Scale-invariant Green-Kubo relation for time-averaged diffusivity

Science.gov (United States)

Meyer, Philipp; Barkai, Eli; Kantz, Holger

2017-12-01

In recent years it was shown both theoretically and experimentally that in certain systems exhibiting anomalous diffusion the time- and ensemble-averaged mean-squared displacement are remarkably different. The ensemble-averaged diffusivity is obtained from a scaling Green-Kubo relation, which connects the scale-invariant nonstationary velocity correlation function with the transport coefficient. Here we obtain the relation between time-averaged diffusivity, usually recorded in single-particle tracking experiments, and the underlying scale-invariant velocity correlation function. The time-averaged mean-squared displacement is given by 〈δ2¯〉 ˜2 DνtβΔν -β , where t is the total measurement time and Δ is the lag time. Here ν is the anomalous diffusion exponent obtained from ensemble-averaged measurements 〈x2〉 ˜tν , while β ≥-1 marks the growth or decline of the kinetic energy 〈v2〉 ˜tβ . Thus, we establish a connection between exponents that can be read off the asymptotic properties of the velocity correlation function and similarly for the transport constant Dν. We demonstrate our results with nonstationary scale-invariant stochastic and deterministic models, thereby highlighting that systems with equivalent behavior in the ensemble average can differ strongly in their time average. If the averaged kinetic energy is finite, β =0 , the time scaling of 〈δ2¯〉 and 〈x2〉 are identical; however, the time-averaged transport coefficient Dν is not identical to the corresponding ensemble-averaged diffusion constant.

On time-dependent diffusion coefficients arising from stochastic processes with memory

Science.gov (United States)

Carpio-Bernido, M. Victoria; Barredo, Wilson I.; Bernido, Christopher C.

2017-08-01

Time-dependent diffusion coefficients arise from anomalous diffusion encountered in many physical systems such as protein transport in cells. We compare these coefficients with those arising from analysis of stochastic processes with memory that go beyond fractional Brownian motion. Facilitated by the Hida white noise functional integral approach, diffusion propagators or probability density functions (pdf) are obtained and shown to be solutions of modified diffusion equations with time-dependent diffusion coefficients. This should be useful in the study of complex transport processes.

Prognostic Relevance of Immunohistochemical Subclassification of Diffuse Large B-Cell Lymphoma in Two Prospective Phase III Clinical Trials

NARCIS (Netherlands)

Rayman, Nazik; Lam, King H.; van der Holt, Bronno; Koss, Clara; Veldhuizen, Dennis; Budel, Leo M.; Mulder, Andries H.; Verdonck, Leo F.; Delwel, Ruud; de Jong, Daphne; van Imhoff, Gustaaf W.; Sonneveld, Pieter

Purpose: Until now molecular biologic techniques have not been easily used in daily clinical practice to stratify patients for therapeutic purposes. Therefore, we have investigated the prognostic relevance of the immunohistochemical (IHC) germinal center B-cell (GCB) versus non-GCB diffuse large

Demonstration of non-Gaussian restricted diffusion in tumor cells using diffusion-time dependent diffusion weighted MR contrast

Directory of Open Access Journals (Sweden)

Tuva Roaldsdatter Hope

2016-08-01

Full Text Available The diffusion weighted imaging (DWI technique enables quantification of water mobility for probing microstructural properties of biological tissue, and has become an effective tool for collecting information about the underlying pathology of cancerous tissue. Measurements using multiple b-values have indicated a bi-exponential signal attenuation, ascribed to fast (high ADC and slow (low ADC diffusion components. In this empirical study, we investigate the properties of the diffusion time (∆ - dependent components of the diffusion-weighted (DW signal in a constant b-value experiment. A Xenograft GBM mouse was imaged using ∆ = 11 ms, 20 ms, 40 ms, 60 ms and b=500-4000 s/mm2 in intervals of 500s/mm2. Data was corrected for EPI distortions and the ∆-dependence on the DW signal was measured within three regions of interest (intermediate- and high-density tumor regions and normal appearing brain tissue regions (NAB. In this empirical study we verify the assumption that the slow decaying component of the DW-signal is non-Gaussian and dependent on ∆, consistent with restricted diffusion of the intracellular space. As the DW-signal as a function of ∆ is specific to restricted diffusion, manipulating ∆ at constant b-value (cb provides a complementary and direct approach for separating the restricted from the hindered diffusion component. Our results show that only tumor tissue signal of our data demonstrate ∆-dependence, based on a bi-exponential model with a restricted diffusion component, we successfully estimated the restricted ADC, signal volume fraction and cell size within each tumor ROI.

Diffusion equations and the time evolution of foreign exchange rates

Energy Technology Data Exchange (ETDEWEB)

Figueiredo, Annibal; Castro, Marcio T. de [Institute of Physics, Universidade de Brasília, Brasília DF 70910-900 (Brazil); Fonseca, Regina C.B. da [Department of Mathematics, Instituto Federal de Goiás, Goiânia GO 74055-110 (Brazil); Gleria, Iram, E-mail: iram@fis.ufal.br [Institute of Physics, Federal University of Alagoas, Brazil, Maceió AL 57072-900 (Brazil)

2013-10-01

We investigate which type of diffusion equation is most appropriate to describe the time evolution of foreign exchange rates. We modify the geometric diffusion model assuming a non-exponential time evolution and the stochastic term is the sum of a Wiener noise and a jump process. We find the resulting diffusion equation to obey the Kramers–Moyal equation. Analytical solutions are obtained using the characteristic function formalism and compared with empirical data. The analysis focus on the first four central moments considering the returns of foreign exchange rate. It is shown that the proposed model offers a good improvement over the classical geometric diffusion model.

Diffusion equations and the time evolution of foreign exchange rates

Science.gov (United States)

Figueiredo, Annibal; de Castro, Marcio T.; da Fonseca, Regina C. B.; Gleria, Iram

2013-10-01

We investigate which type of diffusion equation is most appropriate to describe the time evolution of foreign exchange rates. We modify the geometric diffusion model assuming a non-exponential time evolution and the stochastic term is the sum of a Wiener noise and a jump process. We find the resulting diffusion equation to obey the Kramers-Moyal equation. Analytical solutions are obtained using the characteristic function formalism and compared with empirical data. The analysis focus on the first four central moments considering the returns of foreign exchange rate. It is shown that the proposed model offers a good improvement over the classical geometric diffusion model.

Diffusion equations and the time evolution of foreign exchange rates

International Nuclear Information System (INIS)

Figueiredo, Annibal; Castro, Marcio T. de; Fonseca, Regina C.B. da; Gleria, Iram

2013-01-01

We investigate which type of diffusion equation is most appropriate to describe the time evolution of foreign exchange rates. We modify the geometric diffusion model assuming a non-exponential time evolution and the stochastic term is the sum of a Wiener noise and a jump process. We find the resulting diffusion equation to obey the Kramers–Moyal equation. Analytical solutions are obtained using the characteristic function formalism and compared with empirical data. The analysis focus on the first four central moments considering the returns of foreign exchange rate. It is shown that the proposed model offers a good improvement over the classical geometric diffusion model.

Periodic solutions in reaction–diffusion equations with time delay

International Nuclear Information System (INIS)

Li, Li

2015-01-01

Spatial diffusion and time delay are two main factors in biological and chemical systems. However, the combined effects of them on diffusion systems are not well studied. As a result, we investigate a nonlinear diffusion system with delay and obtain the existence of the periodic solutions using coincidence degree theory. Moreover, two numerical examples confirm our theoretical results. The obtained results can also be applied in other related fields

Long-Time Data Storage: Relevant Time Scales

Directory of Open Access Journals (Sweden)

Miko C. Elwenspoek

2011-02-01

Full Text Available Dynamic processes relevant for long-time storage of information about human kind are discussed, ranging from biological and geological processes to the lifecycle of stars and the expansion of the universe. Major results are that life will end ultimately and the remaining time that the earth is habitable for complex life is about half a billion years. A system retrieved within the next million years will be read by beings very closely related to Homo sapiens. During this time the surface of the earth will change making it risky to place a small number of large memory systems on earth; the option to place it on the moon might be more favorable. For much longer timescales both options do not seem feasible because of geological processes on the earth and the flux of small meteorites to the moon.

