guyan reduction process is used. For non-linear dynamic process where the non-linearity is present at interfaces between different structures, Craig-Bampton models can provide a very rich information, and allow easy selection of the relevant modes with respect to the phenomenon driving the non-linearity. The paper presents the employment of Craig-Bampton models combined with Newmark direct integration for solving non-linear friction problems appearing at the interface between the Hubble Space Telescope and its solar arrays during in-orbit maneuvers. Theory, implementation in the FEM code ASKA, and practical results are shown.
Institute of Scientific and Technical Information of China (English)
Katsuaki Koike
2011-01-01
Sample data in the Earth and environmental sciences are limited in quantity and sampling location and therefore, sophisticated spatial modeling techniques are indispensable for accurate imaging of complicated structures and properties of geomaterials. This paper presents several effective methods that are grouped into two categories depending on the nature of regionalized data used. Type I data originate from plural populations and type II data satisfy the prerequisite of stationarity and have distinct spatial correlations. For the type I data, three methods are shown to be effective and demonstrated to produce plausible results: (1) a spline-based method, (2) a combination of a spline-based method with a stochastic simulation, and (3) a neural network method. Geostatistics proves to be a powerful tool for type II data. Three new approaches of geostatistics are presented with case studies: an application to directional data such as fracture, multi-scale modeling that incorporates a scaling law,and space-time joint analysis for multivariate data. Methods for improving the contribution of such spatial modeling to Earth and environmental sciences are also discussed and future important problems to be solved are summarized.
Linear and Nonlinear Thinking: A Multidimensional Model and Measure
Groves, Kevin S.; Vance, Charles M.
2015-01-01
Building upon previously developed and more general dual-process models, this paper provides empirical support for a multidimensional thinking style construct comprised of linear thinking and multiple dimensions of nonlinear thinking. A self-report assessment instrument (Linear/Nonlinear Thinking Style Profile; LNTSP) is presented and…
Combined forecasts from linear and nonlinear time series models
N. Terui (Nobuhiko); H.K. van Dijk (Herman)
1999-01-01
textabstractCombined forecasts from a linear and a nonlinear model are investigated for time series with possibly nonlinear characteristics. The forecasts are combined by a constant coefficient regression method as well as a time varying method. The time varying method allows for a locally (non)line
Temperature effects in a nonlinear model of monolayer Scheibe aggregates
DEFF Research Database (Denmark)
Bang, Ole; Christiansen, Peter Leth; If, F.
1994-01-01
A nonlinear dynamical model of molecular monolayers arranged in Scheibe aggregates is derived from a proper Hamiltonian. Thermal fluctuations of the phonons are included. The resulting equation for the excitons is the two dimensional nonlinear Schrodinger equation with noise. Two limits...
Linear and Nonlinear Thinking: A Multidimensional Model and Measure
Groves, Kevin S.; Vance, Charles M.
2015-01-01
Building upon previously developed and more general dual-process models, this paper provides empirical support for a multidimensional thinking style construct comprised of linear thinking and multiple dimensions of nonlinear thinking. A self-report assessment instrument (Linear/Nonlinear Thinking Style Profile; LNTSP) is presented and…
DEFF Research Database (Denmark)
Fournier, David A.; Skaug, Hans J.; Ancheta, Johnoel
2011-01-01
Many criteria for statistical parameter estimation, such as maximum likelihood, are formulated as a nonlinear optimization problem.Automatic Differentiation Model Builder (ADMB) is a programming framework based on automatic differentiation, aimed at highly nonlinear models with a large number...
Nonlinear Economic Model Predictive Control Strategy for Active Smart Buildings
DEFF Research Database (Denmark)
Santos, Rui Mirra; Zong, Yi; Sousa, Joao M. C.
2016-01-01
Nowadays, the development of advanced and innovative intelligent control techniques for energy management in buildings is a key issue within the smart grid topic. A nonlinear economic model predictive control (EMPC) scheme, based on the branch-and-bound tree search used as optimization algorithm...... for solving the nonconvex optimization problem is proposed in this paper. A simulation using the nonlinear model-based controller to control the temperature levels of an intelligent office building (PowerFlexHouse) is addressed. Its performance is compared with a linear model-based controller. The nonlinear...
Local Influence Analysis for Semiparametric Reproductive Dispersion Nonlinear Models
Institute of Scientific and Technical Information of China (English)
Xue-dong CHEN; Nian-sheng TANG; Xue-ren WANG
2012-01-01
The present paper proposes a semiparametric reproductive dispersion nonlinear model (SRDNM)which is an extension of the nonlinear reproductive dispersion models and the semiparameter regression models.Maximum penalized likelihood estimates (MPLEs) of unknown parameters and nonparametric functions in SRDNM are presented.Assessment of local influence for various perturbation schemes are investigated.Some local influence diagnostics are given.A simulation study and a real example are used to illustrate the proposed methodologies.
General expression for linear and nonlinear time series models
Institute of Scientific and Technical Information of China (English)
Ren HUANG; Feiyun XU; Ruwen CHEN
2009-01-01
The typical time series models such as ARMA, AR, and MA are founded on the normality and stationarity of a system and expressed by a linear difference equation; therefore, they are strictly limited to the linear system. However, some nonlinear factors are within the practical system; thus, it is difficult to fit the model for real systems with the above models. This paper proposes a general expression for linear and nonlinear auto-regressive time series models (GNAR). With the gradient optimization method and modified AIC information criteria integrated with the prediction error, the parameter estimation and order determination are achieved. The model simulation and experiments show that the GNAR model can accurately approximate to the dynamic characteristics of the most nonlinear models applied in academics and engineering. The modeling and prediction accuracy of the GNAR model is superior to the classical time series models. The proposed GNAR model is flexible and effective.
Bayesian model comparison in nonlinear BOLD fMRI hemodynamics
DEFF Research Database (Denmark)
Jacobsen, Danjal Jakup; Hansen, Lars Kai; Madsen, Kristoffer Hougaard
2008-01-01
Nonlinear hemodynamic models express the BOLD (blood oxygenation level dependent) signal as a nonlinear, parametric functional of the temporal sequence of local neural activity. Several models have been proposed for both the neural activity and the hemodynamics. We compare two such combined models......: the original balloon model with a square-pulse neural model (Friston, Mechelli, Turner, & Price, 2000) and an extended balloon model with a more sophisticated neural model (Buxton, Uludag, Dubowitz, & Liu, 2004). We learn the parameters of both models using a Bayesian approach, where the distribution...
Till, John E; Rood, Arthur S; Garzon, Caroline D; Lagdon, Richard H
2014-09-01
The suitability of a new facility in terms of potential impacts from routine and accidental releases is typically evaluated using conservative models and assumptions to assure dose standards are not exceeded. However, overly conservative dose estimates that exceed target doses can result in unnecessary and costly facility design changes. This paper examines one such case involving the U.S. Department of Energy's pretreatment facility of the Waste Treatment and Immobilization Plant (WTP). The MELCOR Accident Consequence Code System Version 2 (MACCS2) was run using conservative parameter values in prescribed guidance to demonstrate that the dose from a postulated airborne release would not exceed the guideline dose of 0.25 Sv. External review of default model parameters identified the deposition velocity of 1.0 cm s as being non-conservative. The deposition velocity calculated using resistance models was in the range of 0.1 to 0.3 cm s-1. A value of 0.1 cm s-1 would result in the dose guideline being exceeded. To test the overall conservatism of the MACCS2 transport model, the 95th percentile hourly average dispersion factor based on one year of meteorological data was compared to dispersion factors generated from two state-of-the-art Lagrangian puff models. The 95th percentile dispersion factor from MACCS2 was a factor of 3 to 6 higher compared to those of the Lagrangian puff models at a distance of 9.3 km and a deposition velocity of 0.1 cm s-1. Thus, the inherent conservatism in MACCS2 more than compensated for the high deposition velocity used in the assessment. Applications of models like MACCS2 with a conservative set of parameters are essentially screening calculations, and failure to meet dose criteria should not trigger facility design changes but prompt a more in-depth analysis using probabilistic methods with a defined margin of safety in the target dose. A sample application of the probabilistic approach is provided.
Coupled Oscillator Model for Nonlinear Gravitational Perturbations
Yang, Huan; Green, Stephen R; Lehner, Luis
2015-01-01
Motivated by the gravity/fluid correspondence, we introduce a new method for characterizing nonlinear gravitational interactions. Namely we map the nonlinear perturbative form of the Einstein equation to the equations of motion of a collection of nonlinearly-coupled harmonic oscillators. These oscillators correspond to the quasinormal or normal modes of the background spacetime. We demonstrate the mechanics and the utility of this formalism within the context of perturbed asymptotically anti-de Sitter black brane spacetimes. We confirm in this case that the boundary fluid dynamics are equivalent to those of the hydrodynamic quasinormal modes of the bulk spacetime. We expect this formalism to remain valid in more general spacetimes, including those without a fluid dual. In other words, although borne out of the gravity/fluid correspondence, the formalism is fully independent and it has a much wider range of applicability. In particular, as this formalism inspires an especially transparent physical intuition, w...
Reduced Noise Effect in Nonlinear Model Estimation Using Multiscale Representation
Directory of Open Access Journals (Sweden)
Mohamed N. Nounou
2010-01-01
Full Text Available Nonlinear process models are widely used in various applications. In the absence of fundamental models, it is usually relied on empirical models, which are estimated from measurements of the process variables. Unfortunately, measured data are usually corrupted with measurement noise that degrades the accuracy of the estimated models. Multiscale wavelet-based representation of data has been shown to be a powerful data analysis and feature extraction tool. In this paper, these characteristics of multiscale representation are utilized to improve the estimation accuracy of the linear-in-the-parameters nonlinear model by developing a multiscale nonlinear (MSNL modeling algorithm. The main idea in this MSNL modeling algorithm is to decompose the data at multiple scales, construct multiple nonlinear models at multiple scales, and then select among all scales the model which best describes the process. The main advantage of the developed algorithm is that it integrates modeling and feature extraction to improve the robustness of the estimated model to the presence of measurement noise in the data. This advantage of MSNL modeling is demonstrated using a nonlinear reactor model.
Blind channel identication of nonlinear folding mixing model
Institute of Scientific and Technical Information of China (English)
Su Yong; Xu Shangzhi; Ye Zhongfu
2006-01-01
Signals from multi-sensor systems are often mixtures of (statistically) independent sources by unknown mixing method. Blind source separation(BSS) and independent component analysis(ICA) are the methods to identify/recover the channels and the sources. BSS/ICA of nonlinear mixing models are difficult problems. For instance, the post-nonlinear model has been studied by several authors. It is noticed that in most cases, the proposed models are always with an invertible mixing. According to this fact there is an interesting question: how about the situation of the non-invertible non-linear mixing in BSS or ICA? A new simple non-linear mixing model is proposed with a kind of non-invertible mixing, the folding mixing, and method to identify its channel, blindly.
Review of Nonlinear Methods and Modelling
Borg, F G
2005-01-01
The first part of this Review describes a few of the main methods that have been employed in non-linear time series analysis with special reference to biological applications (biomechanics). The second part treats the physical basis of posturogram data (human balance) and EMG (electromyography, a measure of muscle activity).
Exact travelling wave solutions for some important nonlinear physical models
Indian Academy of Sciences (India)
Jonu Lee; Rathinasamy Sakthivel
2013-05-01
The two-dimensional nonlinear physical models and coupled nonlinear systems such as Maccari equations, Higgs equations and Schrödinger–KdV equations have been widely applied in many branches of physics. So, finding exact travelling wave solutions of such equations are very helpful in the theories and numerical studies. In this paper, the Kudryashov method is used to seek exact travelling wave solutions of such physical models. Further, three-dimensional plots of some of the solutions are also given to visualize the dynamics of the equations. The results reveal that the method is a very effective and powerful tool for solving nonlinear partial differential equations arising in mathematical physics.
A reduced order model for nonlinear vibroacoustic problems
Directory of Open Access Journals (Sweden)
Ouisse Morvan
2012-07-01
Full Text Available This work is related to geometrical nonlinearities applied to thin plates coupled with fluid-filled domain. Model reduction is performed to reduce the computation time. Reduced order model (ROM is issued from the uncoupled linear problem and enriched with residues to describe the nonlinear behavior and coupling effects. To show the efficiency of the proposed method, numerical simulations in the case of an elastic plate closing an acoustic cavity are presented.
A Comment on the Renormalization of the Nonlinear Sigma Model
Bettinelli, D; Quadri, A; Bettinelli, Daniele; Ferrari, Ruggero; Quadri, Andrea
2007-01-01
We consider the recently proposed renormalization procedure for the nonlinear sigma model, consisting in the recursive subtraction of the divergences in a symmetric fashion. We compare this subtraction with the conventional procedure in power counting renormalizable (PCR) theories. We argue that symmetric subtraction in the nonlinear sigma model does not follow the lore by which nonrenormalizable theories require an infinite number of parameter fixings. Our conclusion is that only two parameters can be consistently used as physical constants.
Robust Designs for Three Commonly Used Nonlinear Models
Xu, Xiaojian; Chen, Arnold
2011-11-01
In this paper, we study the robust designs for a few nonlinear models, including an exponential model with an intercept, a compartmental model, and a Michaelis-Menten model, when these models are possibly misspecified. The minimax robust designs we considered in this paper are under consideration of not only minimizing the variances but also reducing the possible biases in estimation. Both prediction and extrapolation cases are discussed. The robust designs are found incorporating the approximation of these models with several situations such as homoscedasticity, and heteroscedasticity. Both ordinary and weighted nonlinear least squares methods are utilized.
RECENT PROGRESS IN NONLINEAR EDDY-VISCOSITY TURBULENCE MODELING
Institute of Scientific and Technical Information of China (English)
符松; 郭阳; 钱炜祺; 王辰
2003-01-01
This article presents recent progresses in turbulence modeling in the Unit for Turbulence Simulation in the Department of Engineering Mechanics at Tsinghua University. The main contents include: compact Non-Linear Eddy-Viscosity Model (NLEVM) based on the second-moment closure, near-wall low-Re non-linear eddy-viscosity model and curvature sensitive turbulence model.The models have been validated in a wide range of complex flow test cases and the calculated results show that the present models exhibited overall good performance.
Stochastic versus deterministic systems of differential equations
Ladde, G S
2003-01-01
This peerless reference/text unfurls a unified and systematic study of the two types of mathematical models of dynamic processes-stochastic and deterministic-as placed in the context of systems of stochastic differential equations. Using the tools of variational comparison, generalized variation of constants, and probability distribution as its methodological backbone, Stochastic Versus Deterministic Systems of Differential Equations addresses questions relating to the need for a stochastic mathematical model and the between-model contrast that arises in the absence of random disturbances/flu
Modeling of nonlinear responses for reciprocal transducers involving polarization switching
DEFF Research Database (Denmark)
Willatzen, Morten; Wang, Linxiang
2007-01-01
Nonlinearities and hysteresis effects in a reciprocal PZT transducer are examined by use of a dynamical mathematical model on the basis of phase-transition theory. In particular, we consider the perovskite piezoelectric ceramic in which the polarization process in the material can be modeled....... We present numerical results for the reciprocal-transducer system and identify the influence of nonlinearities on the system dynamics at high and low frequency as well as electrical impedance effects due to tuning by a series inductance. It is found that nonlinear effects are not important at high...... by Landau theory for the first-order phase transformation, in which each polarization state is associated with a minimum of the Landau free-energy function. Nonlinear constitutive laws are obtained by using thermodynamical equilibrium conditions, and hysteretic behavior of the material can be modeled...