Characteristic time scales for diffusion processes through layers and across interfaces

Science.gov (United States)

Carr, Elliot J.

2018-04-01

This paper presents a simple tool for characterizing the time scale for continuum diffusion processes through layered heterogeneous media. This mathematical problem is motivated by several practical applications such as heat transport in composite materials, flow in layered aquifers, and drug diffusion through the layers of the skin. In such processes, the physical properties of the medium vary across layers and internal boundary conditions apply at the interfaces between adjacent layers. To characterize the time scale, we use the concept of mean action time, which provides the mean time scale at each position in the medium by utilizing the fact that the transition of the transient solution of the underlying partial differential equation model, from initial state to steady state, can be represented as a cumulative distribution function of time. Using this concept, we define the characteristic time scale for a multilayer diffusion process as the maximum value of the mean action time across the layered medium. For given initial conditions and internal and external boundary conditions, this approach leads to simple algebraic expressions for characterizing the time scale that depend on the physical and geometrical properties of the medium, such as the diffusivities and lengths of the layers. Numerical examples demonstrate that these expressions provide useful insight into explaining how the parameters in the model affect the time it takes for a multilayer diffusion process to reach steady state.

Diffusive spatio-temporal noise in a first-passage time model for intracellular calcium release

KAUST Repository

Flegg, Mark B.

2013-01-01

The intracellular release of calcium from the endoplasmic reticulum is controlled by ion channels. The resulting calcium signals exhibit a rich spatio-temporal signature, which originates at least partly from microscopic fluctuations. While stochasticity in the gating transition of ion channels has been incorporated into many models, the distribution of calcium is usually described by deterministic reaction-diffusion equations. Here we test the validity of the latter modeling approach by using two different models to calculate the frequency of localized calcium signals (calcium puffs) from clustered IP3 receptor channels. The complexity of the full calcium system is here limited to the basic opening mechanism of the ion channels and, in the mathematical reduction simplifies to the calculation of a first passage time. Two models are then studied: (i) a hybrid model, where channel gating is treated stochastically, while calcium concentration is deterministic and (ii) a fully stochastic model with noisy channel gating and Brownian calcium ion motion. The second model utilises the recently developed two-regime method [M. B. Flegg, S. J. Chapman, and R. Erban, "The two-regime method for optimizing stochastic reaction-diffusion simulations," J. R. Soc., Interface 9, 859-868 (2012)] in order to simulate a large domain with precision required only near the Ca2+ absorbing channels. The expected time for a first channel opening that results in a calcium puff event is calculated. It is found that for a large diffusion constant, predictions of the interpuff time are significantly overestimated using the model (i) with a deterministic non-spatial calcium variable. It is thus demonstrated that the presence of diffusive noise in local concentrations of intracellular Ca2+ ions can substantially influence the occurrence of calcium signals. The presented approach and results may also be relevant for other cell-physiological first-passage time problems with small ligand concentration

Soil water diffusivity as a function of water content and time

International Nuclear Information System (INIS)

Guerrini, I.A.

1976-04-01

The soil-water diffusivity has been studied as a function of water content and time. From the idea of studying the horizontal movement of water in swelling soils, a simple formulation has been achieved which allows for the diffusivity, water content dependency and time dependency, to be estimated, not only of this kind of soil, but for any other soil as well. It was observed that the internal rearrangement of soil particles is a more important phenomenon than swelling, being responsible for time dependency. The method 2γ is utilized, which makes it possible to simultaneously determine the water content and density, point by point, in a soil column. The diffusivity data thus obtained are compared to those obtained when time dependency is not considered. Finally, a new soil parameter, α, is introduced and the values obtained agrees with the internal rearrangment assumption and time dependency for diffusivity (Author) [pt

Nonlinear diffusion problem arising in plasma physics

International Nuclear Information System (INIS)

Berryman, J.G.; Holland, C.J.

1978-01-01

In earlier studies of plasma diffusion with Okuda-Dawson scaling (D approx. n/sup -1/2/), perturbation theory indicated that arbitrary initial data should evolve rapidly toward the separation solution of the relevant nonlinear diffusion equation. Now a Lyapunov functional has been found which is strictly decreasing in time and bounded below. The rigorous proof that arbitrary initial data evolve toeard the separable solution is summarized. Rigorous bounds on the decay time are also presented

Modeling information diffusion in time-varying community networks

Science.gov (United States)

Cui, Xuelian; Zhao, Narisa

2017-12-01

Social networks are rarely static, and they typically have time-varying network topologies. A great number of studies have modeled temporal networks and explored social contagion processes within these models; however, few of these studies have considered community structure variations. In this paper, we present a study of how the time-varying property of a modular structure influences the information dissemination. First, we propose a continuous-time Markov model of information diffusion where two parameters, mobility rate and community attractiveness, are introduced to address the time-varying nature of the community structure. The basic reproduction number is derived, and the accuracy of this model is evaluated by comparing the simulation and theoretical results. Furthermore, numerical results illustrate that generally both the mobility rate and community attractiveness significantly promote the information diffusion process, especially in the initial outbreak stage. Moreover, the strength of this promotion effect is much stronger when the modularity is higher. Counterintuitively, it is found that when all communities have the same attractiveness, social mobility no longer accelerates the diffusion process. In addition, we show that the local spreading in the advantage group has been greatly enhanced due to the agglomeration effect caused by the social mobility and community attractiveness difference, which thus increases the global spreading.

Arbitrary Dimension Convection-Diffusion Schemes for Space-Time Discretizations

Energy Technology Data Exchange (ETDEWEB)

Bank, Randolph E. [Univ. of California, San Diego, CA (United States); Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Zikatanov, Ludmil T. [Bulgarian Academy of Sciences, Sofia (Bulgaria)

2016-01-20

This note proposes embedding a time dependent PDE into a convection-diffusion type PDE (in one space dimension higher) with singularity, for which two discretization schemes, the classical streamline-diffusion and the EAFE (edge average finite element) one, are investigated in terms of stability and error analysis. The EAFE scheme, in particular, is extended to be arbitrary order which is of interest on its own. Numerical results, in combined space-time domain demonstrate the feasibility of the proposed approach.

Solution of time dependent atmospheric diffusion equation with a proposed diffusion coefficient

International Nuclear Information System (INIS)

Mayhoub, A.B.; Essa, KH.S.M.; Aly, SH.

2004-01-01

One-dimensional model for the dispersion of passive atmospheric contaminant (not included chemical reactions) in the atmospheric boundary layer is considered. On the basis of the gradient transfer theory (K-theory), the time dependent diffusion equation represents the dispersion of the pollutants is solved analytically. The solution depends on diffusion coefficient K', which is expressed in terms of the friction velocity 'u the vertical coordinate -L and the depth of the mixing layer 'h'. The solution is obtained to either the vertical coordinate 'z' is less or greater than the mixing height 'h'. The obtained solution may be applied to study the atmospheric dispersion of pollutants

Theory and simulation of time-fractional fluid diffusion in porous media

International Nuclear Information System (INIS)

Carcione, José M; Sanchez-Sesma, Francisco J; Gavilán, Juan J Perez; Luzón, Francisco

2013-01-01

We simulate a fluid flow in inhomogeneous anisotropic porous media using a time-fractional diffusion equation and the staggered Fourier pseudospectral method to compute the spatial derivatives. A fractional derivative of the order of 0 < ν < 2 replaces the first-order time derivative in the classical diffusion equation. It implies a time-dependent permeability tensor having a power-law time dependence, which describes memory effects and accounts for anomalous diffusion. We provide a complete analysis of the physics based on plane waves. The concepts of phase, group and energy velocities are analyzed to describe the location of the diffusion front, and the attenuation and quality factors are obtained to quantify the amplitude decay. We also obtain the frequency-domain Green function. The time derivative is computed with the Grünwald–Letnikov summation, which is a finite-difference generalization of the standard finite-difference operator to derivatives of fractional order. The results match the analytical solution obtained from the Green function. An example of the pressure field generated by a fluid injection in a heterogeneous sandstone illustrates the performance of the algorithm for different values of ν. The calculation requires storing the whole pressure field in the computer memory since anomalous diffusion ‘recalls the past’. (paper)