Nonlinear unmixing of hyperspectral images: models and algorithms
Dobigeon, Nicolas; Richard, Cédric; Bermudez, José C M; McLaughlin, Stephen; Hero, Alfred O
2013-01-01
When considering the problem of unmixing hyperspectral images, most of the literature in the geoscience and image processing areas rely on the widely acknowledged linear mixing model (LMM). However, in specific but common contexts, the LMM may be not valid and other nonlinear models should be invoked. Consequently, over the last few years, several significant contributions have been proposed to overcome the limitations inherent in the LMM. In this paper, we present an overview of recent advances that deal with the nonlinear unmixing problem. The main nonlinear models are introduced and their validity discussed. Then, we describe the main classes of unmixing strategies designed to solve the problem in supervised and unsupervised frameworks. Finally, the problem of detecting nonlinear mixtures in hyperspectral images is addressed.
A Study of Thermal Contact using Nonlinear System Identification Models
Directory of Open Access Journals (Sweden)
M. H. Shojaeefard
2008-01-01
Full Text Available One interesting application of system identification method is to identify and control the heat transfer from the exhaust valve to the seat to keep away the valve from being damaged. In this study, two co-axial cylindrical specimens are used as exhaust valve and its seat. Using the measured temperatures at different locations of the specimens and with a semi-analytical method, the temperature distribution of the specimens is calculated and consequently, the thermal contact conductance is calculated. By applying the system identification method and having the temperatures at both sides of the contact surface, the temperature transfer function is calculated. With regard to the fact that the thermal contact has nonlinear behavior, two nonlinear black-box models called nonlinear ARX and NLN Hammerstein-Wiener models are taken for accurate estimation. Results show that the NLN Hammerstein-Wiener models with wavelet network nonlinear estimator is the best.
The Power of Unit Root Tests Against Nonlinear Local Alternatives
DEFF Research Database (Denmark)
Demetrescu, Matei; Kruse, Robinson
of Econometrics 112, 359-379) in comparison to the linear Dickey-Fuller test. To this end, we consider different adjustment schemes for deterministic terms. We provide asymptotic results which imply that the error variance has a severe impact on the behavior of the tests in the nonlinear case; the reason...... by simulation. Furthermore, our own simulation results suggest that the user-specied adjustment scheme for deterministic components (e.g. OLS, GLS, or recursive adjustment) has a much higher impact on the power of unit root tests than accounting for nonlinearity, at least under local (linear or nonlinear......This article extends the analysis of local power of unit root tests in a nonlinear direction by considering local nonlinear alternatives and tests built specically against stationary nonlinear models. In particular, we focus on the popular test proposed by Kapetanios et al. (2003, Journal...
A Simple Holographic Model of Nonlinear Conductivity
Horowitz, Gary T; Santos, Jorge E
2013-01-01
We present a simple analytic gravitational solution which describes the holographic dual of a 2+1-dimensional conductor which goes beyond the usual linear response. In particular it includes Joule heating. We find that the nonlinear frequency-dependent conductivity is a constant. Surprisingly, the pressure remains isotropic. We also apply an electric field to a holographic insulator and show that there is a maximum electric field below which it can remain an insulator. Above this critical value, we argue that it becomes a conductor due to pair creation of charged particles. Finally, we study 1+1 and 3+1 dimensional conductors at the nonlinear level; here exact solutions are not available and a perturbative analysis shows that the current becomes time dependent, but in a way that is captured by a time-dependent effective temperature.
Nonlinear dynamics new directions models and applications
Ugalde, Edgardo
2015-01-01
This book, along with its companion volume, Nonlinear Dynamics New Directions: Theoretical Aspects, covers topics ranging from fractal analysis to very specific applications of the theory of dynamical systems to biology. This second volume contains mostly new applications of the theory of dynamical systems to both engineering and biology. The first volume is devoted to fundamental aspects and includes a number of important new contributions as well as some review articles that emphasize new development prospects. The topics addressed in the two volumes include a rigorous treatment of fluctuations in dynamical systems, topics in fractal analysis, studies of the transient dynamics in biological networks, synchronization in lasers, and control of chaotic systems, among others. This book also: · Develops applications of nonlinear dynamics on a diversity of topics such as patterns of synchrony in neuronal networks, laser synchronization, control of chaotic systems, and the study of transient dynam...
Modeling of nonlinear propagation in fiber tapers
DEFF Research Database (Denmark)
Lægsgaard, Jesper
2012-01-01
A full-vectorial nonlinear propagation equation for short pulses in tapered optical fibers is developed. Specific emphasis is placed on the importance of the field normalization convention for the structure of the equations, and the interpretation of the resulting field amplitudes. Different...... numerical schemes for interpolation of fiber parameters along the taper are discussed and tested in numerical simulations on soliton propagation and generation of continuum radiation in short photonic-crystal fiber tapers....
Practical Soil-Shallow Foundation Model for Nonlinear Structural Analysis
Directory of Open Access Journals (Sweden)
Moussa Leblouba
2016-01-01
Full Text Available Soil-shallow foundation interaction models that are incorporated into most structural analysis programs generally lack accuracy and efficiency or neglect some aspects of foundation behavior. For instance, soil-shallow foundation systems have been observed to show both small and large loops under increasing amplitude load reversals. This paper presents a practical macroelement model for soil-shallow foundation system and its stability under simultaneous horizontal and vertical loads. The model comprises three spring elements: nonlinear horizontal, nonlinear rotational, and linear vertical springs. The proposed macroelement model was verified using experimental test results from large-scale model foundations subjected to small and large cyclic loading cases.
Geometrically nonlinear creeping mathematic models of shells with variable thickness
Directory of Open Access Journals (Sweden)
V.M. Zhgoutov
2012-08-01
Full Text Available Calculations of strength, stability and vibration of shell structures play an important role in the design of modern devices machines and structures. However, the behavior of thin-walled structures of variable thickness during which geometric nonlinearity, lateral shifts, viscoelasticity (creep of the material, the variability of the profile take place and thermal deformation starts up is not studied enough.In this paper the mathematical deformation models of variable thickness shells (smoothly variable and ribbed shells, experiencing either mechanical load or permanent temperature field and taking into account the geometrical nonlinearity, creeping and transverse shear, were developed. The refined geometrical proportions for geometrically nonlinear and steadiness problems are given.
Haar basis and nonlinear modeling of complex systems
García, P.; Merlitti, A.
2007-04-01
In this work we introduce a technique to perform nonlinear modeling of chaotic time series using the kernel method. The basic idea behind this method is to map the data into a high dimensional space via nonlinear mapping and do a linear regression in this space. Here we use a Haar wavelet-like kernel to achieve the task. This strategy, in contrast to Support Vector Machines technique, shows the conceptual simplicity of least mean square algoritm for linear regression but allows local nonlinear aproximation of the system evolution, with low computational cost.
Physical mechanisms of nonlinear conductivity: A model analysis
Heuer, Andreas; Lühning, Lars
2014-03-01
Nonlinear effects are omnipresent in thin films of ion conducting materials showing up as a significant increase of the conductivity. For a disordered hopping model general physical mechanisms are identified giving rise to the occurrence of positive or negative nonlinear effects, respectively. Analytical results are obtained in the limit of high but finite dimensions. They are compared with the numerical results for 3D up to 6D systems. A very good agreement can be found, in particular for higher dimensions. The results can also be used to rationalize previous numerical simulations. The implications for the interpretation of nonlinear conductivity experiments on inorganic ion conductors are discussed.
Nonlinear analysis of lipid tubules by nonlocal beam model.
Shen, Hui-Shen
2011-05-07
Postbuckling, nonlinear bending and nonlinear vibration analyses are presented for lipid tubules. The lipid tubule is modeled as a nonlocal micro/nano-beam which contains small scale effect. The material properties are assumed to be size-dependent. The governing equation is solved by a two-step perturbation technique. The numerical results reveal that the small scale parameter e₀a reduces the postbuckling equilibrium paths, the static large deflections and natural frequencies of lipid tubules. In contrast, it increases the nonlinear to linear frequency ratios slightly for the lipid tubule with immovable end conditions.
Numerical modelling of nonlinear full-wave acoustic propagation
Energy Technology Data Exchange (ETDEWEB)
Velasco-Segura, Roberto, E-mail: roberto.velasco@ccadet.unam.mx; Rendón, Pablo L., E-mail: pablo.rendon@ccadet.unam.mx [Grupo de Acústica y Vibraciones, Centro de Ciencias Aplicadas y Desarrollo Tecnológico, Universidad Nacional Autónoma de México, Ciudad Universitaria, Apartado Postal 70-186, C.P. 04510, México D.F., México (Mexico)
2015-10-28
The various model equations of nonlinear acoustics are arrived at by making assumptions which permit the observation of the interaction with propagation of either single or joint effects. We present here a form of the conservation equations of fluid dynamics which are deduced using slightly less restrictive hypothesis than those necessary to obtain the well known Westervelt equation. This formulation accounts for full wave diffraction, nonlinearity, and thermoviscous dissipative effects. A two-dimensional, finite-volume method using Roe’s linearisation has been implemented to obtain numerically the solution of the proposed equations. This code, which has been written for parallel execution on a GPU, can be used to describe moderate nonlinear phenomena, at low Mach numbers, in domains as large as 100 wave lengths. Applications range from models of diagnostic and therapeutic HIFU, to parametric acoustic arrays and nonlinear propagation in acoustic waveguides. Examples related to these applications are shown and discussed.
Residual Minimizing Model Reduction for Parameterized Nonlinear Dynamical Systems
Constantine, Paul G
2010-01-01
We present a method for approximating the solution of a parameterized, nonlinear dynamical (or static) system using an affine combination of solutions computed at other points in the input parameter space. The coefficients of the affine combination are computed with a nonlinear least squares procedure that minimizes the residual of the dynamical system. The approximation properties of this residual minimizing scheme are comparable to existing reduced basis and POD-Galerkin model reduction methods, but its implementation requires only independent evaluations of the nonlinear forcing function. We prove some interesting characteristics of the scheme including uniqueness and an interpolatory property, and we present heuristics for mitigating the effects of the ill-conditioning and reducing the overall cost of the method. We apply the method to representative numerical examples from kinetics - a three state system with one parameter controlling the stiffness - and groundwater modeling - a nonlinear parabolic PDE w...
2010-09-30
Hyperfast Modeling of Nonlinear Ocean Waves A. R. Osborne Dipartimento di Fisica Generale, Università di Torino Via Pietro Giuria 1, 10125...PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Universit?i Torino,Dipartimento di Fisica Generale,Via Pietro Giuria 1,10125 Torino, Italy, 8. PERFORMING
Deterministic Global Optimization
Scholz, Daniel
2012-01-01
This monograph deals with a general class of solution approaches in deterministic global optimization, namely the geometric branch-and-bound methods which are popular algorithms, for instance, in Lipschitzian optimization, d.c. programming, and interval analysis.It also introduces a new concept for the rate of convergence and analyzes several bounding operations reported in the literature, from the theoretical as well as from the empirical point of view. Furthermore, extensions of the prototype algorithm for multicriteria global optimization problems as well as mixed combinatorial optimization
Testing and Inference in Nonlinear Cointegrating Vector Error Correction Models
DEFF Research Database (Denmark)
Kristensen, Dennis; Rahbek, Anders
In this paper, we consider a general class of vector error correction models which allow for asymmetric and non-linear error correction. We provide asymptotic results for (quasi-)maximum likelihood (QML) based estimators and tests. General hypothesis testing is considered, where testing...... symmetric non-linear error correction are considered. A simulation study shows that the finite sample properties of the bootstrapped tests are satisfactory with good size and power properties for reasonable sample sizes....
Recent Advances in Explicit Multiparametric Nonlinear Model Predictive Control
Domínguez, Luis F.
2011-01-19
In this paper we present recent advances in multiparametric nonlinear programming (mp-NLP) algorithms for explicit nonlinear model predictive control (mp-NMPC). Three mp-NLP algorithms for NMPC are discussed, based on which novel mp-NMPC controllers are derived. The performance of the explicit controllers are then tested and compared in a simulation example involving the operation of a continuous stirred-tank reactor (CSTR). © 2010 American Chemical Society.
Inference of a nonlinear stochastic model of the cardiorespiratory interaction
Smelyanskiy, V N; Stefanovska, A; McClintock, P V E
2005-01-01
A new technique is introduced to reconstruct a nonlinear stochastic model of the cardiorespiratory interaction. Its inferential framework uses a set of polynomial basis functions representing the nonlinear force governing the system oscillations. The strength and direction of coupling, and the noise intensity are simultaneously inferred from a univariate blood pressure signal, monitored in a clinical environment. The technique does not require extensive global optimization and it is applicable to a wide range of complex dynamical systems subject to noise.
Asymmetric and common absorption of shocks in nonlinear autoregressive models
D.J.C. van Dijk (Dick); Ph.H.B.F. Franses (Philip Hans); H.P. Boswijk (Peter)
2000-01-01
textabstractA key feature of many nonlinear time series models is that they allow for the possibility that the model structure experiences changes, depending on for example the state of the economy or of the financial market. A common property of these models is that it generally is not possible to
Asymmetric and common absorption of shocks in nonlinear autoregressive models
D.J.C. van Dijk (Dick); Ph.H.B.F. Franses (Philip Hans); H.P. Boswijk (Peter)
2000-01-01
textabstractA key feature of many nonlinear time series models is that they allow for the possibility that the model structure experiences changes, depending on for example the state of the economy or of the financial market. A common property of these models is that it generally is not possible to
Modeling and nonlinear heading control for sailing yachts
DEFF Research Database (Denmark)
Xiao, Lin; Jouffroy, Jerome
2011-01-01
This paper presents a study on the development and testing of a model-based heading controller for a sailing yacht. Using Fossen's compact notation for marine vehicles, we first describe a nonlinear 4-DOF dynamic model for a sailing yacht, including roll. Starting from this model, we then design ...
Modeling and nonlinear heading control for sailing yachts
DEFF Research Database (Denmark)
Xiao, Lin; Jouffroy, Jerome
2014-01-01
This paper presents a study on the development and testing of a model-based heading controller for a sailing yacht. Using Fossen’s compact notation for marine vehicles, we first describe a nonlinear four-degree-of-freedom (DOF) dynamic model for a sailing yacht, including roll. Our model also inc...
Modeling of Nonlinear Signal Distortion in Fiber-Optical Networks
Johannisson, Pontus
2013-01-01
A low-complexity model for signal quality prediction in a nonlinear fiber-optical network is developed. The model, which builds on the Gaussian noise model, takes into account the signal degradation caused by a combination of chromatic dispersion, nonlinear signal distortion, and amplifier noise. The center frequencies, bandwidths, and transmit powers can be chosen independently for each channel, which makes the model suitable for analysis and optimization of resource allocation, routing, and scheduling in large-scale optical networks applying flexible-grid wavelength-division multiplexing.
An Improved Nonlinear Five-Point Model for Photovoltaic Modules
Directory of Open Access Journals (Sweden)
Sakaros Bogning Dongue
2013-01-01
Full Text Available This paper presents an improved nonlinear five-point model capable of analytically describing the electrical behaviors of a photovoltaic module for each generic operating condition of temperature and solar irradiance. The models used to replicate the electrical behaviors of operating PV modules are usually based on some simplified assumptions which provide convenient mathematical model which can be used in conventional simulation tools. Unfortunately, these assumptions cause some inaccuracies, and hence unrealistic economic returns are predicted. As an alternative, we used the advantages of a nonlinear analytical five-point model to take into account the nonideal diode effects and nonlinear effects generally ignored, which PV modules operation depends on. To verify the capability of our method to fit PV panel characteristics, the procedure was tested on three different panels. Results were compared with the data issued by manufacturers and with the results obtained using the five-parameter model proposed by other authors.
Non-linear Growth Models in Mplus and SAS.
Grimm, Kevin J; Ram, Nilam
2009-10-01
Non-linear growth curves or growth curves that follow a specified non-linear function in time enable researchers to model complex developmental patterns with parameters that are easily interpretable. In this paper we describe how a variety of sigmoid curves can be fit using the Mplus structural modeling program and the non-linear mixed-effects modeling procedure NLMIXED in SAS. Using longitudinal achievement data collected as part of a study examining the effects of preschool instruction on academic gain we illustrate the procedures for fitting growth models of logistic, Gompertz, and Richards functions. Brief notes regarding the practical benefits, limitations, and choices faced in the fitting and estimation of such models are included.
Earthquake analysis of structures using nonlinear models
Cemalovic, Miran
2015-01-01
Throughout the governing design codes, several different methods are presented for the evaluation of seismic problems. This thesis assesses the non-linear static and dynamic procedures presented in EN 1998-1 through the structural response of a RC wall-frame building. The structure is designed in detail according to the guidelines for high ductility (DCH) in EN 1998-1. The applied procedures are meticulously evaluated and the requirements in EN 1998-1 are reviewed. In addition, the finite ele...
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.
Bayesian parameter estimation for nonlinear modelling of biological pathways
Directory of Open Access Journals (Sweden)
Ghasemi Omid
2011-12-01
Full Text Available Abstract Background The availability of temporal measurements on biological experiments has significantly promoted research areas in systems biology. To gain insight into the interaction and regulation of biological systems, mathematical frameworks such as ordinary differential equations have been widely applied to model biological pathways and interpret the temporal data. Hill equations are the preferred formats to represent the reaction rate in differential equation frameworks, due to their simple structures and their capabilities for easy fitting to saturated experimental measurements. However, Hill equations are highly nonlinearly parameterized functions, and parameters in these functions cannot be measured easily. Additionally, because of its high nonlinearity, adaptive parameter estimation algorithms developed for linear parameterized differential equations cannot be applied. Therefore, parameter estimation in nonlinearly parameterized differential equation models for biological pathways is both challenging and rewarding. In this study, we propose a Bayesian parameter estimation algorithm to estimate parameters in nonlinear mathematical models for biological pathways using time series data. Results We used the Runge-Kutta method to transform differential equations to difference equations assuming a known structure of the differential equations. This transformation allowed us to generate predictions dependent on previous states and to apply a Bayesian approach, namely, the Markov chain Monte Carlo (MCMC method. We applied this approach to the biological pathways involved in the left ventricle (LV response to myocardial infarction (MI and verified our algorithm by estimating two parameters in a Hill equation embedded in the nonlinear model. We further evaluated our estimation performance with different parameter settings and signal to noise ratios. Our results demonstrated the effectiveness of the algorithm for both linearly and nonlinearly
Variable structure control of nonlinear systems through simplified uncertain models
Sira-Ramirez, Hebertt
1986-01-01
A variable structure control approach is presented for the robust stabilization of feedback equivalent nonlinear systems whose proposed model lies in the same structural orbit of a linear system in Brunovsky's canonical form. An attempt to linearize exactly the nonlinear plant on the basis of the feedback control law derived for the available model results in a nonlinearly perturbed canonical system for the expanded class of possible equivalent control functions. Conservatism tends to grow as modeling errors become larger. In order to preserve the internal controllability structure of the plant, it is proposed that model simplification be carried out on the open-loop-transformed system. As an example, a controller is developed for a single link manipulator with an elastic joint.
A Simple Model for Nonlinear Confocal Ultrasonic Beams
Institute of Scientific and Technical Information of China (English)
ZHANG Dong; ZHOU Lin; SI Li-Sheng; GONG Xiu-Fen
2007-01-01
@@ A confocally and coaxially arranged pair of focused transmitter and receiver represents one of the best geometries for medical ultrasonic imaging and non-invasive detection. We develop a simple theoretical model for describing the nonlinear propagation of a confocal ultrasonic beam in biological tissues. On the basis of the parabolic approximation and quasi-linear approximation, the nonlinear Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation is solved by using the angular spectrum approach. Gaussian superposition technique is applied to simplify the solution, and an analytical solution for the second harmonics in the confocal ultrasonic beam is presented.Measurements are performed to examine the validity of the theoretical model. This model provides a preliminary model for acoustic nonlinear microscopy.
Nonlinear dispersion effects in elastic plates: numerical modelling and validation
Kijanka, Piotr; Radecki, Rafal; Packo, Pawel; Staszewski, Wieslaw J.; Uhl, Tadeusz; Leamy, Michael J.
2017-04-01
Nonlinear features of elastic wave propagation have attracted significant attention recently. The particular interest herein relates to complex wave-structure interactions, which provide potential new opportunities for feature discovery and identification in a variety of applications. Due to significant complexity associated with wave propagation in nonlinear media, numerical modeling and simulations are employed to facilitate design and development of new measurement, monitoring and characterization systems. However, since very high spatio- temporal accuracy of numerical models is required, it is critical to evaluate their spectral properties and tune discretization parameters for compromise between accuracy and calculation time. Moreover, nonlinearities in structures give rise to various effects that are not present in linear systems, e.g. wave-wave interactions, higher harmonics generation, synchronism and | recently reported | shifts to dispersion characteristics. This paper discusses local computational model based on a new HYBRID approach for wave propagation in nonlinear media. The proposed approach combines advantages of the Local Interaction Simulation Approach (LISA) and Cellular Automata for Elastodynamics (CAFE). The methods are investigated in the context of their accuracy for predicting nonlinear wavefields, in particular shifts to dispersion characteristics for finite amplitude waves and secondary wavefields. The results are validated against Finite Element (FE) calculations for guided waves in copper plate. Critical modes i.e., modes determining accuracy of a model at given excitation frequency - are identified and guidelines for numerical model parameters are proposed.
Notes on holographic superconductor models with the nonlinear electrodynamics
Zhao, Zixu; Chen, Songbai; Jing, Jiliang
2013-01-01
We investigate systematically the effect of the nonlinear correction to the usual Maxwell electrodynamics on the holographic dual models in the backgrounds of AdS black hole and AdS soliton. Considering three types of typical nonlinear electrodynamics, we observe that in the black hole background the higher nonlinear electrodynamics correction makes the condensation harder to form and changes the expected relation in the gap frequency, which is similar to that caused by the curvature correction. However, in strong contrast to the influence of the curvature correction, we find that in the AdS soliton background the nonlinear electrodynamics correction will not affect the properties of the holographic superconductor and insulator phase transitions, which may be a quite general feature for the s-wave holographic superconductor/insulator system.
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.
Modeling Autoregressive Processes with Moving-Quantiles-Implied Nonlinearity
Directory of Open Access Journals (Sweden)
Isao Ishida
2015-01-01
Full Text Available We introduce and investigate some properties of a class of nonlinear time series models based on the moving sample quantiles in the autoregressive data generating process. We derive a test fit to detect this type of nonlinearity. Using the daily realized volatility data of Standard & Poor’s 500 (S&P 500 and several other indices, we obtained good performance using these models in an out-of-sample forecasting exercise compared with the forecasts obtained based on the usual linear heterogeneous autoregressive and other models of realized volatility.
A propagation model of computer virus with nonlinear vaccination probability
Gan, Chenquan; Yang, Xiaofan; Liu, Wanping; Zhu, Qingyi
2014-01-01
This paper is intended to examine the effect of vaccination on the spread of computer viruses. For that purpose, a novel computer virus propagation model, which incorporates a nonlinear vaccination probability, is proposed. A qualitative analysis of this model reveals that, depending on the value of the basic reproduction number, either the virus-free equilibrium or the viral equilibrium is globally asymptotically stable. The results of simulation experiments not only demonstrate the validity of our model, but also show the effectiveness of nonlinear vaccination strategies. Through parameter analysis, some effective strategies for eradicating viruses are suggested.
Survivability of Deterministic Dynamical Systems
Hellmann, Frank; Schultz, Paul; Grabow, Carsten; Heitzig, Jobst; Kurths, Jürgen
2016-07-01
The notion of a part of phase space containing desired (or allowed) states of a dynamical system is important in a wide range of complex systems research. It has been called the safe operating space, the viability kernel or the sunny region. In this paper we define the notion of survivability: Given a random initial condition, what is the likelihood that the transient behaviour of a deterministic system does not leave a region of desirable states. We demonstrate the utility of this novel stability measure by considering models from climate science, neuronal networks and power grids. We also show that a semi-analytic lower bound for the survivability of linear systems allows a numerically very efficient survivability analysis in realistic models of power grids. Our numerical and semi-analytic work underlines that the type of stability measured by survivability is not captured by common asymptotic stability measures.
Nonlinear model predictive control of a packed distillation column
Energy Technology Data Exchange (ETDEWEB)
Patwardhan, A.A.; Edgar, T.F. (Univ. of Texas, Austin, TX (United States). Dept. of Chemical Engineering)
1993-10-01
A rigorous dynamic model based on fundamental chemical engineering principles was formulated for a packed distillation column separating a mixture of cyclohexane and n-heptane. This model was simplified to a form suitable for use in on-line model predictive control calculations. A packed distillation column was operated at several operating conditions to estimate two unknown model parameters in the rigorous and simplified models. The actual column response to step changes in the feed rate, distillate rate, and reboiler duty agreed well with dynamic model predictions. One unusual characteristic observed was that the packed column exhibited gain-sign changes, which are very difficult to treat using conventional linear feedback control. Nonlinear model predictive control was used to control the distillation column at an operating condition where the process gain changed sign. An on-line, nonlinear model-based scheme was used to estimate unknown/time-varying model parameters.
Schemes for Deterministic Polynomial Factoring
Ivanyos, Gábor; Saxena, Nitin
2008-01-01
In this work we relate the deterministic complexity of factoring polynomials (over finite fields) to certain combinatorial objects we call m-schemes. We extend the known conditional deterministic subexponential time polynomial factoring algorithm for finite fields to get an underlying m-scheme. We demonstrate how the properties of m-schemes relate to improvements in the deterministic complexity of factoring polynomials over finite fields assuming the generalized Riemann Hypothesis (GRH). In particular, we give the first deterministic polynomial time algorithm (assuming GRH) to find a nontrivial factor of a polynomial of prime degree n where (n-1) is a smooth number.
Finite element model calibration of a nonlinear perforated plate
Ehrhardt, David A.; Allen, Matthew S.; Beberniss, Timothy J.; Neild, Simon A.
2017-03-01
This paper presents a case study in which the finite element model for a curved circular plate is calibrated to reproduce both the linear and nonlinear dynamic response measured from two nominally identical samples. The linear dynamic response is described with the linear natural frequencies and mode shapes identified with a roving hammer test. Due to the uncertainty in the stiffness characteristics from the manufactured perforations, the linear natural frequencies are used to update the effective modulus of elasticity of the full order finite element model (FEM). The nonlinear dynamic response is described with nonlinear normal modes (NNMs) measured using force appropriation and high speed 3D digital image correlation (3D-DIC). The measured NNMs are used to update the boundary conditions of the full order FEM through comparison with NNMs calculated from a nonlinear reduced order model (NLROM). This comparison revealed that the nonlinear behavior could not be captured without accounting for the small curvature of the plate from manufacturing as confirmed in literature. So, 3D-DIC was also used to identify the initial static curvature of each plate and the resulting curvature was included in the full order FEM. The updated models are then used to understand how the stress distribution changes at large response amplitudes providing a possible explanation of failures observed during testing.
Nonlinear systems in medicine.
Higgins, John P
2002-01-01
Many achievements in medicine have come from applying linear theory to problems. Most current methods of data analysis use linear models, which are based on proportionality between two variables and/or relationships described by linear differential equations. However, nonlinear behavior commonly occurs within human systems due to their complex dynamic nature; this cannot be described adequately by linear models. Nonlinear thinking has grown among physiologists and physicians over the past century, and non-linear system theories are beginning to be applied to assist in interpreting, explaining, and predicting biological phenomena. Chaos theory describes elements manifesting behavior that is extremely sensitive to initial conditions, does not repeat itself and yet is deterministic. Complexity theory goes one step beyond chaos and is attempting to explain complex behavior that emerges within dynamic nonlinear systems. Nonlinear modeling still has not been able to explain all of the complexity present in human systems, and further models still need to be refined and developed. However, nonlinear modeling is helping to explain some system behaviors that linear systems cannot and thus will augment our understanding of the nature of complex dynamic systems within the human body in health and in disease states.
Institute of Scientific and Technical Information of China (English)
孙文凯; 胡晓华; 蒋文江
2015-01-01
From the perspective of pure mathematics, Deterministic multivariate time series were multiply accumulated to produce some new sequences, studying relationship among them and establishing the multiple linear or nonlinear regression model. If a significance levelαwas given, the significance test for every regression equation was carried out. At confidence level 1-α, the differential equations models were established to reveal the relationship among all the time series, and fore⁃cast or control them. Finally, using the data for the value of GDP and the number of tourist reception in Hainan province from 1995 to 2014, differential equations model is established to forecast.%从纯数学的角度，对多个关联确定性时间序列分别进行多次累加产生新序列，研究序列之间的关系，建立多元线性（或非线性）回归方程。给定显著性水平α，对每个回归方程进行显著性检验。在置信度1-α下建立微分方程组模型，从而揭示这些时间序列之间的关系，实现对原序列的预测和控制。最后用1995-2014年海南省GDP和接待旅游人数建立微分方程组模型并进行预测。
Geometry of exponential family nonlinear models and some asymptotic inference
Institute of Scientific and Technical Information of China (English)
韦博成
1995-01-01
A differential geometric framework in Euclidean space for exponential family nonlinear models is presented. Based on this framework, some asymptotic inference related to statistical curvatures and Fisher information are studied. This geometric framework can also be extended to more genera) dass of models and used to study some other problems.
A Novel Nonlinear Programming Model for Distribution Protection Optimization
Zambon, Eduardo; Bossois, Débora Z.; Garcia, Berilhes B.; Azeredo, Elias F.
2009-01-01
This paper presents a novel nonlinear binary programming model designed to improve the reliability indices of a distribution network. This model identifies the type and location of protection devices that should be installed in a distribution feeder and is a generalization of the classical optimizat
STABILITY OF INNOVATION DIFFUSION MODEL WITH NONLINEAR ACCEPTANCE
Institute of Scientific and Technical Information of China (English)
Yu Yumei; Wang Wendi
2007-01-01
In this article, an innovation diffusion model with the nonlinear acceptance is proposed to describe the dynamics of three competing products in a market. It is proved that the model admits a unique positive equilibrium, which is globally stable by excluding the existence of periodic solutions and by using the theory of three dimensional competition systems.
Modeling of Nonlinear Marine Cooling Systems with Closed Circuit Flow
DEFF Research Database (Denmark)
Hansen, Michael; Stoustrup, Jakob; Bendtsen, Jan Dimon
2011-01-01
of container ships. The purpose of the model is to describe the important dynamics of the system, such as nonlinearities, transport delays and closed circuit flow dynamics to enable the model to be used for control design and simulation. The control challenge is related to the highly non-standard type of step...
A toolkit for analyzing nonlinear dynamic stochastic models easily
Uhlig, H.F.H.V.S.
1995-01-01
Often, researchers wish to analyze nonlinear dynamic discrete-time stochastic models. This paper provides a toolkit for solving such models easily, building on log-linearizing the necessary equations characterizing the equilibrium and solving for the recursive equilibrium law of motion with the meth
A toolkit for analyzing nonlinear dynamic stochastic models easily
Uhlig, H.F.H.V.S.