Time evolution of negative binomial optical field in a diffusion channel

International Nuclear Information System (INIS)

Liu Tang-Kun; Wu Pan-Pan; Shan Chuan-Jia; Liu Ji-Bing; Fan Hong-Yi

2015-01-01

We find the time evolution law of a negative binomial optical field in a diffusion channel. We reveal that by adjusting the diffusion parameter, the photon number can be controlled. Therefore, the diffusion process can be considered a quantum controlling scheme through photon addition. (paper)

Time scale of diffusion in molecular and cellular biology

International Nuclear Information System (INIS)

Holcman, D; Schuss, Z

2014-01-01

Diffusion is the driver of critical biological processes in cellular and molecular biology. The diverse temporal scales of cellular function are determined by vastly diverse spatial scales in most biophysical processes. The latter are due, among others, to small binding sites inside or on the cell membrane or to narrow passages between large cellular compartments. The great disparity in scales is at the root of the difficulty in quantifying cell function from molecular dynamics and from simulations. The coarse-grained time scale of cellular function is determined from molecular diffusion by the mean first passage time of molecular Brownian motion to a small targets or through narrow passages. The narrow escape theory (NET) concerns this issue. The NET is ubiquitous in molecular and cellular biology and is manifested, among others, in chemical reactions, in the calculation of the effective diffusion coefficient of receptors diffusing on a neuronal cell membrane strewn with obstacles, in the quantification of the early steps of viral trafficking, in the regulation of diffusion between the mother and daughter cells during cell division, and many other cases. Brownian trajectories can represent the motion of a molecule, a protein, an ion in solution, a receptor in a cell or on its membrane, and many other biochemical processes. The small target can represent a binding site or an ionic channel, a hidden active site embedded in a complex protein structure, a receptor for a neurotransmitter on the membrane of a neuron, and so on. The mean time to attach to a receptor or activator determines diffusion fluxes that are key regulators of cell function. This review describes physical models of various subcellular microdomains, in which the NET coarse-grains the molecular scale to a higher cellular-level, thus clarifying the role of cell geometry in determining subcellular function. (topical review)

Time scale of diffusion in molecular and cellular biology

Science.gov (United States)

Holcman, D.; Schuss, Z.

2014-05-01

Diffusion is the driver of critical biological processes in cellular and molecular biology. The diverse temporal scales of cellular function are determined by vastly diverse spatial scales in most biophysical processes. The latter are due, among others, to small binding sites inside or on the cell membrane or to narrow passages between large cellular compartments. The great disparity in scales is at the root of the difficulty in quantifying cell function from molecular dynamics and from simulations. The coarse-grained time scale of cellular function is determined from molecular diffusion by the mean first passage time of molecular Brownian motion to a small targets or through narrow passages. The narrow escape theory (NET) concerns this issue. The NET is ubiquitous in molecular and cellular biology and is manifested, among others, in chemical reactions, in the calculation of the effective diffusion coefficient of receptors diffusing on a neuronal cell membrane strewn with obstacles, in the quantification of the early steps of viral trafficking, in the regulation of diffusion between the mother and daughter cells during cell division, and many other cases. Brownian trajectories can represent the motion of a molecule, a protein, an ion in solution, a receptor in a cell or on its membrane, and many other biochemical processes. The small target can represent a binding site or an ionic channel, a hidden active site embedded in a complex protein structure, a receptor for a neurotransmitter on the membrane of a neuron, and so on. The mean time to attach to a receptor or activator determines diffusion fluxes that are key regulators of cell function. This review describes physical models of various subcellular microdomains, in which the NET coarse-grains the molecular scale to a higher cellular-level, thus clarifying the role of cell geometry in determining subcellular function.

Investigating the tradeoffs between spatial resolution and diffusion sampling for brain mapping with diffusion tractography: time well spent?

Science.gov (United States)

Calabrese, Evan; Badea, Alexandra; Coe, Christopher L; Lubach, Gabriele R; Styner, Martin A; Johnson, G Allan

2014-11-01

Interest in mapping white matter pathways in the brain has peaked with the recognition that altered brain connectivity may contribute to a variety of neurologic and psychiatric diseases. Diffusion tractography has emerged as a popular method for postmortem brain mapping initiatives, including the ex-vivo component of the human connectome project, yet it remains unclear to what extent computer-generated tracks fully reflect the actual underlying anatomy. Of particular concern is the fact that diffusion tractography results vary widely depending on the choice of acquisition protocol. The two major acquisition variables that consume scan time, spatial resolution, and diffusion sampling, can each have profound effects on the resulting tractography. In this analysis, we determined the effects of the temporal tradeoff between spatial resolution and diffusion sampling on tractography in the ex-vivo rhesus macaque brain, a close primate model for the human brain. We used the wealth of autoradiography-based connectivity data available for the rhesus macaque brain to assess the anatomic accuracy of six time-matched diffusion acquisition protocols with varying balance between spatial and diffusion sampling. We show that tractography results vary greatly, even when the subject and the total acquisition time are held constant. Further, we found that focusing on either spatial resolution or diffusion sampling at the expense of the other is counterproductive. A balanced consideration of both sampling domains produces the most anatomically accurate and consistent results. Copyright © 2014 Wiley Periodicals, Inc.

Relationship between timed 25-foot walk and diffusion tensor imaging in multiple sclerosis.

Science.gov (United States)

Klineova, Sylvia; Farber, Rebecca; Saiote, Catarina; Farrell, Colleen; Delman, Bradley N; Tanenbaum, Lawrence N; Friedman, Joshua; Inglese, Matilde; Lublin, Fred D; Krieger, Stephen

2016-01-01

The majority of multiple sclerosis patients experience impaired walking ability, which impacts quality of life. Timed 25-foot walk is commonly used to gauge gait impairment but results can be broadly variable. Objective biological markers that correlate closely with patients' disability are needed. Diffusion tensor imaging, quantifying fiber tract integrity, might provide such information. In this project we analyzed relationships between timed 25-foot walk, conventional and diffusion tensor imaging magnetic resonance imaging markers. A cohort of gait impaired multiple sclerosis patients underwent brain and cervical spinal cord magnetic resonance imaging. Diffusion tensor imaging mean diffusivity and fractional anisotropy were measured on the brain corticospinal tracts and spinal restricted field of vision at C2/3. We analyzed relationships between baseline timed 25-foot walk, conventional and diffusion tensor imaging magnetic resonance imaging markers. Multivariate linear regression analysis showed a statistically significant association between several magnetic resonance imaging and diffusion tensor imaging metrics and timed 25-foot walk: brain mean diffusivity corticospinal tracts (p = 0.004), brain corticospinal tracts axial and radial diffusivity (P = 0.004 and 0.02), grey matter volume (p = 0.05), white matter volume (p = 0.03) and normalized brain volume (P = 0.01). The linear regression model containing mean diffusivity corticospinal tracts and controlled for gait assistance was the best fit model (p = 0.004). Our results suggest an association between diffusion tensor imaging metrics and gait impairment, evidenced by brain mean diffusivity corticospinal tracts and timed 25-foot walk.

Continuous-time random-walk model for anomalous diffusion in expanding media

Science.gov (United States)

Le Vot, F.; Abad, E.; Yuste, S. B.

2017-09-01

Expanding media are typical in many different fields, e.g., in biology and cosmology. In general, a medium expansion (contraction) brings about dramatic changes in the behavior of diffusive transport properties such as the set of positional moments and the Green's function. Here, we focus on the characterization of such effects when the diffusion process is described by the continuous-time random-walk (CTRW) model. As is well known, when the medium is static this model yields anomalous diffusion for a proper choice of the probability density function (pdf) for the jump length and the waiting time, but the behavior may change drastically if a medium expansion is superimposed on the intrinsic random motion of the diffusing particle. For the case where the jump length and the waiting time pdfs are long-tailed, we derive a general bifractional diffusion equation which reduces to a normal diffusion equation in the appropriate limit. We then study some particular cases of interest, including Lévy flights and subdiffusive CTRWs. In the former case, we find an analytical exact solution for the Green's function (propagator). When the expansion is sufficiently fast, the contribution of the diffusive transport becomes irrelevant at long times and the propagator tends to a stationary profile in the comoving reference frame. In contrast, for a contracting medium a competition between the spreading effect of diffusion and the concentrating effect of contraction arises. In the specific case of a subdiffusive CTRW in an exponentially contracting medium, the latter effect prevails for sufficiently long times, and all the particles are eventually localized at a single point in physical space. This "big crunch" effect, totally absent in the case of normal diffusion, stems from inefficient particle spreading due to subdiffusion. We also derive a hierarchy of differential equations for the moments of the transport process described by the subdiffusive CTRW model in an expanding medium

Continuous-time random-walk model for anomalous diffusion in expanding media.

Science.gov (United States)

Le Vot, F; Abad, E; Yuste, S B

2017-09-01

Expanding media are typical in many different fields, e.g., in biology and cosmology. In general, a medium expansion (contraction) brings about dramatic changes in the behavior of diffusive transport properties such as the set of positional moments and the Green's function. Here, we focus on the characterization of such effects when the diffusion process is described by the continuous-time random-walk (CTRW) model. As is well known, when the medium is static this model yields anomalous diffusion for a proper choice of the probability density function (pdf) for the jump length and the waiting time, but the behavior may change drastically if a medium expansion is superimposed on the intrinsic random motion of the diffusing particle. For the case where the jump length and the waiting time pdfs are long-tailed, we derive a general bifractional diffusion equation which reduces to a normal diffusion equation in the appropriate limit. We then study some particular cases of interest, including Lévy flights and subdiffusive CTRWs. In the former case, we find an analytical exact solution for the Green's function (propagator). When the expansion is sufficiently fast, the contribution of the diffusive transport becomes irrelevant at long times and the propagator tends to a stationary profile in the comoving reference frame. In contrast, for a contracting medium a competition between the spreading effect of diffusion and the concentrating effect of contraction arises. In the specific case of a subdiffusive CTRW in an exponentially contracting medium, the latter effect prevails for sufficiently long times, and all the particles are eventually localized at a single point in physical space. This "big crunch" effect, totally absent in the case of normal diffusion, stems from inefficient particle spreading due to subdiffusion. We also derive a hierarchy of differential equations for the moments of the transport process described by the subdiffusive CTRW model in an expanding medium

FEM for time-fractional diffusion equations, novel optimal error analyses

OpenAIRE

Mustapha, Kassem

2016-01-01

A semidiscrete Galerkin finite element method applied to time-fractional diffusion equations with time-space dependent diffusivity on bounded convex spatial domains will be studied. The main focus is on achieving optimal error results with respect to both the convergence order of the approximate solution and the regularity of the initial data. By using novel energy arguments, for each fixed time $t$, optimal error bounds in the spatial $L^2$- and $H^1$-norms are derived for both cases: smooth...

Simulation of diffusion time of small molecules in protein crystals.

Science.gov (United States)

Geremia, Silvano; Campagnolo, Mara; Demitri, Nicola; Johnson, Louise N

2006-03-01

A simple model for evaluation of diffusion times of small molecule into protein crystals has been developed, which takes into account the physical and chemical properties both of protein crystal and the diffusing molecules. The model also includes consideration of binding and the binding affinity of a ligand to the protein. The model has been validated by simulation of experimental set-ups of several examples found in the literature. These experiments cover a wide range of situations: from small to relatively large diffusing molecules, crystals having low, medium, or high protein density, and different size. The reproduced experiments include ligand exchange in protein crystals by soaking techniques. Despite the simplifying assumptions of the model, theoretical and experimental data are in agreement with available data, with experimental diffusion times ranging from a few seconds to several hours. The method has been used successfully for planning intermediate cryotrapping experiments in maltodextrin phosphorylase crystals.

Electrochemical Impedance Imaging via the Distribution of Diffusion Times

Science.gov (United States)

Song, Juhyun; Bazant, Martin Z.

2018-03-01

We develop a mathematical framework to analyze electrochemical impedance spectra in terms of a distribution of diffusion times (DDT) for a parallel array of random finite-length Warburg (diffusion) or Gerischer (reaction-diffusion) circuit elements. A robust DDT inversion method is presented based on complex nonlinear least squares regression with Tikhonov regularization and illustrated for three cases of nanostructured electrodes for energy conversion: (i) a carbon nanotube supercapacitor, (ii) a silicon nanowire Li-ion battery, and (iii) a porous-carbon vanadium flow battery. The results demonstrate the feasibility of nondestructive "impedance imaging" to infer microstructural statistics of random, heterogeneous materials.

First-Passage-Time Distribution for Variable-Diffusion Processes

Science.gov (United States)

Barney, Liberty; Gunaratne, Gemunu H.

2017-05-01

First-passage-time distribution, which presents the likelihood of a stock reaching a pre-specified price at a given time, is useful in establishing the value of financial instruments and in designing trading strategies. First-passage-time distribution for Wiener processes has a single peak, while that for stocks exhibits a notable second peak within a trading day. This feature has only been discussed sporadically—often dismissed as due to insufficient/incorrect data or circumvented by conversion to tick time—and to the best of our knowledge has not been explained in terms of the underlying stochastic process. It was shown previously that intra-day variations in the market can be modeled by a stochastic process containing two variable-diffusion processes (Hua et al. in, Physica A 419:221-233, 2015). We show here that the first-passage-time distribution of this two-stage variable-diffusion model does exhibit a behavior similar to the empirical observation. In addition, we find that an extended model incorporating overnight price fluctuations exhibits intra- and inter-day behavior similar to those of empirical first-passage-time distributions.

Direct measurement of time dependent diffusion for Ag and Au under ambient conditions

Energy Technology Data Exchange (ETDEWEB)

Yoo, Pil Sun; Jo, Han Yeol; Kim, Tae Kyeong [Hankuk University of Foreign Studies, Yongin (Korea, Republic of)

2014-12-15

Time-dependent diffusion for Ag and Au metal atoms was measured using the scanning tunneling microscope break-junction technique in ambient conditions. We observed that Ag contacts do not form long single-atomic chains compared to Au contacts during the elongation of each metal electrode, and Ag atoms diffuse more quickly than Au atoms after metal contact rupture. This is consistent with previous results of molecular dynamic simulations. Further, we found a correlation between diffusion length and the evolution time on an atomic scale to reveal the time-dependent diffusion for Ag and Au metal atoms.

Thermal fatigue testing of a diffusion-bonded beryllium divertor mock-up under ITER relevant conditions

International Nuclear Information System (INIS)

Youchison, D.L.; Guiniiatouline, R.; Watson, R.D.

1994-01-01

Thermal response and thermal fatigue tests of four 5 mm thick beryllium tiles on a Russian divertor mock-up were completed on the Electron Beam Test System at Sandia National Laboratories. The beryllium tiles were diffusion bonded onto an OFHC copper saddleblock and a DSCu (MAGT) tube containing a porous coating. Thermal response tests were performed on the tiles to an absorbed heat flux of 5 MW/m 2 and surface temperatures near 300 degrees C using 1.4 MPa water at 5.0 m/s flow velocity and an inlet temperature of 8-15 degrees C. One tile was exposed to incrementally increasing heat fluxes up to 9.5 MW/m 2 and surface temperatures up to 690 degrees C before debonding at 10 MW/m 2 . A third tile debonded after 9200 thermal fatigue cycles at 5 MW/m 2 , while another debonded after 6800 cycles. In all cases, fatigue failure occurred in the intermetallic layers between the beryllium and copper. No fatigue cracking of the bulk beryllium was observed. During thermal cycling, a gradual loss of porous coating produced increasing sample temperatures. These experiments indicate that diffusion-bonded beryllium tiles can survive several thousand thermal cycles under ITER relevant conditions without failure. However, the reliability of the diffusion bonded Joint remains a serious issue

The precise time-dependent solution of the Fokker–Planck equation with anomalous diffusion

International Nuclear Information System (INIS)