1995-01-01
Often, researchers wish to analyze nonlinear dynamic discrete-time stochastic models. This paper provides a toolkit for solving such models easily, building on log-linearizing the necessary equations characterizing the equilibrium and solving for the recursive equilibrium law of motion with the meth
Locally supersymmetric D=3 non-linear sigma models
Wit, B. de; Tollsten, A. K.; Nicolai, H.
1992-01-01
We study non-linear sigma models with N local supersymmetries in three space-time dimensions. For N=1 and 2 the target space of these models is Riemannian or Kahler, respectively. All N>2 theories are associated with Einstein spaces. For N=3 the target space is quaternionic, while for N=4 it general
Structure and Asymptotic theory for Nonlinear Models with GARCH Errors
F. Chan (Felix); M.J. McAleer (Michael); M.C. Medeiros (Marcelo)
2011-01-01
textabstractNonlinear time series models, especially those with regime-switching and conditionally heteroskedastic errors, have become increasingly popular in the economics and finance literature. However, much of the research has concentrated on the empirical applications of various models, with li
An Alternative Approach for Nonlinear Latent Variable Models
Mooijaart, Ab; Bentler, Peter M.
2010-01-01
In the last decades there has been an increasing interest in nonlinear latent variable models. Since the seminal paper of Kenny and Judd, several methods have been proposed for dealing with these kinds of models. This article introduces an alternative approach. The methodology involves fitting some third-order moments in addition to the means and…
A Multilevel Nonlinear Profile Analysis Model for Dichotomous Data
Culpepper, Steven Andrew
2009-01-01
This study linked nonlinear profile analysis (NPA) of dichotomous responses with an existing family of item response theory models and generalized latent variable models (GLVM). The NPA method offers several benefits over previous internal profile analysis methods: (a) NPA is estimated with maximum likelihood in a GLVM framework rather than…
Nonlinear Kalman Filtering in Affine Term Structure Models
DEFF Research Database (Denmark)
Christoffersen, Peter; Dorion, Christian; Jacobs, Kris;
When the relationship between security prices and state variables in dynamic term structure models is nonlinear, existing studies usually linearize this relationship because nonlinear fi…ltering is computationally demanding. We conduct an extensive investigation of this linearization and analyze...... Monte Carlo experiment demonstrates that the unscented Kalman fi…lter is much more accurate than its extended counterpart in fi…ltering the states and forecasting swap rates and caps. Our fi…ndings suggest that the unscented Kalman fi…lter may prove to be a good approach for a number of other problems...... in fi…xed income pricing with nonlinear relationships between the state vector and the observations, such as the estimation of term structure models using coupon bonds and the estimation of quadratic term structure models....
Interval standard neural network models for nonlinear systems
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A neural-network-based robust control design is suggested for control of a class of nonlinear systems. The design approach employs a neural network, whose activation functions satisfy the sector conditions, to approximate the nonlinear system. To improve the approximation performance and to account for the parameter perturbations during operation, a novel neural network model termed standard neural network model (SNNM) is proposed. If the uncertainty is bounded, the SNNM is called an interval SNNM (ISNNM). A state-feedback control law is designed for the nonlinear system modelled by an ISNNM such that the closed-loop system is globally, robustly, and asymptotically stable. The control design equations are shown to be a set of linear matrix inequalities (LMIs) that can be easily solved by available convex optimization algorithms. An example is given to illustrate the control design procedure, and the performance of the proposed approach is compared with that of a related method reported in literature.
Adaptive modeling of shallow fully nonlinear gravity waves
Dutykh, Denys; Mitsotakis, Dimitrios
2014-01-01
This paper presents an extended version of the celebrated Serre-Green-Naghdi (SGN) system. This extension is based on the well-known Bona-Smith-Nwogu trick which aims to improve the linear dispersion properties. We show that in the fully nonlinear setting it results in modifying the vertical acceleration. Even if this technique is well-known, the effect of this modification on the nonlinear properties of the model is not clear. The first goal of this study is to shed some light on the properties of solitary waves, as the most important class of nonlinear permanent solutions. Then, we propose a simple adaptive strategy to choose the optimal value of the free parameter at every instance of time. This strategy is validated by comparing the model prediction with the reference solutions of the full Euler equations and its classical counterpart. Numerical simulations show that the new adaptive model provides a much better accuracy for the same computational complexity.
Nonlinear Modeling and Neuro-Fuzzy Control of PEMFC
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
The proton exchange membrane generation technology is highly efficient, and clean and is considered as the most hopeful "green" power technology. The operating principles of proton exchange membrane fuel cell (PEMFC) system involve thermodynamics, electrochemistry, hydrodynamics and mass transfer theory, which comprise a complex nonlinear system, for which it is difficult to establish a mathematical model and control online.This paper analyzed the characters of the PEMFC; and used the approach and self-study ability of artificial neural networks to build the model of nonlinear system, and adopted the adaptive neural-networks fuzzy infer system to build the temperature model of PEMFC which is used as the reference model of the control system, and adjusted the model parameters to control online. The model and control were implemented in SIMULINK environment.The results of simulation show the test data and model have a good agreement. The model is useful for the optimal and real time control of PEMFC system.
极小Cayley图的确定性小世界网络模型%Deterministic small-world network model based on minimal Cayley graph
Institute of Scientific and Technical Information of China (English)
刘艳霞; 奚建清; 张芩
2014-01-01
小世界网络的确定性模型研究是复杂网络建模领域的重要分支，通过分析Cayley图的极小性与小世界特性的关联，提出一种基于极小Cayley图构造小世界网络的确定性模型。模型通过选择满足条件的极小Cayley图，恰当地扩展其生成集，构造出一类对称性强且结构规则的小世界网络。结果表明，和现有模型不同，该模型可根据需求构造常数度或非常数度网络，且生成网络不仅具有较高的聚集系数和低的网络直径，而且是节点对称的，在通信网络、结构化P2P 覆盖网络等实际领域的拓扑结构设计中具有重要应用。%The research on deterministic small-world network model is an important branch of complex network modeling. This paper analyzes the small-world property of the minimal Cayley graph and proposes a deterministic small-world network model based on minimal Cayley graph. The model constructs a class of small-world networks with high symmetry by selecting a minimal Cayley graph, and appropriately expands its generating set. Compared with the existing models, this model can be used flexibly to get small-world networks with const degree or variable degree, which is adaptable for the disign and analysis of the real networks such as communication network and P2P overlay network.
Groundwater transport modeling with nonlinear sorption and intraparticle diffusion
Singh, Anshuman; Allen-King, Richelle M.; Rabideau, Alan J.
2014-08-01
Despite recent advances in the mechanistic understanding of sorption in groundwater systems, most contaminant transport models provide limited support for nonideal sorption processes such as nonlinear isotherms and/or diffusion-limited sorption. However, recent developments in the conceptualization of "dual mode" sorption for hydrophobic organic contaminants have provided more realistic and mechanistically sound alternatives to the commonly used Langmuir and Freundlich models. To support the inclusion of both nonlinear and diffusion-limited sorption processes in groundwater transport models, this paper presents two numerical algorithms based on the split operator approach. For the nonlinear equilibrium scenario, the commonly used two-step split operator algorithm has been modified to provide a more robust treatment of complex multi-parameter isotherms such as the Polanyi-partitioning model. For diffusion-limited sorption, a flexible three step split-operator procedure is presented to simulate intraparticle diffusion in multiple spherical particles with different sizes and nonlinear isotherms. Numerical experiments confirmed the accuracy of both algorithms for several candidate isotherms. However, the primary advantages of the algorithms are: (1) flexibility to accommodate any isotherm equation including "dual mode" and similar expressions, and (2) ease of adapting existing grid-based transport models of any dimensionality to include nonlinear sorption and/or intraparticle diffusion. Comparisons are developed for one-dimensional transport scenarios with different isotherms and particle configurations. Illustrative results highlight (1) the potential influence of isotherm model selection on solute transport predictions, and (2) the combined effects of intraparticle diffusion and nonlinear sorption on the plume transport and flushing for both single-particle and multi-particle scenarios.
Deterministic Graphical Games Revisited
DEFF Research Database (Denmark)
Andersson, Klas Olof Daniel; Hansen, Kristoffer Arnsfelt; Miltersen, Peter Bro
2012-01-01
Starting from Zermelo’s classical formal treatment of chess, we trace through history the analysis of two-player win/lose/draw games with perfect information and potentially infinite play. Such chess-like games have appeared in many different research communities, and methods for solving them......, such as retrograde analysis, have been rediscovered independently. We then revisit Washburn’s deterministic graphical games (DGGs), a natural generalization of chess-like games to arbitrary zero-sum payoffs. We study the complexity of solving DGGs and obtain an almost-linear time comparison-based algorithm...... for finding optimal strategies in such games. The existence of a linear time comparison-based algorithm remains an open problem....
Deterministic Graphical Games Revisited
DEFF Research Database (Denmark)
Andersson, Klas Olof Daniel; Hansen, Kristoffer Arnsfelt; Miltersen, Peter Bro
2012-01-01
Starting from Zermelo’s classical formal treatment of chess, we trace through history the analysis of two-player win/lose/draw games with perfect information and potentially infinite play. Such chess-like games have appeared in many different research communities, and methods for solving them......, such as retrograde analysis, have been rediscovered independently. We then revisit Washburn’s deterministic graphical games (DGGs), a natural generalization of chess-like games to arbitrary zero-sum payoffs. We study the complexity of solving DGGs and obtain an almost-linear time comparison-based algorithm...... for finding optimal strategies in such games. The existence of a linear time comparison-based algorithm remains an open problem....
Inferring deterministic causal relations
Daniusis, Povilas; Mooij, Joris; Zscheischler, Jakob; Steudel, Bastian; Zhang, Kun; Schoelkopf, Bernhard
2012-01-01
We consider two variables that are related to each other by an invertible function. While it has previously been shown that the dependence structure of the noise can provide hints to determine which of the two variables is the cause, we presently show that even in the deterministic (noise-free) case, there are asymmetries that can be exploited for causal inference. Our method is based on the idea that if the function and the probability density of the cause are chosen independently, then the distribution of the effect will, in a certain sense, depend on the function. We provide a theoretical analysis of this method, showing that it also works in the low noise regime, and link it to information geometry. We report strong empirical results on various real-world data sets from different domains.
Nonlinear Dynamic Modeling of Langevin-Type Piezoelectric Transducers
Directory of Open Access Journals (Sweden)
Nicolás Peréz Alvarez
2015-11-01
Full Text Available Langevin transducers are employed in several applications, such as power ultrasound systems, naval hydrophones, and high-displacement actuators. Nonlinear effects can influence their performance, especially at high vibration amplitude levels. These nonlinear effects produce variations in the resonant frequency, harmonics of the excitation frequency, in addition to loss of symmetry in the frequency response and “frequency domain hysteresis”. In this context, this paper presents a simplified nonlinear dynamic model of power ultrasound transducers requiring only two parameters for simulating the most relevant nonlinear effects. One parameter reproduces the changes in the resonance frequency and the other introduces the dependence of the frequency response on the history of the system. The piezoelectric constitutive equations are extended by a linear dependence of the elastic constant on the mechanical displacement amplitude. For introducing the frequency hysteresis, the elastic constant is computed by combining the current value of the mechanical amplitude with the previous state amplitude. The model developed in this work is applied for predicting the dynamic responses of a 26 kHz ultrasonic transducer. The comparison of theoretical and experimental responses, obtained at several input voltages around the tuned frequency, shows a good agreement, indicating that the model can accurately describe the transducer nonlinear behavior.
Parallel Evolutionary Modeling for Nonlinear Ordinary Differential Equations
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
We introduce a new parallel evolutionary algorithm in modeling dynamic systems by nonlinear higher-order ordinary differential equations (NHODEs). The NHODEs models are much more universal than the traditional linear models. In order to accelerate the modeling process, we propose and realize a parallel evolutionary algorithm using distributed CORBA object on the heterogeneous networking. Some numerical experiments show that the new algorithm is feasible and efficient.
Likelihood-Based Inference in Nonlinear Error-Correction Models
DEFF Research Database (Denmark)
Kristensen, Dennis; Rahbæk, Anders
We consider a class of vector nonlinear error correction models where the transfer function (or loadings) of the stationary relation- ships is nonlinear. This includes in particular the smooth transition models. A general representation theorem is given which establishes the dynamic properties...... and a linear trend in general. Gaussian likelihood-based estimators are considered for the long- run cointegration parameters, and the short-run parameters. Asymp- totic theory is provided for these and it is discussed to what extend asymptotic normality and mixed normaity can be found. A simulation study...
Modeling and stability analysis of the nonlinear reactive sputtering process
Directory of Open Access Journals (Sweden)
György Katalin
2011-12-01
Full Text Available The model of the reactive sputtering process has been determined from the dynamic equilibrium of the reactive gas inside the chamber and the dynamic equilibrium of the sputtered metal atoms which form the compound with the reactive gas atoms on the surface of the substrate. The analytically obtained dynamical model is a system of nonlinear differential equations which can result in a histeresis-type input/output nonlinearity. The reactive sputtering process has been simulated by integrating these differential equations. Linearization has been applied for classical analysis of the sputtering process and control system design.
Modeling and equalization of nonlinear bandlimited satellite channels
Konstantinides, K.; Yao, K.
1986-01-01
The problem of modeling and equalization of a nonlinear satellite channel is considered. The channel is assumed to be bandlimited and exhibits both amplitude and phase nonlinearities. A discrete time satellite link is modeled under both uplink and downlink white Gaussian noise. Under conditions of practical interest, a simple and computationally efficient design technique for the minimum mean square error linear equalizer is presented. The bit error probability and some numerical results for a binary phase shift keyed (BPSK) system demonstrate that the proposed equalization technique outperforms standard linear receiver structures.
A Nonlinear Vortex Induced Vibration Model of Marine Risers
Institute of Scientific and Technical Information of China (English)
LIU Juan; HUANG Weiping
2013-01-01
With the exploitation of oil and gas in deep water,the traditional vortex induced vibration (VIV) theory is challenged by the unprecedented flexibility of risers.A nonlinear time-dependent VIV model is developed in this paper based on a VIV lift force model and the Morison equation.Both the inline vibration induced by the flow due to vortex shedding and the fluid-structure interaction in the transverse direction are included in the model.One of the characteristics of the model is the response-dependent lift force with nonlinear damping,which is different from other VIV models.The calculations show that the model can well describe the VIV of deepwater risers with the results agreeing with those calculated by other models.
Testing linearity against nonlinear moving average models
de Gooijer, J.G.; Brännäs, K.; Teräsvirta, T.
1998-01-01
Lagrange multiplier (LM) test statistics are derived for testing a linear moving average model against an additive smooth transition moving average model. The latter model is introduced in the paper. The small sample performance of the proposed tests are evaluated in a Monte Carlo study and compared
Mathematical models for suspension bridges nonlinear structural instability
Gazzola, Filippo
2015-01-01
This work provides a detailed and up-to-the-minute survey of the various stability problems that can affect suspension bridges. In order to deduce some experimental data and rules on the behavior of suspension bridges, a number of historical events are first described, in the course of which several questions concerning their stability naturally arise. The book then surveys conventional mathematical models for suspension bridges and suggests new nonlinear alternatives, which can potentially supply answers to some stability questions. New explanations are also provided, based on the nonlinear structural behavior of bridges. All the models and responses presented in the book employ the theory of differential equations and dynamical systems in the broader sense, demonstrating that methods from nonlinear analysis can allow us to determine the thresholds of instability.