Guo, Ran; Du, Jiulin

2015-01-01

We study the time behavior of the Fokker–Planck equation in Zwanzig’s rule (the backward-Ito’s rule) based on the Langevin equation of Brownian motion with an anomalous diffusion in a complex medium. The diffusion coefficient is a function in momentum space and follows a generalized fluctuation–dissipation relation. We obtain the precise time-dependent analytical solution of the Fokker–Planck equation and at long time the solution approaches to a stationary power-law distribution in nonextensive statistics. As a test, numerically we have demonstrated the accuracy and validity of the time-dependent solution. - Highlights: • The precise time-dependent solution of the Fokker–Planck equation with anomalous diffusion is found. • The anomalous diffusion satisfies a generalized fluctuation–dissipation relation. • At long time the time-dependent solution approaches to a power-law distribution in nonextensive statistics. • Numerically we have demonstrated the accuracy and validity of the time-dependent solution

The precise time-dependent solution of the Fokker–Planck equation with anomalous diffusion

Energy Technology Data Exchange (ETDEWEB)

Guo, Ran; Du, Jiulin, E-mail: jiulindu@aliyun.com

2015-08-15

We study the time behavior of the Fokker–Planck equation in Zwanzig’s rule (the backward-Ito’s rule) based on the Langevin equation of Brownian motion with an anomalous diffusion in a complex medium. The diffusion coefficient is a function in momentum space and follows a generalized fluctuation–dissipation relation. We obtain the precise time-dependent analytical solution of the Fokker–Planck equation and at long time the solution approaches to a stationary power-law distribution in nonextensive statistics. As a test, numerically we have demonstrated the accuracy and validity of the time-dependent solution. - Highlights: • The precise time-dependent solution of the Fokker–Planck equation with anomalous diffusion is found. • The anomalous diffusion satisfies a generalized fluctuation–dissipation relation. • At long time the time-dependent solution approaches to a power-law distribution in nonextensive statistics. • Numerically we have demonstrated the accuracy and validity of the time-dependent solution.

Real-time MR diffusion tensor and Q-ball imaging using Kalman filtering

International Nuclear Information System (INIS)

Poupon, C.; Roche, A.; Dubois, J.; Mangin, J.F.; Poupon, F.

2008-01-01

Diffusion magnetic resonance imaging (dMRI) has become an established research tool for the investigation of tissue structure and orientation. In this paper, we present a method for real-time processing of diffusion tensor and Q-ball imaging. The basic idea is to use Kalman filtering framework to fit either the linear tensor or Q-ball model. Because the Kalman filter is designed to be an incremental algorithm, it naturally enables updating the model estimate after the acquisition of any new diffusion-weighted volume. Processing diffusion models and maps during ongoing scans provides a new useful tool for clinicians, especially when it is not possible to predict how long a subject may remain still in the magnet. First, we introduce the general linear models corresponding to the two diffusion tensor and analytical Q-ball models of interest. Then, we present the Kalman filtering framework and we focus on the optimization of the diffusion orientation sets in order to speed up the convergence of the online processing. Last, we give some results on a healthy volunteer for the online tensor and the Q-ball model, and we make some comparisons with the conventional offline techniques used in the literature. We could achieve full real-time for diffusion tensor imaging and deferred time for Q-ball imaging, using a single workstation. (authors)

Modeling and experiments for the time-dependent diffusion coefficient during methane desorption from coal

Science.gov (United States)

Cheng-Wu, Li; Hong-Lai, Xue; Cheng, Guan; Wen-biao, Liu

2018-04-01

Statistical analysis shows that in the coal matrix, the diffusion coefficient for methane is time-varying, and its integral satisfies the formula μt κ /(1 + β κ ). Therefore, a so-called dynamic diffusion coefficient model (DDC model) is developed. To verify the suitability and accuracy of the DDC model, a series of gas diffusion experiments were conducted using coal particles of different sizes. The results show that the experimental data can be accurately described by the DDC and bidisperse models, but the fit to the DDC model is slightly better. For all coal samples, as time increases, the effective diffusion coefficient first shows a sudden drop, followed by a gradual decrease before stabilizing at longer times. The effective diffusion coefficient has a negative relationship with the size of the coal particle. Finally, the relationship between the constants of the DDC model and the effective diffusion coefficient is discussed. The constant α (μ/R 2 ) denotes the effective coefficient at the initial time, and the constants κ and β control the attenuation characteristic of the effective diffusion coefficient.

Preoperative diffusion-weighted imaging of single brain metastases correlates with patient survival times.

Directory of Open Access Journals (Sweden)

Anna Sophie Berghoff

Full Text Available BACKGROUND: MRI-based diffusion-weighted imaging (DWI visualizes the local differences in water diffusion in vivo. The prognostic value of DWI signal intensities on the source images and apparent diffusion coefficient (ADC maps respectively has not yet been studied in brain metastases (BM. METHODS: We included into this retrospective analysis all patients operated for single BM at our institution between 2002 and 2010, in whom presurgical DWI and BM tissue samples were available. We recorded relevant clinical data, assessed DWI signal intensity and apparent diffusion coefficient (ADC values and performed histopathological analysis of BM tissues. Statistical analyses including uni- and multivariate survival analyses were performed. RESULTS: 65 patients (34 female, 31 male with a median overall survival time (OS of 15 months (range 0-99 months were available for this study. 19 (29.2% patients presented with hyper-, 3 (4.6% with iso-, and 43 (66.2% with hypointense DWI. ADCmean values could be determined in 32 (49.2% patients, ranged from 456.4 to 1691.8*10⁻⁶ mm²/s (median 969.5 and showed a highly significant correlation with DWI signal intensity. DWI hyperintensity correlated significantly with high amount of interstitial reticulin deposition. In univariate analysis, patients with hyperintense DWI (5 months and low ADCmean values (7 months had significantly worse OS than patients with iso/hypointense DWI (16 months and high ADCmean values (30 months, respectively. In multivariate survival analysis, high ADCmean values retained independent statistical significance. CONCLUSIONS: Preoperative DWI findings strongly and independently correlate with OS in patients operated for single BM and are related to interstitial fibrosis. Inclusion of DWI parameters into established risk stratification scores for BM patients should be considered.

TaDb: A time-aware diffusion-based recommender algorithm

Science.gov (United States)

Li, Wen-Jun; Xu, Yuan-Yuan; Dong, Qiang; Zhou, Jun-Lin; Fu, Yan

2015-02-01

Traditional recommender algorithms usually employ the early and recent records indiscriminately, which overlooks the change of user interests over time. In this paper, we show that the interests of a user remain stable in a short-term interval and drift during a long-term period. Based on this observation, we propose a time-aware diffusion-based (TaDb) recommender algorithm, which assigns different temporal weights to the leading links existing before the target user's collection and the following links appearing after that in the diffusion process. Experiments on four real datasets, Netflix, MovieLens, FriendFeed and Delicious show that TaDb algorithm significantly improves the prediction accuracy compared with the algorithms not considering temporal effects.

Space-Time Fractional Diffusion-Advection Equation with Caputo Derivative

Directory of Open Access Journals (Sweden)

José Francisco Gómez Aguilar

2014-01-01

Full Text Available An alternative construction for the space-time fractional diffusion-advection equation for the sedimentation phenomena is presented. The order of the derivative is considered as 0<β, γ≤1 for the space and time domain, respectively. The fractional derivative of Caputo type is considered. In the spatial case we obtain the fractional solution for the underdamped, undamped, and overdamped case. In the temporal case we show that the concentration has amplitude which exhibits an algebraic decay at asymptotically large times and also shows numerical simulations where both derivatives are taken in simultaneous form. In order that the equation preserves the physical units of the system two auxiliary parameters σx and σt are introduced characterizing the existence of fractional space and time components, respectively. A physical relation between these parameters is reported and the solutions in space-time are given in terms of the Mittag-Leffler function depending on the parameters β and γ. The generalization of the fractional diffusion-advection equation in space-time exhibits anomalous behavior.

Impact of time-of-day on diffusivity measures of brain tissue derived from diffusion tensor imaging.