Testing and Inference in Nonlinear Cointegrating Vector Error Correction Models
DEFF Research Database (Denmark)
Kristensen, Dennis; Rahbek, Anders
In this paper, we consider a general class of vector error correction models which allow for asymmetric and non-linear error correction. We provide asymptotic results for (quasi-)maximum likelihood (QML) based estimators and tests. General hypothesis testing is considered, where testing...... for linearity is of particular interest as parameters of non-linear components vanish under the null. To solve the latter type of testing, we use the so-called sup tests, which here requires development of new (uniform) weak convergence results. These results are potentially useful in general for analysis...... of non-stationary non-linear time series models. Thus the paper provides a full asymptotic theory for estimators as well as standard and non-standard test statistics. The derived asymptotic results prove to be new compared to results found elsewhere in the literature due to the impact of the estimated...
Robust state estimation for uncertain linear systems with deterministic input signals
Institute of Scientific and Technical Information of China (English)
Huabo LIU; Tong ZHOU
2014-01-01
In this paper, we investigate state estimations of a dynamical system in which not only process and measurement noise, but also parameter uncertainties and deterministic input signals are involved. The sensitivity penalization based robust state estimation is extended to uncertain linear systems with deterministic input signals and parametric uncertainties which may nonlinearly affect a state-space plant model. The form of the derived robust estimator is similar to that of the well-known Kalman filter with a comparable computational complexity. Under a few weak assumptions, it is proved that though the derived state estimator is biased, the bound of estimation errors is finite and the covariance matrix of estimation errors is bounded. Numerical simulations show that the obtained robust filter has relatively nice estimation performances.
An Eﬃcient and Flexible Deterministic Framework for Multithreaded Programs
Institute of Scientific and Technical Information of China (English)
卢凯; 周旭; 王小平; 陈沉
2015-01-01
Determinism is very useful to multithreaded programs in debugging, testing, etc. Many deterministic ap-proaches have been proposed, such as deterministic multithreading (DMT) and deterministic replay. However, these sys-tems either are ineﬃcient or target a single purpose, which is not flexible. In this paper, we propose an eﬃcient and flexible deterministic framework for multithreaded programs. Our framework implements determinism in two steps: relaxed determinism and strong determinism. Relaxed determinism solves data races eﬃciently by using a proper weak memory consistency model. After that, we implement strong determinism by solving lock contentions deterministically. Since we can apply different approaches for these two steps independently, our framework provides a spectrum of deterministic choices, including nondeterministic system (fast), weak deterministic system (fast and conditionally deterministic), DMT system, and deterministic replay system. Our evaluation shows that the DMT configuration of this framework could even outperform a state-of-the-art DMT system.
Non-linear calibration models for near infrared spectroscopy.
Ni, Wangdong; Nørgaard, Lars; Mørup, Morten
2014-02-27
Different calibration techniques are available for spectroscopic applications that show nonlinear behavior. This comprehensive comparative study presents a comparison of different nonlinear calibration techniques: kernel PLS (KPLS), support vector machines (SVM), least-squares SVM (LS-SVM), relevance vector machines (RVM), Gaussian process regression (GPR), artificial neural network (ANN), and Bayesian ANN (BANN). In this comparison, partial least squares (PLS) regression is used as a linear benchmark, while the relationship of the methods is considered in terms of traditional calibration by ridge regression (RR). The performance of the different methods is demonstrated by their practical applications using three real-life near infrared (NIR) data sets. Different aspects of the various approaches including computational time, model interpretability, potential over-fitting using the non-linear models on linear problems, robustness to small or medium sample sets, and robustness to pre-processing, are discussed. The results suggest that GPR and BANN are powerful and promising methods for handling linear as well as nonlinear systems, even when the data sets are moderately small. The LS-SVM is also attractive due to its good predictive performance for both linear and nonlinear calibrations.
Modeling and non-linear responses of MEMS capacitive accelerometer
Directory of Open Access Journals (Sweden)
Sri Harsha C.
2014-01-01
Full Text Available A theoretical investigation of an electrically actuated beam has been illustrated when the electrostatic-ally actuated micro-cantilever beam is separated from the electrode by a moderately large gap for two distinct types of geometric configurations of MEMS accelerometer. Higher order nonlinear terms have been taken into account for studying the pull in voltage analysis. A nonlinear model of gas film squeezing damping, another source of nonlinearity in MEMS devices is included in obtaining the dynamic responses. Moreover, in the present work, the possible source of nonlinearities while formulating the mathematical model of a MEMS accelerometer and their influences on the dynamic responses have been investigated. The theoretical results obtained by using MATLAB has been verified with the results obtained in FE software and has been found in good agreement. Criterion towards stable micro size accelerometer for each configuration has been investigated. This investigation clearly provides an understanding of nonlinear static and dynamics characteristics of electrostatically micro cantilever based device in MEMS.
Nonlinear Pressure Wave Analysis by Concentrated Mass Model
Ishikawa, Satoshi; Kondou, Takahiro; Matsuzaki, Kenichiro
A pressure wave propagating in a tube often changes to a shock wave because of the nonlinear effect of fluid. Analyzing this phenomenon by the finite difference method requires high computational cost. To lessen the computational cost, a concentrated mass model is proposed. This model consists of masses, connecting nonlinear springs, connecting dampers, and base support dampers. The characteristic of a connecting nonlinear spring is derived from the adiabatic change of fluid, and the equivalent mass and equivalent damping coefficient of the base support damper are derived from the equation of motion of fluid in a cylindrical tube. Pressure waves generated in a hydraulic oil tube, a sound tube and a plane-wave tube are analyzed numerically by the proposed model to confirm the validity of the model. All numerical computational results agree very well with the experimental results carried out by Okamura, Saenger and Kamakura. Especially, the numerical analysis reproduces the phenomena that a pressure wave with large amplitude propagating in a sound tube or in a plane tube changes to a shock wave. Therefore, it is concluded that the proposed model is valid for the numerical analysis of nonlinear pressure wave problem.
Full Hydrodynamic Model of Nonlinear Electromagnetic Response in Metallic Metamaterials
Fang, Ming; Sha, Wei E I; Xiong, Xiaoyan Y Z; Wu, Xianliang
2016-01-01
Applications of metallic metamaterials have generated significant interest in recent years. Electromagnetic behavior of metamaterials in the optical range is usually characterized by a local-linear response. In this article, we develop a finite-difference time-domain (FDTD) solution of the hydrodynamic model that describes a free electron gas in metals. Extending beyond the local-linear response, the hydrodynamic model enables numerical investigation of nonlocal and nonlinear interactions between electromagnetic waves and metallic metamaterials. By explicitly imposing the current continuity constraint, the proposed model is solved in a self-consistent manner. Charge, energy and angular momentum conservation laws of high-order harmonic generation have been demonstrated for the first time by the Maxwell-hydrodynamic FDTD model. The model yields nonlinear optical responses for complex metallic metamaterials irradiated by a variety of waveforms. Consequently, the multiphysics model opens up unique opportunities f...
Estimating Nonlinear Structural Models: EMM and the Kenny-Judd Model
Lyhagen, Johan
2007-01-01
The estimation of nonlinear structural models is not trivial. One reason for this is that a closed form solution of the likelihood may not be feasible or does not exist. We propose to estimate nonlinear structural models using the efficient method of moments, as generating data according to the models is often very easy. A simulation study of the…
Identification methods for nonlinear stochastic systems.
Fullana, Jose-Maria; Rossi, Maurice
2002-03-01
Model identifications based on orbit tracking methods are here extended to stochastic differential equations. In the present approach, deterministic and statistical features are introduced via the time evolution of ensemble averages and variances. The aforementioned quantities are shown to follow deterministic equations, which are explicitly written within a linear as well as a weakly nonlinear approximation. Based on such equations and the observed time series, a cost function is defined. Its minimization by simulated annealing or backpropagation algorithms then yields a set of best-fit parameters. This procedure is successfully applied for various sampling time intervals, on a stochastic Lorenz system.
A unified theory of chaos linking nonlinear dynamics and statistical physics
Poon, Chi-Sang; Wu, Guo-Qiang
2010-01-01
A fundamental issue in nonlinear dynamics and statistical physics is how to distinguish chaotic from stochastic fluctuations in short experimental recordings. This dilemma underlies many complex systems models from stochastic gene expression or stock exchange to quantum chaos. Traditionally, deterministic chaos is characterized by "sensitive dependence on initial conditions" as indicated by a positive Lyapunov exponent. However, ambiguity arises when applying this criterion to real-world data that are corrupted by measurement noise or perturbed nonautonomously by exogenous deterministic or stochastic inputs. Here, we show that a positive Lyapunov exponent is surprisingly neither necessary nor sufficient proof of deterministic chaos, and that a nonlinear dynamical system under deterministic or stochastic forcing may exhibit multiple forms of nonautonomous chaos assessable by a noise titration assay. These findings lay the foundation for reliable analysis of low-dimensional chaos for complex systems modeling an...
The Nonlinear Sigma Model With Distributed Adaptive Mesh Refinement
Liebling, S L
2004-01-01
An adaptive mesh refinement (AMR) scheme is implemented in a distributed environment using Message Passing Interface (MPI) to find solutions to the nonlinear sigma model. Previous work studied behavior similar to black hole critical phenomena at the threshold for singularity formation in this flat space model. This work is a follow-up describing extensions to distribute the grid hierarchy and presenting tests showing the correctness of the model.
INFLUENCE ANALYSIS ON EXPONENTIAL NONLINEAR MODELS WITH RANDOM EFFECTS
Institute of Scientific and Technical Information of China (English)
宗序平; 赵俊; 王海斌; 韦博成
2003-01-01
This paper presents a unified diagnostic method for exponential nonlinear models with random effects based upon the joint likelihood given by Robinson in 1991.The authors show that the case deletion model is equivalent to mean shift outlier model.From this point of view,several diagnostic measures,such as Cook distance,score statistics are derived.The local influence measure of Cook is also presented.Numerical example illustrates that our method is available.
INFLUENCE ANALYSIS IN NONLINEAR MODELS WITH RANDOM EFFECTS
Institute of Scientific and Technical Information of China (English)
WeiBocheng; ZhongXuping
2001-01-01
Abstract. In this paper,a unified diagnostic method for the nonlinear models with random ef-fects based upon the joint likelihood given by Robinson in 1991 is presented. It is shown that thecase deletion model is equivalent to the mean shift outlier model. From this point of view ,sever-al diagnostic measures, such as Cook distance, score statistics are derived. The local influencemeasure of Cook is also presented. A numerical example illustrates that the method is avail-able
Analyzing the Dynamics of Nonlinear Multivariate Time Series Models
Institute of Scientific and Technical Information of China (English)
DenghuaZhong; ZhengfengZhang; DonghaiLiu; StefanMittnik
2004-01-01
This paper analyzes the dynamics of nonlinear multivariate time series models that is represented by generalized impulse response functions and asymmetric functions. We illustrate the measures of shock persistences and asymmetric effects of shocks derived from the generalized impulse response functions and asymmetric function in bivariate smooth transition regression models. The empirical work investigates a bivariate smooth transition model of US GDP and the unemployment rate.
Nonlinear diffusion model for Rayleigh-Taylor mixing.
Boffetta, G; De Lillo, F; Musacchio, S
2010-01-22
The complex evolution of turbulent mixing in Rayleigh-Taylor convection is studied in terms of eddy diffusivity models for the mean temperature profile. It is found that a nonlinear model, derived within the general framework of Prandtl mixing theory, reproduces accurately the evolution of turbulent profiles obtained from numerical simulations. Our model allows us to give very precise predictions for the turbulent heat flux and for the Nusselt number in the ultimate state regime of thermal convection.
Nonlinear diffusion model for Rayleigh-Taylor mixing
Boffetta, G; Musacchio, S
2010-01-01
The complex evolution of turbulent mixing in Rayleigh-Taylor convection is studied in terms of eddy diffusiviy models for the mean temperature profile. It is found that a non-linear model, derived within the general framework of Prandtl mixing theory, reproduces accurately the evolution of turbulent profiles obtained from numerical simulations. Our model allows to give very precise predictions for the turbulent heat flux and for the Nusselt number in the ultimate state regime of thermal convection.
Hybrid nonlinear model of the angular vestibulo-ocular reflex.
Ranjbaran, Mina; Galiana, Henrietta L
2013-01-01
A hybrid nonlinear bilateral model for the horizontal angular vestibulo-ocular reflex (AVOR) is presented in this paper. The model relies on known interconnections between saccadic burst circuits in the brainstem and ocular premotor areas in the vestibular nuclei during slow and fast phase intervals. A viable switching strategy for the timing of nystagmus events is proposed. Simulations show that this hybrid model replicates AVOR nystagmus patterns that are observed in experimentally recorded data.
Cryptology transmitted message protection from deterministic chaos up to optical vortices
Izmailov, Igor; Romanov, Ilia; Smolskiy, Sergey
2016-01-01
This book presents methods to improve information security for protected communication. It combines and applies interdisciplinary scientific engineering concepts, including cryptography, chaos theory, nonlinear and singular optics, radio-electronics and self-changing artificial systems. It also introduces additional ways to improve information security using optical vortices as information carriers and self-controlled nonlinearity, with nonlinearity playing a key "evolving" role. The proposed solutions allow the universal phenomenon of deterministic chaos to be discussed in the context of information security problems on the basis of examples of both electronic and optical systems. Further, the book presents the vortex detector and communication systems and describes mathematical models of the chaos oscillator as a coder in the synchronous chaotic communication and appropriate decoders, demonstrating their efficiency both analytically and experimentally. Lastly it discusses the cryptologic features of analyze...
Nonlinear stochastic inflation modelling using SEASETARs
de Gooijer, J.G.; Vidiella-i-Anguera, A.
2003-01-01
The development of stochastic inflation models for actuarial and investment applications has become an important topic to actuaries since Wilkie [Transactions of the Faculty of Actuaries 39 (1986) 341] introduced his first investment model. Two empirical features of monthly inflation rates are dynam
Prediction of peptide bonding affinity: kernel methods for nonlinear modeling
Bergeron, Charles; Sundling, C Matthew; Krein, Michael; Katt, Bill; Sukumar, Nagamani; Breneman, Curt M; Bennett, Kristin P
2011-01-01
This paper presents regression models obtained from a process of blind prediction of peptide binding affinity from provided descriptors for several distinct datasets as part of the 2006 Comparative Evaluation of Prediction Algorithms (COEPRA) contest. This paper finds that kernel partial least squares, a nonlinear partial least squares (PLS) algorithm, outperforms PLS, and that the incorporation of transferable atom equivalent features improves predictive capability.
Nonlinear dynamics of incommensurately contacting surfaces : a model study
Consoli, Luca
2002-01-01
This PhD thesis is about the nonlinear dynamics of contacting surfaces. More specifically, it deals with the problem of modelling at the microscopic level some of the contributions that lead to the macroscopic effect of dry sliding friction. In chapter 1, we try to give an overview of the physical q
RF Circuit linearity optimization using a general weak nonlinearity model
Cheng, W.; Oude Alink, M.S.; Annema, Anne J.; Croon, Jeroen A.; Nauta, Bram
2012-01-01
This paper focuses on optimizing the linearity in known RF circuits, by exploring the circuit design space that is usually available in today’s deep submicron CMOS technologies. Instead of using brute force numerical optimizers we apply a generalized weak nonlinearity model that only involves AC
UAV Formation Flight Based on Nonlinear Model Predictive Control
Directory of Open Access Journals (Sweden)
Zhou Chao
2012-01-01
Full Text Available We designed a distributed collision-free formation flight control law in the framework of nonlinear model predictive control. Formation configuration is determined in the virtual reference point coordinate system. Obstacle avoidance is guaranteed by cost penalty, and intervehicle collision avoidance is guaranteed by cost penalty combined with a new priority strategy.
Dynamics of breathers in discrete nonlinear Schrodinger models
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Johansson, Magnus; Aubry, Serge
1998-01-01
We review some recent results concerning the existence and stability of spatially localized and temporally quasiperiodic (non-stationary) excitations in discrete nonlinear Schrodinger (DNLS) models. In two dimensions, we show the existence of linearly stable, stationary and non-stationary localized...
Control mechanisms for a nonlinear model of international relations
Energy Technology Data Exchange (ETDEWEB)
Pentek, A.; Kadtke, J. [Univ. of California, San Diego, La Jolla, CA (United States). Inst. for Pure and Applied Physical Sciences; Lenhart, S. [Univ. of Tennessee, Knoxville, TN (United States). Mathematics Dept.; Protopopescu, V. [Oak Ridge National Lab., TN (United States). Computer Science and Mathematics Div.
1997-07-15
Some issues of control in complex dynamical systems are considered. The authors discuss two control mechanisms, namely: a short range, reactive control based on the chaos control idea and a long-term strategic control based on an optimal control algorithm. They apply these control ideas to simple examples in a discrete nonlinear model of a multi-nation arms race.
Two-dimensional effects in nonlinear Kronig-Penney models
DEFF Research Database (Denmark)
Gaididei, Yuri Borisovich; Christiansen, Peter Leth; Rasmussen, Kim
1997-01-01
An analysis of two-dimensional (2D) effects in the nonlinear Kronig-Penney model is presented. We establish an effective one-dimensional description of the 2D effects, resulting in a set of pseudodifferential equations. The stationary states of the 2D system and their stability is studied...
Maximum Likelihood Estimation of Nonlinear Structural Equation Models.
Lee, Sik-Yum; Zhu, Hong-Tu
2002-01-01
Developed an EM type algorithm for maximum likelihood estimation of a general nonlinear structural equation model in which the E-step is completed by a Metropolis-Hastings algorithm. Illustrated the methodology with results from a simulation study and two real examples using data from previous studies. (SLD)
Case-Deletion Diagnostics for Nonlinear Structural Equation Models
Lee, Sik-Yum; Lu, Bin
2003-01-01
In this article, a case-deletion procedure is proposed to detect influential observations in a nonlinear structural equation model. The key idea is to develop the diagnostic measures based on the conditional expectation of the complete-data log-likelihood function in the EM algorithm. An one-step pseudo approximation is proposed to reduce the…
Local Influence Analysis of Nonlinear Structural Equation Models
Lee, Sik-Yum; Tang, Nian-Sheng
2004-01-01
By regarding the latent random vectors as hypothetical missing data and based on the conditional expectation of the complete-data log-likelihood function in the EM algorithm, we investigate assessment of local influence of various perturbation schemes in a nonlinear structural equation model. The basic building blocks of local influence analysis…
Unstructured Spectral Element Model for Dispersive and Nonlinear Wave Propagation
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Eskilsson, Claes; Bigoni, Daniele
2016-01-01
). In the present paper we use a single layer of quadratic (in 2D) and prismatic (in 3D) elements. The model has been stabilized through a combination of over-integration of the Galerkin projections and a mild modal filter. We present numerical tests of nonlinear waves serving as a proof-of-concept validation...
S-AMP for non-linear observation models
DEFF Research Database (Denmark)
Cakmak, Burak; Winther, Ole; Fleury, Bernard H.
2015-01-01
Recently we presented the S-AMP approach, an extension of approximate message passing (AMP), to be able to handle general invariant matrix ensembles. In this contribution we extend S-AMP to non-linear observation models. We obtain generalized AMP (GAMP) as the special case when the measurement...
A nonlinear regression model-based predictive control algorithm.
Dubay, R; Abu-Ayyad, M; Hernandez, J M
2009-04-01
This paper presents a unique approach for designing a nonlinear regression model-based predictive controller (NRPC) for single-input-single-output (SISO) and multi-input-multi-output (MIMO) processes that are common in industrial applications. The innovation of this strategy is that the controller structure allows nonlinear open-loop modeling to be conducted while closed-loop control is executed every sampling instant. Consequently, the system matrix is regenerated every sampling instant using a continuous function providing a more accurate prediction of the plant. Computer simulations are carried out on nonlinear plants, demonstrating that the new approach is easily implemented and provides tight control. Also, the proposed algorithm is implemented on two real time SISO applications; a DC motor, a plastic injection molding machine and a nonlinear MIMO thermal system comprising three temperature zones to be controlled with interacting effects. The experimental closed-loop responses of the proposed algorithm were compared to a multi-model dynamic matrix controller (MPC) with improved results for various set point trajectories. Good disturbance rejection was attained, resulting in improved tracking of multi-set point profiles in comparison to multi-model MPC.
Nonlinear Hyperbolic-Parabolic System Modeling Some Biological Phenomena
Institute of Scientific and Technical Information of China (English)
WU Shaohua; CHEN Hua
2011-01-01
In this paper, we study a nonlinear hyperbolic-parabolic system modeling some biological phenomena. By semigroup theory and Leray-Schauder fixed point argument, the local existence and uniqueness of the weak solutions for this system are proved. For the spatial dimension N = 1, the global existence of the weak solution will be established by the bootstrap argument.
Visualization of nonlinear kernel models in neuroimaging by sensitivity maps
DEFF Research Database (Denmark)
Rasmussen, Peter Mondrup; Madsen, Kristoffer Hougaard; Lund, Torben Ellegaard
2011-01-01
There is significant current interest in decoding mental states from neuroimages. In this context kernel methods, e.g., support vector machines (SVM) are frequently adopted to learn statistical relations between patterns of brain activation and experimental conditions. In this paper we focus......, and conclude that the sensitivity map is a versatile and computationally efficient tool for visualization of nonlinear kernel models in neuroimaging....
Deterministic polarization chaos from a laser diode
Virte, Martin; Thienpont, Hugo; Sciamanna, Marc
2014-01-01
Fifty years after the invention of the laser diode and fourty years after the report of the butterfly effect - i.e. the unpredictability of deterministic chaos, it is said that a laser diode behaves like a damped nonlinear oscillator. Hence no chaos can be generated unless with additional forcing or parameter modulation. Here we report the first counter-example of a free-running laser diode generating chaos. The underlying physics is a nonlinear coupling between two elliptically polarized modes in a vertical-cavity surface-emitting laser. We identify chaos in experimental time-series and show theoretically the bifurcations leading to single- and double-scroll attractors with characteristics similar to Lorenz chaos. The reported polarization chaos resembles at first sight a noise-driven mode hopping but shows opposite statistical properties. Our findings open up new research areas that combine the high speed performances of microcavity lasers with controllable and integrated sources of optical chaos.
An Adaptive Neural Network Model for Nonlinear Programming Problems
Institute of Scientific and Technical Information of China (English)
Xiang-sun Zhang; Xin-jian Zhuo; Zhu-jun Jing
2002-01-01
In this paper a canonical neural network with adaptively changing synaptic weights and activation function parameters is presented to solve general nonlinear programming problems. The basic part of the model is a sub-network used to find a solution of quadratic programming problems with simple upper and lower bounds. By sequentially activating the sub-network under the control of an external computer or a special analog or digital processor that adjusts the weights and parameters, one then solves general nonlinear programming problems. Convergence proof and numerical results are given.
NONLINEAR MICRO－MECHANICAL MODEL FOR PLAIN WOVEN FABRIC
Institute of Scientific and Technical Information of China (English)
ZhangYitong; XieYuxin
2003-01-01
The warp yarns and weft yarns of plain woven fabric which, being the principal axes of material of fabric, are orthogonal in the original configuration, but are obliquely crossed in the deformed configuration in general. The orthotropic constitutive model is unsuitable for fabric. In the oblique principal axes system the relations between loaded stress vectors and stress tensor are investigated, the stress fields of micro-weaving structures of fabric due to pure shear are carefully studied and, finally, a nonlinear micro-mechanical model for plain woven fabric is proposed. This model can accurately describe the nonlinear mechanical behavior of fabric observed in experiments. Under the assumption of small deformation and linearity of mechanical properties of fabric the model will degenerate into the existing linear model.
Nonlinear Model Identification from Operating Records.
1980-11-01
34, Submitted July 1979 to Proc. IEEE. [13] Wellstead , P., "Model Order Identification Using an Auxillary System," Proc. IEEE, vol. 123, No. 12, December...C and Systems, Nov. 1979 . I I ~I lt( -~ I -l.. .... .. . ... . .. . . , _. . - -"
Population mixture model for nonlinear telomere dynamics
Itzkovitz, Shalev; Shlush, Liran I.; Gluck, Dan; Skorecki, Karl
2008-12-01
Telomeres are DNA repeats protecting chromosomal ends which shorten with each cell division, eventually leading to cessation of cell growth. We present a population mixture model that predicts an exponential decrease in telomere length with time. We analytically solve the dynamics of the telomere length distribution. The model provides an excellent fit to available telomere data and accounts for the previously unexplained observation of telomere elongation following stress and bone marrow transplantation, thereby providing insight into the nature of the telomere clock.
Validating a quasi-linear transport model versus nonlinear simulations
Casati, A.; Bourdelle, C.; Garbet, X.; Imbeaux, F.; Candy, J.; Clairet, F.; Dif-Pradalier, G.; Falchetto, G.; Gerbaud, T.; Grandgirard, V.; Gürcan, Ö. D.; Hennequin, P.; Kinsey, J.; Ottaviani, M.; Sabot, R.; Sarazin, Y.; Vermare, L.; Waltz, R. E.
2009-08-01
In order to gain reliable predictions on turbulent fluxes in tokamak plasmas, physics based transport models are required. Nonlinear gyrokinetic electromagnetic simulations for all species are still too costly in terms of computing time. On the other hand, interestingly, the quasi-linear approximation seems to retain the relevant physics for fairly reproducing both experimental results and nonlinear gyrokinetic simulations. Quasi-linear fluxes are made of two parts: (1) the quasi-linear response of the transported quantities and (2) the saturated fluctuating electrostatic potential. The first one is shown to follow well nonlinear numerical predictions; the second one is based on both nonlinear simulations and turbulence measurements. The resulting quasi-linear fluxes computed by QuaLiKiz (Bourdelle et al 2007 Phys. Plasmas 14 112501) are shown to agree with the nonlinear predictions when varying various dimensionless parameters, such as the temperature gradients, the ion to electron temperature ratio, the dimensionless collisionality, the effective charge and ranging from ion temperature gradient to trapped electron modes turbulence.
Model Reduction of Nonlinear Aeroelastic Systems Experiencing Hopf Bifurcation
Abdelkefi, Abdessattar
2013-06-18
In this paper, we employ the normal form to derive a reduced - order model that reproduces nonlinear dynamical behavior of aeroelastic systems that undergo Hopf bifurcation. As an example, we consider a rigid two - dimensional airfoil that is supported by nonlinear springs in the pitch and plunge directions and subjected to nonlinear aerodynamic loads. We apply the center manifold theorem on the governing equations to derive its normal form that constitutes a simplified representation of the aeroelastic sys tem near flutter onset (manifestation of Hopf bifurcation). Then, we use the normal form to identify a self - excited oscillator governed by a time - delay ordinary differential equation that approximates the dynamical behavior while reducing the dimension of the original system. Results obtained from this oscillator show a great capability to predict properly limit cycle oscillations that take place beyond and above flutter as compared with the original aeroelastic system.
Nonlinear analysis of traffic jams in an anisotropic continuum model
Institute of Scientific and Technical Information of China (English)
Arvind Kumar Gupta; Sapna Sharma
2010-01-01
This paper presents our study of the nonlinear stability of a new anisotropic continuum traffic flow model in which the dimensionless parameter or anisotropic factor controls the non-isotropic character and diffusive influence. In order to establish traffic flow stability criterion or to know the critical parameters that lead, on one hand, to a stable response to perturbations or disturbances or, on the other hand, to an unstable response and therefore to a possible congestion, a nonlinear stability criterion is derived by using a wavefront expansion technique. The stability criterion is illustrated by numerical results using the finite difference method for two different values of anisotropic parameter. It is also been observed that the newly derived stability results are consistent with previously reported results obtained using approximate linearisation methods. Moreover, the stability criterion derived in this paper can provide more refined information from the perspective of the capability to reproduce nonlinear traffic flow behaviors observed in real traffic than previously established methodologies.
Nonlinear Dynamical Modeling and Forecast of ENSO Variability
Feigin, Alexander; Mukhin, Dmitry; Gavrilov, Andrey; Seleznev, Aleksey; Loskutov, Evgeny
2017-04-01
New methodology of empirical modeling and forecast of nonlinear dynamical system variability [1] is applied to study of ENSO climate system. The methodology is based on two approaches: (i) nonlinear decomposition of data [2], that provides low-dimensional embedding for further modeling, and (ii) construction of empirical model in the form of low dimensional random dynamical ("stochastic") system [3]. Three monthly data sets are used for ENSO modeling and forecast: global sea surface temperature anomalies, troposphere zonal wind speed, and thermocline depth; all data sets are limited by 30 S, 30 N and have horizontal resolution 10x10 . We compare results of optimal data decomposition as well as prognostic skill of the constructed models for different combinations of involved data sets. We also present comparative analysis of ENSO indices forecasts fulfilled by our models and by IRI/CPC ENSO Predictions Plume. [1] A. Gavrilov, D. Mukhin, E. Loskutov, A. Feigin, 2016: Construction of Optimally Reduced Empirical Model by Spatially Distributed Climate Data. 2016 AGU Fall Meeting, Abstract NG31A-1824. [2] D. Mukhin, A. Gavrilov, E. Loskutov , A.Feigin, J.Kurths, 2015: Principal nonlinear dynamical modes of climate variability, Scientific Reports, rep. 5, 15510; doi: 10.1038/srep15510. [3] Ya. Molkov, D. Mukhin, E. Loskutov, A. Feigin, 2012: Random dynamical models from time series. Phys. Rev. E, Vol. 85, n.3.
Submicroscopic Deterministic Quantum Mechanics
Krasnoholovets, V
2002-01-01
So-called hidden variables introduced in quantum mechanics by de Broglie and Bohm have changed their initial enigmatic meanings and acquired quite reasonable outlines of real and measurable characteristics. The start viewpoint was the following: All the phenomena, which we observe in the quantum world, should reflect structural properties of the real space. Thus the scale 10^{-28} cm at which three fundamental interactions (electromagnetic, weak, and strong) intersect has been treated as the size of a building block of the space. The appearance of a massive particle is associated with a local deformation of the cellular space, i.e. deformation of a cell. The mechanics of a moving particle that has been constructed is deterministic by its nature and shows that the particle interacts with cells of the space creating elementary excitations called "inertons". The further study has disclosed that inertons are a substructure of the matter waves which are described by the orthodox wave \\psi-function formalism. The c...
Adaptive Predistortion Using Cubic Spline Nonlinearity Based Hammerstein Modeling
Wu, Xiaofang; Shi, Jianghong
In this paper, a new Hammerstein predistorter modeling for power amplifier (PA) linearization is proposed. The key feature of the model is that the cubic splines, instead of conventional high-order polynomials, are utilized as the static nonlinearities due to the fact that the splines are able to represent hard nonlinearities accurately and circumvent the numerical instability problem simultaneously. Furthermore, according to the amplifier's AM/AM and AM/PM characteristics, real-valued cubic spline functions are utilized to compensate the nonlinear distortion of the amplifier and the following finite impulse response (FIR) filters are utilized to eliminate the memory effects of the amplifier. In addition, the identification algorithm of the Hammerstein predistorter is discussed. The predistorter is implemented on the indirect learning architecture, and the separable nonlinear least squares (SNLS) Levenberg-Marquardt algorithm is adopted for the sake that the separation method reduces the dimension of the nonlinear search space and thus greatly simplifies the identification procedure. However, the convergence performance of the iterative SNLS algorithm is sensitive to the initial estimation. Therefore an effective normalization strategy is presented to solve this problem. Simulation experiments were carried out on a single-carrier WCDMA signal. Results show that compared to the conventional polynomial predistorters, the proposed Hammerstein predistorter has a higher linearization performance when the PA is near saturation and has a comparable linearization performance when the PA is mildly nonlinear. Furthermore, the proposed predistorter is numerically more stable in all input back-off cases. The results also demonstrate the validity of the convergence scheme.