Science.gov (United States)

Thomas, Cibu; Sadeghi, Neda; Nayak, Amrita; Trefler, Aaron; Sarlls, Joelle; Baker, Chris I; Pierpaoli, Carlo

2018-06-01

Diurnal fluctuations in MRI measures of structural and functional properties of the brain have been reported recently. These fluctuations may have a physiological origin, since they have been detected using different MRI modalities, and cannot be explained by factors that are typically known to confound MRI measures. While preliminary evidence suggests that measures of structural properties of the brain based on diffusion tensor imaging (DTI) fluctuate as a function of time-of-day (TOD), the underlying mechanism has not been investigated. Here, we used a longitudinal within-subjects design to investigate the impact of time-of-day on DTI measures. In addition to using the conventional monoexponential tensor model to assess TOD-related fluctuations, we used a dual compartment tensor model that allowed us to directly assess if any change in DTI measures is due to an increase in CSF/free-water volume fraction or due to an increase in water diffusivity within the parenchyma. Our results show that Trace or mean diffusivity, as measured using the conventional monoexponential tensor model tends to increase systematically from morning to afternoon scans at the interface of grey matter/CSF, most prominently in the major fissures and the sulci of the brain. Interestingly, in a recent study of the glymphatic system, these same regions were found to show late enhancement after intrathecal injection of a CSF contrast agent. The increase in Trace also impacts DTI measures of diffusivity such as radial and axial diffusivity, but does not affect fractional anisotropy. The dual compartment analysis revealed that the increase in diffusivity measures from PM to AM was driven by an increase in the volume fraction of CSF-like free-water. Taken together, our findings provide important insight into the likely physiological origins of diurnal fluctuations in MRI measurements of structural properties of the brain. Published by Elsevier Inc.

Choice of reference measurements affects quantification of long diffusion time behaviour using stimulated echoes.

Science.gov (United States)

Kleinnijenhuis, Michiel; Mollink, Jeroen; Lam, Wilfred W; Kinchesh, Paul; Khrapitchev, Alexandre A; Smart, Sean C; Jbabdi, Saad; Miller, Karla L

2018-02-01

To demonstrate how reference data affect the quantification of the apparent diffusion coefficient (ADC) in long diffusion time measurements with diffusion-weighted stimulated echo acquisition mode (DW-STEAM) measurements, and to present a modification to avoid contribution from crusher gradients in DW-STEAM. For DW-STEAM, reference measurements at long diffusion times have significant b 0 value, because b = 0 cannot be achieved in practice as a result of the need for signal spoiling. Two strategies for acquiring reference data over a range of diffusion times were considered: constant diffusion weighting (fixed-b 0 ) and constant gradient area (fixed-q 0 ). Fixed-b 0 and fixed-q 0 were compared using signal calculations for systems with one and two diffusion coefficients, and experimentally using data from postmortem human corpus callosum samples. Calculations of biexponential diffusion decay show that the ADC is underestimated for reference images with b > 0, which can induce an apparent time-dependence for fixed-q 0 . Restricted systems were also found to be affected. Experimentally, the exaggeration of the diffusion time-dependent effect under fixed-q 0 versus fixed-b 0 was in a range predicted theoretically, accounting for 62% (longitudinal) and 35% (radial) of the time dependence observed in white matter. Variation in the b-value of reference measurements in DW-STEAM can induce artificial diffusion time dependence in ADC, even in the absence of restriction. Magn Reson Med 79:952-959, 2018. © 2017 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. © 2017 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of

Assessment of perceptual diffuseness in the time domain

DEFF Research Database (Denmark)

Garcia, Julian Martinez-Villalba; Jeong, Cheol-Ho; Brunskog, Jonas

2017-01-01

This study proposes a numerical and experimental framework for evaluating the perceptual aspect of the diffuse field condition with intended final use in music auditoria. Multiple Impulse Responses are simulated based on the time domain Poisson process with increasing reflection density. Different...

Mix and Inject: Reaction Initiation by Diffusion for Time-Resolved Macromolecular Crystallography

Directory of Open Access Journals (Sweden)

Marius Schmidt

2013-01-01

Full Text Available Time-resolved macromolecular crystallography unifies structure determination with chemical kinetics, since the structures of transient states and chemical and kinetic mechanisms can be determined simultaneously from the same data. To start a reaction in an enzyme, typically, an initially inactive substrate present in the crystal is activated. This has particular disadvantages that are circumvented when active substrate is directly provided by diffusion. However, then it is prohibitive to use macroscopic crystals because diffusion times become too long. With small micro- and nanocrystals diffusion times are adequately short for most enzymes and the reaction can be swiftly initiated. We demonstrate here that a time-resolved crystallographic experiment becomes feasible by mixing substrate with enzyme nanocrystals which are subsequently injected into the X-ray beam of a pulsed X-ray source.

Assessing the scientific relevance of a single publication over time

Directory of Open Access Journals (Sweden)

Philipp A. Bloching

2013-09-01

Full Text Available Quantitatively assessing the scientific relevance of a research paper is challenging for two reasons. Firstly, scientific relevance may change over time, and secondly, it is unclear how to evaluate a recently published paper. The temporally averaged paper-specific impact factor is defined as the yearly average of citations to the paper until now including bonus citations equal to the journal impact factor in the publication year. This new measure subsequently allows relevance rankings and annual updates of all (i.e. both recent and older scientific papers of a department, or even a whole scientific field, on a more objective basis. It can also be used to assess both the average and overall time-dependent scientific relevance of researchers in a specific department or scientific field.

NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION

OpenAIRE

Liu, F.; Meerschaert, M.M.; McGough, R.J.; Zhuang, P.; Liu, Q.

2013-01-01

In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and technique...

Motoneuron membrane potentials follow a time inhomogeneous jump diffusion process

DEFF Research Database (Denmark)

Jahn, Patrick; Berg, Rune W; Hounsgaard, Jørn

2011-01-01

models can only be applied over short time windows. However, experimental data show varying time constants, state dependent noise, a graded firing threshold and time-inhomogeneous input. In the present study we build a jump diffusion model that incorporates these features, and introduce a firing...

NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION.

Science.gov (United States)

Liu, F; Meerschaert, M M; McGough, R J; Zhuang, P; Liu, Q

2013-03-01

In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.

Diffuse charge dynamics in ionic thermoelectrochemical systems.

Science.gov (United States)

Stout, Robert F; Khair, Aditya S

2017-08-01

Thermoelectrics are increasingly being studied as promising electrical generators in the ongoing search for alternative energy sources. In particular, recent experimental work has examined thermoelectric materials containing ionic charge carriers; however, the majority of mathematical modeling has been focused on their steady-state behavior. Here, we determine the time scales over which the diffuse charge dynamics in ionic thermoelectrochemical systems occur by analyzing the simplest model thermoelectric cell: a binary electrolyte between two parallel, blocking electrodes. We consider the application of a temperature gradient across the device while the electrodes remain electrically isolated from each other. This results in a net voltage, called the thermovoltage, via the Seebeck effect. At the same time, the Soret effect results in migration of the ions toward the cold electrode. The charge dynamics are described mathematically by the Poisson-Nernst-Planck equations for dilute solutions, in which the ion flux is driven by electromigration, Brownian diffusion, and thermal diffusion under a temperature gradient. The temperature evolves according to the heat equation. This nonlinear set of equations is linearized in the (experimentally relevant) limit of a "weak" temperature gradient. From this, we show that the time scale on which the thermovoltage develops is the Debye time, 1/Dκ^{2}, where D is the Brownian diffusion coefficient of both ion species, and κ^{-1} is the Debye length. However, the concentration gradient due to the Soret effect develops on the bulk diffusion time, L^{2}/D, where L is the distance between the electrodes. For thin diffuse layers, which is the condition under which most real devices operate, the Debye time is orders of magnitude less than the diffusion time. Therefore, rather surprisingly, the majority of ion motion occurs after the steady thermovoltage has developed. Moreover, the dynamics are independent of the thermal diffusion

Diffuse charge dynamics in ionic thermoelectrochemical systems

Science.gov (United States)

Stout, Robert F.; Khair, Aditya S.

2017-08-01

Thermoelectrics are increasingly being studied as promising electrical generators in the ongoing search for alternative energy sources. In particular, recent experimental work has examined thermoelectric materials containing ionic charge carriers; however, the majority of mathematical modeling has been focused on their steady-state behavior. Here, we determine the time scales over which the diffuse charge dynamics in ionic thermoelectrochemical systems occur by analyzing the simplest model thermoelectric cell: a binary electrolyte between two parallel, blocking electrodes. We consider the application of a temperature gradient across the device while the electrodes remain electrically isolated from each other. This results in a net voltage, called the thermovoltage, via the Seebeck effect. At the same time, the Soret effect results in migration of the ions toward the cold electrode. The charge dynamics are described mathematically by the Poisson-Nernst-Planck equations for dilute solutions, in which the ion flux is driven by electromigration, Brownian diffusion, and thermal diffusion under a temperature gradient. The temperature evolves according to the heat equation. This nonlinear set of equations is linearized in the (experimentally relevant) limit of a "weak" temperature gradient. From this, we show that the time scale on which the thermovoltage develops is the Debye time, 1 /D κ2 , where D is the Brownian diffusion coefficient of both ion species, and κ-1 is the Debye length. However, the concentration gradient due to the Soret effect develops on the bulk diffusion time, L2/D , where L is the distance between the electrodes. For thin diffuse layers, which is the condition under which most real devices operate, the Debye time is orders of magnitude less than the diffusion time. Therefore, rather surprisingly, the majority of ion motion occurs after the steady thermovoltage has developed. Moreover, the dynamics are independent of the thermal diffusion

Diffusion of epicenters of earthquake aftershocks, Omori's law, and generalized continuous-time random walk models

International Nuclear Information System (INIS)

Helmstetter, A.; Sornette, D.

2002-01-01

The epidemic-type aftershock sequence (ETAS) model is a simple stochastic process modeling seismicity, based on the two best-established empirical laws, the Omori law (power-law decay ∼1/t 1+θ of seismicity after an earthquake) and Gutenberg-Richter law (power-law distribution of earthquake energies). In order to describe also the space distribution of seismicity, we use in addition a power-law distribution ∼1/r 1+μ of distances between triggered and triggering earthquakes. The ETAS model has been studied for the last two decades to model real seismicity catalogs and to obtain short-term probabilistic forecasts. Here, we present a mapping between the ETAS model and a class of CTRW (continuous time random walk) models, based on the identification of their corresponding master equations. This mapping allows us to use the wealth of results previously obtained on anomalous diffusion of CTRW. After translating into the relevant variable for the ETAS model, we provide a classification of the different regimes of diffusion of seismic activity triggered by a mainshock. Specifically, we derive the relation between the average distance between aftershocks and the mainshock as a function of the time from the mainshock and of the joint probability distribution of the times and locations of the aftershocks. The different regimes are fully characterized by the two exponents θ and μ. Our predictions are checked by careful numerical simulations. We stress the distinction between the 'bare' Omori law describing the seismic rate activated directly by a mainshock and the 'renormalized' Omori law taking into account all possible cascades from mainshocks to aftershocks of aftershock of aftershock, and so on. In particular, we predict that seismic diffusion or subdiffusion occurs and should be observable only when the observed Omori exponent is less than 1, because this signals the operation of the renormalization of the bare Omori law, also at the origin of seismic diffusion in

Communication: Distinguishing between short-time non-Fickian diffusion and long-time Fickian diffusion for a random walk on a crowded lattice

Energy Technology Data Exchange (ETDEWEB)

Ellery, Adam J.; Simpson, Matthew J. [School of Mathematical Sciences, Queensland University of Technology (QUT), Brisbane (Australia); Baker, Ruth E. [Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford (United Kingdom)

2016-05-07

The motion of cells and molecules through biological environments is often hindered by the presence of other cells and molecules. A common approach to modeling this kind of hindered transport is to examine the mean squared displacement (MSD) of a motile tracer particle in a lattice-based stochastic random walk in which some lattice sites are occupied by obstacles. Unfortunately, stochastic models can be computationally expensive to analyze because we must average over a large ensemble of identically prepared realizations to obtain meaningful results. To overcome this limitation we describe an exact method for analyzing a lattice-based model of the motion of an agent moving through a crowded environment. Using our approach we calculate the exact MSD of the motile agent. Our analysis confirms the existence of a transition period where, at first, the MSD does not follow a power law with time. However, after a sufficiently long period of time, the MSD increases in proportion to time. This latter phase corresponds to Fickian diffusion with a reduced diffusivity owing to the presence of the obstacles. Our main result is to provide a mathematically motivated, reproducible, and objective estimate of the amount of time required for the transport to become Fickian. Our new method to calculate this crossover time does not rely on stochastic simulations.

Communication: Distinguishing between short-time non-Fickian diffusion and long-time Fickian diffusion for a random walk on a crowded lattice

International Nuclear Information System (INIS)

Ellery, Adam J.; Simpson, Matthew J.; Baker, Ruth E.

2016-01-01

The motion of cells and molecules through biological environments is often hindered by the presence of other cells and molecules. A common approach to modeling this kind of hindered transport is to examine the mean squared displacement (MSD) of a motile tracer particle in a lattice-based stochastic random walk in which some lattice sites are occupied by obstacles. Unfortunately, stochastic models can be computationally expensive to analyze because we must average over a large ensemble of identically prepared realizations to obtain meaningful results. To overcome this limitation we describe an exact method for analyzing a lattice-based model of the motion of an agent moving through a crowded environment. Using our approach we calculate the exact MSD of the motile agent. Our analysis confirms the existence of a transition period where, at first, the MSD does not follow a power law with time. However, after a sufficiently long period of time, the MSD increases in proportion to time. This latter phase corresponds to Fickian diffusion with a reduced diffusivity owing to the presence of the obstacles. Our main result is to provide a mathematically motivated, reproducible, and objective estimate of the amount of time required for the transport to become Fickian. Our new method to calculate this crossover time does not rely on stochastic simulations.

Nonlinear diffusion in the presence of a time-dependent external electric field

International Nuclear Information System (INIS)

Lima e Silva, T. de; Galvao, R.M.O.

1987-09-01

The influence of a time-dependent external electric field on the nonlinear diffusion process of weakly ionized plasmas is investigated. A new solution of the diffusion equation is obtained for the case when electron-ion collisions can be neglected. (author) [pt

Accelerating proton spin diffusion in perdeuterated proteins at 100 kHz MAS

Energy Technology Data Exchange (ETDEWEB)

Wittmann, Johannes J.; Agarwal, Vipin; Hellwagner, Johannes; Lends, Alons; Cadalbert, Riccardo; Meier, Beat H., E-mail: beme@ethz.ch; Ernst, Matthias, E-mail: maer@ethz.ch [ETH Zurich, Physical Chemistry (Switzerland)

2016-12-15

Fast magic-angle spinning (>60 kHz) has many advantages but makes spin-diffusion-type proton–proton long-range polarization transfer inefficient and highly dependent on chemical-shift offset. Using 100%-HN-[{sup 2}H,{sup 13}C,{sup 15}N]-ubiquitin as a model substance, we quantify the influence of the chemical-shift difference on the spin diffusion between proton spins and compare two experiments which lead to an improved chemical-shift compensation of the transfer: rotating-frame spin diffusion and a new experiment, reverse amplitude-modulated MIRROR. Both approaches enable broadband spin diffusion, but the application of the first variant is limited due to fast spin relaxation in the rotating frame. The reverse MIRROR experiment, in contrast, is a promising candidate for the determination of structurally relevant distance restraints. The applied tailored rf-irradiation schemes allow full control over the range of recoupled chemical shifts and efficiently drive spin diffusion. Here, the relevant relaxation time is the larger longitudinal relaxation time, which leads to a higher signal-to-noise ratio in the spectra.

Asymptotic equilibrium diffusion analysis of time-dependent Monte Carlo methods for grey radiative transfer

International Nuclear Information System (INIS)

Densmore, Jeffery D.; Larsen, Edward W.