Nonclassical measurements errors in nonlinear models
DEFF Research Database (Denmark)
Madsen, Edith; Mulalic, Ismir
Discrete choice models and in particular logit type models play an important role in understanding and quantifying individual or household behavior in relation to transport demand. An example is the choice of travel mode for a given trip under the budget and time restrictions that the individuals...... estimates of the income effect it is of interest to investigate the magnitude of the estimation bias and if possible use estimation techniques that take the measurement error problem into account. We use data from the Danish National Travel Survey (NTS) and merge it with administrative register data...... of a households face. In this case an important policy parameter is the effect of income (reflecting the household budget) on the choice of travel mode. This paper deals with the consequences of measurement error in income (an explanatory variable) in discrete choice models. Since it is likely to give misleading...
Nuckelt, J.; Schack, M.; T. Kürner
2011-01-01
This paper presents a physical (PHY) layer simulator of the IEEE 802.11p standard for Wireless Access in Vehicular Environments (WAVE). This simulator allows the emulation of data transmission via different radio channels as well as the analysis of the resulting system behavior. The PHY layer simulator is part of an integrated simulation platform including a traffic model to generate realistic mobility of vehicles and a 3D ray-optical model to calculate the multipath propaga...
David, Hamilton P; Carey, Cayelan C.; Arvola, Lauri; Arzberger, Peter; Brewer, Carol A.; Cole, Jon J; Gaiser, Evelyn; Hanson, Paul C.; Ibelings, Bas W; Jennings, Eleanor; Kratz, Tim K; Lin, Fang-Pang; McBride, Christopher G.; de Motta Marques, David; Muraoka, Kohji; Nishri, Ami; Qin, Boqiang; Read, Jordan S.; Rose, Kevin C.; Ryder, Elizabeth; Weathers, Kathleen C.; Zhu, Guangwei; Trolle, Dennis; Brookes, Justin D
2014-01-01
A Global Lake Ecological Observatory Network (GLEON; www.gleon.org) has formed to provide a coordinated response to the need for scientific understanding of lake processes, utilising technological advances available from autonomous sensors. The organisation embraces a grassroots approach to engage researchers from varying disciplines, sites spanning geographic and ecological gradients, and novel sensor and cyberinfrastructure to synthesise high-frequency lake data at scales ranging from local to global. The high-frequency data provide a platform to rigorously validate process- based ecological models because model simulation time steps are better aligned with sensor measurements than with lower-frequency, manual samples. Two case studies from Trout Bog, Wisconsin, USA, and Lake Rotoehu, North Island, New Zealand, are presented to demonstrate that in the past, ecological model outputs (e.g., temperature, chlorophyll) have been relatively poorly validated based on a limited number of directly comparable measurements, both in time and space. The case studies demonstrate some of the difficulties of mapping sensor measurements directly to model state variable outputs as well as the opportunities to use deviations between sensor measurements and model simulations to better inform process understanding. Well-validated ecological models provide a mechanism to extrapolate high-frequency sensor data in space and time, thereby potentially creating a fully 3-dimensional simulation of key variables of interest.
Nonlinear dynamic phenomena in the beer model
DEFF Research Database (Denmark)
Mosekilde, Erik; Laugesen, Jakob Lund
2007-01-01
The production-distribution system or "beer game" is one of the most well-known system dynamics models. Notorious for the complex dynamics it produces, the beer game has been used for nearly five decades to illustrate how structure generates behavior and to explore human decision making. Here we...
Noise propagation in hybrid models of nonlinear systems: The Ginzburg–Landau equation
Energy Technology Data Exchange (ETDEWEB)
Taverniers, Søren [Department of Mechanical and Aerospace Engineering, University of California, San Diego, 9500 Gilman Dr., La Jolla, CA 92093 (United States); Alexander, Francis J. [Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Tartakovsky, Daniel M. [Department of Mechanical and Aerospace Engineering, University of California, San Diego, 9500 Gilman Dr., La Jolla, CA 92093 (United States)
2014-04-01
Every physical phenomenon can be described by multiple models with varying degrees of fidelity. The computational cost of higher fidelity models (e.g., molecular dynamics simulations) is invariably higher than that of their lower fidelity counterparts (e.g., a continuum model based on differential equations). While the former might not be suitable for large-scale simulations, the latter are not universally valid. Hybrid algorithms provide a compromise between the computational efficiency of a coarse-scale model and the representational accuracy of a fine-scale description. This is achieved by conducting a fine-scale computation in subdomains where it is absolutely required (e.g., due to a local breakdown of a continuum model) and coupling it with a coarse-scale computation in the rest of a computational domain. We analyze the effects of random fluctuations generated by the fine-scale component of a nonlinear hybrid on the hybrid's overall accuracy and stability. Two variants of the time-dependent Ginzburg–Landau equation (GLE) and their discrete representations provided by a nearest-neighbor Ising model serve as a computational testbed. Our analysis shows that coupling these descriptions in a one-dimensional simulation leads to erroneous results. Adding a random source term to the GLE provides accurate prediction of the mean behavior of the quantity of interest (magnetization). It also allows the two GLE variants to correctly capture the strength of the microscale fluctuations. Our work demonstrates the importance of fine-scale noise in hybrid simulations, and suggests the need for replacing an otherwise deterministic coarse-scale component of the hybrid with its stochastic counterpart.
A multi-objective model for cordon-based congestion pricing schemes with nonlinear distance tolls
Institute of Scientific and Technical Information of China (English)
孙鑫; 刘志远; THOMPSON Russell G; 别一鸣; 翁金贤; 陈淑燕
2016-01-01
Congestion pricing is an important component of urban intelligent transport system. The efficiency, equity and the environmental impacts associated with road pricing schemes are key issues that should be considered before such schemes are implemented. This paper focuses on the cordon-based pricing with distance tolls, where the tolls are determined by a nonlinear function of a vehicles’ travel distance within a cordon, termed as toll charge function. The optimal tolls can give rise to:1) higher total social benefits, 2) better levels of equity, and 3) reduced environmental impacts (e.g., less emission). Firstly, a deterministic equilibrium (DUE) model with elastic demand is presented to evaluate any given toll charge function. The distance tolls are non-additive, thus a modified path-based gradient projection algorithm is developed to solve the DUE model. Then, to quantitatively measure the equity level of each toll charge function, the Gini coefficient is adopted to measure the equity level of the flows in the entire transport network based on equilibrium flows. The total emission level is used to reflect the impacts of distance tolls on the environment. With these two indexes/measurements for the efficiency, equity and environmental issues as well as the DUE model, a multi-objective bi-level programming model is then developed to determine optimal distance tolls. The multi-objective model is converted to a single level model using the goal programming. A genetic algorithm (GA) is adopted to determine solutions. Finally, a numerical example is presented to verify the methodology.
Castellanza, Riccardo; Fernandez Merodo, Josè Antonio; di Prisco, Claudio; Frigerio, Gabriele; Crosta, Giovanni B.; Orlandi, Gianmarco
2013-04-01
Aim of the study is the assessment of stability conditions for an abandoned gypsum mine (Bologna , Italy). Mining was carried out til the end of the 70s by the room and pillar method. During mining a karst cave was crossed karstic waters flowed into the mine. As a consequence, the lower level of the mining is completely flooded and portions of the mining levels show critical conditions and are structurally prone to instability. Buildings and infrastructures are located above the first and second level and a large portion of the area below the mine area, and just above of the Savena river, is urbanised. Gypsum geomechanical properties change over time; water, or even air humidity, dissolves or weaken gypsum pillars, leading progressively to collapse. The mine is located in macro-crystalline gypsum beds belonging to the Messinian Gessoso Solfifera Formation. Selenitic gypsum beds are interlayered with by centimetre to meter thick shales layers. In order to evaluate the risk related to the collapse of the flooded level (level 3) a deterministic approach based on 3D numerical analyses has been considered. The entire abandoned mine system up to the ground surface has been generated in 3D. The considered critical scenario implies the collapse of the pillars and roof of the flooded level 3. In a first step, a sequential collapse starting from the most critical pillar has been simulated by means of a 3D Finite Element code. This allowed the definition of the subsidence basin at the ground surface and the interaction with the buildings in terms of ground displacements. 3D numerical analyses have been performed with an elasto-perfectly plastic constitutive model. In a second step, the effect of a simultaneous collapse of the entire level 3 has been considered in order to evaluate the risk of a flooding due to the water outflow from the mine system. Using a 3D CFD (Continuum Fluid Dynamics) finite element code the collapse of the level 3 has been simulated and the volume of
Directory of Open Access Journals (Sweden)
Asoke Kumar Bhunia
2014-06-01
Full Text Available In this paper, an attempt is made to develop two inventory models for deteriorating items with variable demand dependent on the selling price and frequency of advertisement of items. In the first model, shortages are not allowed whereas in the second, these are allowed and partially backlogged with a variable rate dependent on the duration of waiting time up to the arrival of next lot. In both models, the deterioration rate follows three-parameter Weibull distribution and the transportation cost is considered explicitly for replenishing the order quantity. This cost is dependent on the lot-size as well as the distance from the source to the destination. The corresponding models have been formulated and solved. Two numerical examples have been considered to illustrate the results and the significant features of the results are discussed. Finally, based on these examples, the effects of different parameters on the initial stock level, shortage level (in case of second model only, cycle length along with the optimal profit have been studied by sensitivity analyses taking one parameter at a time keeping the other parameters as same.
Directory of Open Access Journals (Sweden)
Olaf Lubeck
2009-01-01
Full Text Available The IBM Cell Broadband Engine (BE is a novel multi-core chip with the potential for the demanding floating point performance that is required for high-fidelity scientific simulations. However, data movement within the chip can be a major challenge to realizing the benefits of the peak floating point rates. In this paper, we present the results of implementing Sweep3D on the Cell/B.E. using an intra-chip message passing model that minimizes data movement. We compare the advantages/disadvantages of this programming model with a previous implementation using a master–worker threading strategy. We apply a previously validated micro-architecture performance model for the application executing on the Cell/B.E. (based on our previous work in Monte Carlo performance models, that predicts overall CPI (cycles per instruction, and gives a detailed breakdown of processor stalls. Finally, we use the micro-architecture model to assess the performance of future design parameters for the Cell/B.E. micro-architecture. The methodologies and results have broader implications that extend to multi-core architectures.
Defects in the discrete non-linear Schroedinger model
Energy Technology Data Exchange (ETDEWEB)
Doikou, Anastasia, E-mail: adoikou@upatras.gr [University of Patras, Department of Engineering Sciences, Physics Division, GR-26500 Patras (Greece)
2012-01-01
The discrete non-linear Schroedinger (NLS) model in the presence of an integrable defect is examined. The problem is viewed from a purely algebraic point of view, starting from the fundamental algebraic relations that rule the model. The first charges in involution are explicitly constructed, as well as the corresponding Lax pairs. These lead to sets of difference equations, which include particular terms corresponding to the impurity point. A first glimpse regarding the corresponding continuum limit is also provided.
Non-linear models: coal combustion efficiency and emissions control
Energy Technology Data Exchange (ETDEWEB)
Bulsari, A.; Wemberg, A.; Anttila, A.; Multas, A. [Nonlinear Solutions Oy, Turku (Finland)
2009-04-15
Today's power plants feel the pressure to limit their NOx emissions and improve their production economics. The article describes how nonlinear models are effective for process guidance of various kinds of processes, including coal fired boilers. These models were developed for the Naantati 2 boiler at the electricity and heat generating coal-fired plant in Naantali, near Turku, Finland. 4 refs., 6 figs.
Nonlinear modeling of neural population dynamics for hippocampal prostheses
Song, Dong; Chan, Rosa H.M.; Vasilis Z Marmarelis; Hampson, Robert E.; Deadwyler, Sam A.; Berger, Theodore W.
2009-01-01
Developing a neural prosthesis for the damaged hippocampus requires restoring the transformation of population neural activities performed by the hippocampal circuitry. To bypass a damaged region, output spike trains need to be predicted from the input spike trains and then reinstated through stimulation. We formulate a multiple-input, multiple-output (MIMO) nonlinear dynamic model for the input–output transformation of spike trains. In this approach, a MIMO model comprises a series of physio...
Geometric Properties of AR（q） Nonlinear Regression Models
Institute of Scientific and Technical Information of China (English)
LIUYing-ar; WEIBo-cheng
2004-01-01
This paper is devoted to a study of geometric properties of AR(q) nonlinear regression models. We present geometric frameworks for regression parameter space and autoregression parameter space respectively based on the weighted inner product by fisher information matrix. Several geometric properties related to statistical curvatures are given for the models. The results of this paper extended the work of Bates & Watts(1980,1988)[1.2] and Seber & Wild (1989)[3].
Solutions to a nonlinear drift-diffusion model for semiconductors
Directory of Open Access Journals (Sweden)
Weifu Fang
1999-05-01
Full Text Available A nonlinear drift-diffusion model for semiconductors is analyzed to show the existence of non-vacuum global solutions and stationary solutions. The long time behavior of the solutions is studied by establishing the existence of an absorbing set and a compact attractor of the dynamical system. Parallel results on vacuum solutions are also obtained under weaker conditions on model parameters.
CONSERVATIVE ESTIMATING FUNCTIONIN THE NONLINEAR REGRESSION MODEL WITHAGGREGATED DATA
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The purpose of this paper is to study the theory of conservative estimating functions in nonlinear regression model with aggregated data. In this model, a quasi-score function with aggregated data is defined. When this function happens to be conservative, it is projection of the true score function onto a class of estimation functions. By constructing, the potential function for the projected score with aggregated data is obtained, which have some properties of log-likelihood function.
Supersymmetric Q-Lumps in the Grassmannian nonlinear sigma models
Bak, D; Lee, J; Oh, P; Bak, Dongsu; Hahn, Sang-Ok; Lee, Joohan; Oh, Phillial
2007-01-01
We construct the N=2 supersymmetric Grassmannian nonlinear sigma model for the massless case and extend it to massive N=2 model by adding an appropriate superpotential. We then study their BPS equations leading to supersymmetric Q-lumps carrying both topological and Noether charges. These solutions are shown to be always time dependent even sometimes involving multiple frequencies. Thus we illustrate explicitly that the time dependence is consistent with remaining supersymmetries of solitons.
Nonlinear Dynamic Model of PMBLDC Motor Considering Core Losses
DEFF Research Database (Denmark)
Fasil, Muhammed; Mijatovic, Nenad; Jensen, Bogi Bech
2017-01-01
The phase variable model is used commonly when simulating a motor drive system with a three-phase permanent magnet brushless DC (PMBLDC) motor. The phase variable model neglects core losses and this affects its accuracy when modelling fractional-slot machines. The inaccuracy of phase variable model...... on the detailed analysis of the flux path and the variation of flux in different components of the machine. A prototype of fractional slot axial flux PMBLDC in-wheel motor is used to assess the proposed nonlinear dynamic model....
Akushevich, Igor V; Veremeyeva, Galina A; Dimov, Georgy P; Ukraintseva, Svetlana V; Arbeev, Konstantin G; Akleyev, Alexander V; Yashin, Anatoly I
2010-09-01
A new model of the hematopoietic system for humans chronically exposed to ionizing radiation allows for quantitative description of the initial hematopoiesis inhibition and subsequent increase in the risks of late stochastic effects such as leukemia. This model describes the dynamics of the hematopoietic stem cell compartment as well as the dynamics of each of the three blood cell types (leukocytes, erythrocytes, and platelets). The model parameters are estimated from the results of other experiments. They include the steady-state numbers of hematopoietic stem cells and peripheral blood cell lines for an unexposed organism, amplification parameters for each blood cell line, parameters describing the proliferation and apoptosis, parameters of feedback functions regulating the steady-state numbers, and characteristics of radiosensitivity in respect to cell death and non-lethal cell damages. The dynamic model of hematopoiesis is applied to the data on a subcohort of the Techa River residents with hematological measurements (e.g., blood counts) performed in 1950-1956 (which totals to about 3,500 exposed individuals). Among well-described effects observed in these data are the slope values of the dose-effect curves describing the hematopoietic inhibition and the dose rate patterns of the fractions of cytopenic states (e.g., leukopenia, thrombocytopenia). The model has been further generalized by inclusion of the component describing the risk of late stochastic effects. The risks of the development of late effects (such as leukemia) in population groups with specific patterns of early reactions in hematopoiesis (such as leukopenia induced by ionizing radiation) are investigated using simulation studies and compared to data.
The dynamical system of weathering: deterministic and stochastic analysis
Calabrese, S.; Parolari, A.; Porporato, A. M.
2016-12-01
The critical zone is fundamental to human society as it provides most of the ecosystem services such as food and fresh water. However, climate change and intense land use are threatening the critical zone, so that theoretical frameworks, to predict its future response, are needed. In this talk, a new modeling approach to evaluate the effect of hydrologic fluctuations on soil water chemistry and weathering reactions is analyzed by means of a dynamical system approach. In this model, equilibrium is assumed for the aqueous carbonate system while a kinetic law is adopted for the weathering reaction. Also, through an algebraic manipulation, we eliminate the equilibrium reactions and reduce the order of the system. We first analyze the deterministic temporal evolution, and study the stability of the nonlinear system and its trajectories, as a function of the hydro-climatic parameters. By introducing a stochastic rainfall forcing, we then analyze the system probabilistically, and through averaging techniques determine the inter-annual response of the nonlinear stochastic system to the climatic regime and hydrologic parameters (e.g., ET, soil texture). Some fundamental thermodynamic aspects of the chemical reactions are also discussed. By introducing the weathering reaction into the system, any mineral, such as calcium carbonate or a silicate mineral, can be considered.
Westermann, S.; Berntsen, T.; Etzelmüller, B.; Gisnås, K.; Hagen, J. O.; Kristjansson, J. E.; Schuler, T.; Stordal, F.
2012-12-01
Snow is a crucial factor in arctic and high-mountain ecosystems, e.g. for the thermal regime of permafrost and the mass balance on glaciers. However, the snow depth and properties can vary considerably on small scales due to wind redistribution, which for instance leads to distinctly different soil temperatures in permafrost areas on distances of tens of meters. The spatial resolution of standard atmospheric models is clearly insufficient to capture such small-scale variability. CryoMET is a new collaborative project between atmospheric modeling, glacier and permafrost research groups funded by the Norwegian Research Council. It seeks to bridge the scale gap between coarsely-resolved Earth System Models providing climate projections and the process and impact scales on the ground, on which permafrost temperatures and glacier mass balance are projected to change. CryoMET will explore a seamless downscaling procedure for the variables snow depth and snow water equivalent. In a first step, we use the state-of-the-art regional model PolarWRF to downscale atmospheric variables, including precipitation, air temperature and wind speed, to the so-called interface scale, where these variables are constant to a good approximation. In CryoMET, we aim for a spatial resolution of 1 to 3 km, which is determined by the topography of the project's target areas in Norway and Svalbard. In a second step, we will employ probabilistic downscaling of the average snow water equivalent at the interface scale (as delivered by PolarWRF) using snow redistribution models, which can resolve small-scale variations of snow depth due to wind drift down to the meter scale. With probability density functions of snow depth, we can infer the distribution of environmental parameters affected by snow within one grid cell at the interface scale, e.g. of permafrost temperatures. Thus, CryoMET ultimately aims for a scaling concept capable of bridging up to five orders of magnitude in space without
Robust nonlinear system identification using neural-network models.
Lu, S; Basar, T
1998-01-01
We study the problem of identification for nonlinear systems in the presence of unknown driving noise, using both feedforward multilayer neural network and radial basis function network models. Our objective is to resolve the difficulty associated with the persistency of excitation condition inherent to the standard schemes in the neural identification literature. This difficulty is circumvented here by a novel formulation and by using a new class of identification algorithms recently obtained by Didinsky et al. We show how these algorithms can be exploited to successfully identify the nonlinearity in the system using neural-network models. By embedding the original problem in one with noise-perturbed state measurements, we present a class of identifiers (under L1 and L2 cost criteria) which secure a good approximant for the system nonlinearity provided that some global optimization technique is used. In this respect, many available learning algorithms in the current neural-network literature, e.g., the backpropagation scheme and the genetic algorithms-based scheme, with slight modifications, can ensure the identification of the system nonlinearity. Subsequently, we address the same problem under a third, worst case L(infinity) criterion for an RBF modeling. We present a neural-network version of an H(infinity)-based identification algorithm from Didinsky et al and show how, along with an appropriate choice of control input to enhance excitation, under both full-state-derivative information (FSDI) and noise-perturbed full-state-information (NPFSI), it leads to satisfaction of a relevant persistency of excitation condition, and thereby to robust identification of the nonlinearity. Results from several simulation studies have been included to demonstrate the effectiveness of these algorithms.
Directory of Open Access Journals (Sweden)
A. K. Bhunia
2011-01-01
Full Text Available This paper deals with an inventory model, which considers the impact of marketing strategies such as pricing and advertising as well as the displayed inventory level on the demand rate of the system. In addition, the demand rate during the stock-out period differs from that during the stock-in period by a function varied on the waiting time up to the beginning of the next cycle. Shortage are allowed and partially backlogged. Here, the deterioration rate is assumed to follow the Weibull distribution. Considering all these factors with others, different scenarios of the system are investigated. To obtain the solutions of these cases and to illustrate the model, an example is considered. Finally, to study the effects of changes of different parameters of the system, sensitivity analyses have been carried out with respect to the different parameters of the system.
Reduced Complexity Volterra Models for Nonlinear System Identification
Directory of Open Access Journals (Sweden)
Hacıoğlu Rıfat
2001-01-01
Full Text Available A broad class of nonlinear systems and filters can be modeled by the Volterra series representation. However, its practical use in nonlinear system identification is sometimes limited due to the large number of parameters associated with the Volterra filter′s structure. The parametric complexity also complicates design procedures based upon such a model. This limitation for system identification is addressed in this paper using a Fixed Pole Expansion Technique (FPET within the Volterra model structure. The FPET approach employs orthonormal basis functions derived from fixed (real or complex pole locations to expand the Volterra kernels and reduce the number of estimated parameters. That the performance of FPET can considerably reduce the number of estimated parameters is demonstrated by a digital satellite channel example in which we use the proposed method to identify the channel dynamics. Furthermore, a gradient-descent procedure that adaptively selects the pole locations in the FPET structure is developed in the paper.
Structure and asymptotic theory for nonlinear models with GARCH errors
Directory of Open Access Journals (Sweden)
Felix Chan
2015-01-01
Full Text Available Nonlinear time series models, especially those with regime-switching and/or conditionally heteroskedastic errors, have become increasingly popular in the economics and finance literature. However, much of the research has concentrated on the empirical applications of various models, with little theoretical or statistical analysis associated with the structure of the processes or the associated asymptotic theory. In this paper, we derive sufficient conditions for strict stationarity and ergodicity of three different specifications of the first-order smooth transition autoregressions with heteroskedastic errors. This is essential, among other reasons, to establish the conditions under which the traditional LM linearity tests based on Taylor expansions are valid. We also provide sufficient conditions for consistency and asymptotic normality of the Quasi-Maximum Likelihood Estimator for a general nonlinear conditional mean model with first-order GARCH errors.
Modeling and study of nonlinear effects in electrodynamic shakers
Saraswat, Abhishek; Tiwari, Nachiketa
2017-02-01
An electrodynamic shaker is inherently a nonlinear electro-mechanical system. In this work, we have developed a lumped parameter model for the entire electromechanical system, developed an approach to non-destructively determine these parameters, and predict the nonlinear response of the shaker. This predicted response has been validated using experimental data. Through such an approach, we have been able to accurately predict the resulting distortions in the response of the shaker and other nonlinear effects like DC offset in the displacement response. Our approach offers a key advantage vis-à-vis other approaches which rely on techniques involving Volterra Series expansions or techniques based on blackbox models like neural networks, which is that in our approach, apart from predicting the response of the shaker, the model parameters obtained have a physical significance and changes in the parameters can be directly mapped to modification in key design parameters of the shaker. The proposed approach is also advantageous in one more way: it requires measurement of only four parameters, voltage, current, displacement and acceleration for estimating shaker model parameters non-destructively. The proposed model can be used for the design of linearization controllers, prototype testing and simulation of new shaker designs as well as for performance prediction of shakers under testing conditions.
Large-N Analysis of Three Dimensional Nonlinear Sigma Models
Higashijima, K; Tsuzuki, M; Higashijima, Kiyoshi; Itou, Etsuko; Tsuzuki, Makoto
2005-01-01
Non-perturbative renormalization group approach suggests that a large class of nonlinear sigma models are renormalizable in three dimensional space-time, while they are non-renormalizable in perturbation theory. ${\\cal N}=2$ supersymmetric nonlinear sigma models whose target spaces are Einstein-K\\"{a}hler manifolds with positive scalar curvature belongs to this class. hermitian symmetric spaces, being homogeneous, are specially simple examples of these manifolds. To find an independent evidence of the nonperturbative renormalizability of these models, the large N method, another nonperturbative method, is applied to 3-dimensional ${\\cal N}=2$ supersymmetric nonlinear sigma models on the target spaces $CP^{N-1}=SU(N)/[SU(N-1)\\times U(1)]$ and $Q^{N-2}=SO(N)/[SO(N-2)\\times SO(2)]$, two typical examples of hermitian symmetric spaces. We find that $\\beta$ functions in these models agree with the results of the nonperturbative renormalization group approach in the next-to-leading order of 1/N expansion, and have n...
Nonlinear analysis and prediction of time series in multiphase reactors
Liu, Mingyan
2014-01-01
This book reports on important nonlinear aspects or deterministic chaos issues in the systems of multi-phase reactors. The reactors treated in the book include gas-liquid bubble columns, gas-liquid-solid fluidized beds and gas-liquid-solid magnetized fluidized beds. The authors take pressure fluctuations in the bubble columns as time series for nonlinear analysis, modeling and forecasting. They present qualitative and quantitative non-linear analysis tools which include attractor phase plane plot, correlation dimension, Kolmogorov entropy and largest Lyapunov exponent calculations and local non-linear short-term prediction.
Wireless Network Information Flow: A Deterministic Approach
Avestimehr, Salman; Tse, David
2009-01-01
In contrast to wireline networks, not much is known about the flow of information over wireless networks. The main barrier is the complexity of the signal interaction in wireless channels in addition to the noise in the channel. A widely accepted model is the the additive Gaussian channel model, and for this model, the capacity of even a network with a single relay node is open for 30 years. In this paper, we present a deterministic approach to this problem by focusing on the signal interaction rather than the noise. To this end, we propose a deterministic channel model which is analytically simpler than the Gaussian model but still captures two key wireless channel properties of broadcast and superposition. We consider a model for a wireless relay network with nodes connected by such deterministic channels, and present an exact characterization of the end-to-end capacity when there is a single source and one or more destinations (all interested in the same information) and an arbitrary number of relay nodes....
DEFF Research Database (Denmark)
Nielsen, Steen
2000-01-01
This paper expands the traditional product costing technique be including a stochastic form in a complex production process for product costing. The stochastic phenomenon in flesbile manufacturing technologies is seen as an important phenomenon that companies try to decreas og eliminate. DFM has...... been used for evaluating the appropriateness of the firm's production capability. In this paper a simulation model is developed to analyze the relevant cost behaviour with respect to DFM and to develop a more streamlined process in the layout of the manufacturing process....
Reduction of the curvature of a class of nonlinear regression models
Institute of Scientific and Technical Information of China (English)
吴翊; 易东云
2000-01-01
It is proved that the curvature of nonlinear model can be reduced to zero by increasing measured data for a class of nonlinear regression models. The result is important to actual problem and has obtained satisfying effect on data fusing.
Estimation of Nonlinear DC-Motor Models Using a Sensitivity Approach
DEFF Research Database (Denmark)
Knudsen, Morten; Jensen, J.G.
1995-01-01
A nonlinear model structure for a permanent magnet DC-motor, appropriate for simulation and controller design, is developed.......A nonlinear model structure for a permanent magnet DC-motor, appropriate for simulation and controller design, is developed....
Enhanced Model of Nonlinear Spiral High Voltage Divider
Directory of Open Access Journals (Sweden)
V. Panko
2015-04-01
Full Text Available This paper deals with the enhanced accurate DC and RF model of nonlinear spiral polysilicon voltage divider. The high resistance polysilicon divider is a sensing part of the high voltage start-up MOSFET transistor that can operate up to 700 V. This paper presents the structure of a proposed model, implemented voltage, frequency and temperature dependency, and scalability. A special attention is paid to the ability of the created model to cover the mismatch and influence of a variation of process parameters on the device characteristics. Finally, the comparison of measured data vs. simulation is presented in order to confirm the model validity and a typical application is demonstrated.
Spatio-temporal modeling of nonlinear distributed parameter systems
Li, Han-Xiong
2011-01-01
The purpose of this volume is to provide a brief review of the previous work on model reduction and identifi cation of distributed parameter systems (DPS), and develop new spatio-temporal models and their relevant identifi cation approaches. In this book, a systematic overview and classifi cation on the modeling of DPS is presented fi rst, which includes model reduction, parameter estimation and system identifi cation. Next, a class of block-oriented nonlinear systems in traditional lumped parameter systems (LPS) is extended to DPS, which results in the spatio-temporal Wiener and Hammerstein s
Nonlinear Reynolds stress models and the renormalization group
Rubinstein, Robert; Barton, J. Michael
1990-01-01
The renormalization group is applied to derive a nonlinear algebraic Reynolds stress model of anisotropic turbulence in which the Reynolds stresses are quadratic functions of the mean velocity gradients. The model results from a perturbation expansion that is truncated systematically at second order with subsequent terms contributing no further information. The resulting turbulence model applied to both low and high Reynolds number flows without requiring wall functions or ad hoc modifications of the equations. All constants are derived from the renormalization group procedure; no adjustable constants arise. The model permits inequality of the Reynolds normal stresses, a necessary condition for calculating turbulence-driven secondary flows in noncircular ducts.
Yan, Ping; Feng, Zhilan
2010-03-01
We use distribution theory and ordering of non-negative random variables to study the Susceptible-Exposed-Infectious-Removed (SEIR) model with two control measures, quarantine and isolation, to reduce the spread of an infectious disease. We identify that the probability distributions of the latent period and the infectious period are primary features of the SEIR model to formulate the epidemic threshold and to evaluate the effectiveness of the intervention measures. If the primary features are changed, the conclusions will be altered in an importantly different way. For the latent and infectious periods with known mean values, it is the dilation, a generalization of variance, of their distributions that ranks the effectiveness of these control measures. We further propose ways to set quarantine and isolation targets to reduce the controlled reproduction number below the threshold using observed initial growth rate from outbreak data. If both quarantine and isolation are 100% effective, one can directly use the observed growth rate for setting control targets. If they are not 100% effective, some further knowledge of the distributions is required.