2004-01-01

The equations of nonlinear, time-dependent radiative transfer are known to yield the equilibrium diffusion equation as the leading-order solution of an asymptotic analysis when the mean-free path and mean-free time of a photon become small. We apply this same analysis to the Fleck-Cummings, Carter-Forest, and N'kaoua Monte Carlo approximations for grey (frequency-independent) radiative transfer. Although Monte Carlo simulation usually does not require the discretizations found in deterministic transport techniques, Monte Carlo methods for radiative transfer require a time discretization due to the nonlinearities of the problem. If an asymptotic analysis of the equations used by a particular Monte Carlo method yields an accurate time-discretized version of the equilibrium diffusion equation, the method should generate accurate solutions if a time discretization is chosen that resolves temperature changes, even if the time steps are much larger than the mean-free time of a photon. This analysis is of interest because in many radiative transfer problems, it is a practical necessity to use time steps that are large compared to a mean-free time. Our asymptotic analysis shows that: (i) the N'kaoua method has the equilibrium diffusion limit, (ii) the Carter-Forest method has the equilibrium diffusion limit if the material temperature change during a time step is small, and (iii) the Fleck-Cummings method does not have the equilibrium diffusion limit. We include numerical results that verify our theoretical predictions

Existence and Stability of Traveling Waves for Degenerate Reaction-Diffusion Equation with Time Delay

Science.gov (United States)

Huang, Rui; Jin, Chunhua; Mei, Ming; Yin, Jingxue

2018-01-01

This paper deals with the existence and stability of traveling wave solutions for a degenerate reaction-diffusion equation with time delay. The degeneracy of spatial diffusion together with the effect of time delay causes us the essential difficulty for the existence of the traveling waves and their stabilities. In order to treat this case, we first show the existence of smooth- and sharp-type traveling wave solutions in the case of c≥c^* for the degenerate reaction-diffusion equation without delay, where c^*>0 is the critical wave speed of smooth traveling waves. Then, as a small perturbation, we obtain the existence of the smooth non-critical traveling waves for the degenerate diffusion equation with small time delay τ >0 . Furthermore, we prove the global existence and uniqueness of C^{α ,β } -solution to the time-delayed degenerate reaction-diffusion equation via compactness analysis. Finally, by the weighted energy method, we prove that the smooth non-critical traveling wave is globally stable in the weighted L^1 -space. The exponential convergence rate is also derived.

Existence and Stability of Traveling Waves for Degenerate Reaction-Diffusion Equation with Time Delay

Science.gov (United States)

Huang, Rui; Jin, Chunhua; Mei, Ming; Yin, Jingxue

2018-06-01

This paper deals with the existence and stability of traveling wave solutions for a degenerate reaction-diffusion equation with time delay. The degeneracy of spatial diffusion together with the effect of time delay causes us the essential difficulty for the existence of the traveling waves and their stabilities. In order to treat this case, we first show the existence of smooth- and sharp-type traveling wave solutions in the case of c≥c^* for the degenerate reaction-diffusion equation without delay, where c^*>0 is the critical wave speed of smooth traveling waves. Then, as a small perturbation, we obtain the existence of the smooth non-critical traveling waves for the degenerate diffusion equation with small time delay τ >0. Furthermore, we prove the global existence and uniqueness of C^{α ,β }-solution to the time-delayed degenerate reaction-diffusion equation via compactness analysis. Finally, by the weighted energy method, we prove that the smooth non-critical traveling wave is globally stable in the weighted L^1-space. The exponential convergence rate is also derived.

Time step size selection for radiation diffusion calculations

International Nuclear Information System (INIS)

Rider, W.J.; Knoll, D.A.

1999-01-01

The purpose of this note is to describe a time step control technique as applied to radiation diffusion. Standard practice only provides a heuristic criteria related to the relative change in the dependent variables. The authors propose an alternative based on relatively simple physical principles. This time step control applies to methods of solution that are unconditionally stable and converges nonlinearities within a time step in the governing equations. Commonly, nonlinearities in the governing equations are evaluated using existing (old time) data. The authors refer to this as the semi-implicit (SI) method. When a method converges nonlinearities within a time step, the entire governing equation including all nonlinearities is self-consistently evaluated using advance time data (with appropriate time centering for accuracy)

Semianalytic Solution of Space-Time Fractional Diffusion Equation

Directory of Open Access Journals (Sweden)

A. Elsaid

2016-01-01

Full Text Available We study the space-time fractional diffusion equation with spatial Riesz-Feller fractional derivative and Caputo fractional time derivative. The continuation of the solution of this fractional equation to the solution of the corresponding integer order equation is proved. The series solution of this problem is obtained via the optimal homotopy analysis method (OHAM. Numerical simulations are presented to validate the method and to show the effect of changing the fractional derivative parameters on the solution behavior.

Linking the Diffusion of Water in Compacted Clays at Two Different Time Scales: Tracer Through-Diffusion and QENS

International Nuclear Information System (INIS)

Juranyi, Fanni; Gonzalez Sanchez, Fatima; Gimmi, Thomas; Bestel, Martina; Van Loon, Luc; Diamond, Larryn W.

2013-01-01

Observable water diffusion processes in clays and their parameters depend on the spatial- and time-scale of the measurement. Comparing the diffusion coefficients of quasielastic neutron scattering and tracer through-diffusion, 'chemical' and 'geometrical' effects can be distinguished and quantified. Results for montmorillonite and illite in the Na- and Ca- form illustrate this very well. Swelling clays such as montmorillonite are especially interesting because of the interlayer water. This water is confined in form of few layers such that the diffusion occurs essentially in 2D. Furthermore the ratio of interlayer- and external- (macro-pore) water changes as a function of bulk dry density and degree of water saturation. Therefore it is of interest to describe the diffusion process using these parameters. Finally, the activation energy of the diffusion should be equal for both methods assuming that the geometrical factor does not depend on temperature. For the montmorillonites this was not the case, which might also indicate that the main processes on the two scales are different. We conclude that the geometrical factor and the electrostatic constraint can be determined from a comparison of the diffusion coefficients measured by the two different techniques: quasielastic neutron scattering and tracer through diffusion. Furthermore, activation energies obtained at the two scales are similar for clays having no interlayer water. For montmorillonite the activation energy values are different. Further investigations are required to clarify the reason. (authors)

Magnetic field line diffusion at the onset of stochasticity

International Nuclear Information System (INIS)

Elsaesser, K.; Deeskow, P.

1987-01-01

The Hamiltonian equations of a particle in a random set of waves just above the stochasticity threshold are considered both theoretically and numerically. First we derive the diffusion coefficient and the autocorrelation time perturbatively without using the thermodynamic limit, and we discuss the relevance of the Hamiltonian problem for particle acceleration and magnetic field line flow. Then we integrate the equations for an ensemble of magnetic field lines numerically for a model problem and show the time evolution of moments and correlations. Twice above the threshold we observe diffusive behaviour from the beginning, but the diffusion coefficient includes also the non-resonant modes. Just at threshold we find first a short phase of free acceleration, later a diffusion which is lower than predicted by the theoretical formula. The best way to analyze the problem is in terms of cumulants, but a reliable comparison with any theory requires also a time integration of the corresponding kinetic equations. (orig.)

Putting atomic diffusion theory of magnetic ApBp stars to the test: evaluation of the predictions of time-dependent diffusion models

Science.gov (United States)

Kochukhov, O.; Ryabchikova, T. A.

2018-02-01

A series of recent theoretical atomic diffusion studies has address the challenging problem of predicting inhomogeneous vertical and horizontal chemical element distributions in the atmospheres of magnetic ApBp stars. Here we critically assess the most sophisticated of such diffusion models - based on a time-dependent treatment of the atomic diffusion in a magnetized stellar atmosphere - by direct comparison with observations as well by testing the widely used surface mapping tools with the spectral line profiles predicted by this theory. We show that the mean abundances of Fe and Cr are grossly underestimated by the time-dependent theoretical diffusion model, with discrepancies reaching a factor of 1000 for Cr. We also demonstrate that Doppler imaging inversion codes, based either on modelling of individual metal lines or line-averaged profiles simulated according to theoretical three-dimensional abundance distribution, are able to reconstruct correct horizontal chemical spot maps despite ignoring the vertical abundance variation. These numerical experiments justify a direct comparison of the empirical two-dimensional Doppler maps with theoretical diffusion calculations. This comparison is generally unfavourable for the current diffusion theory, as very few chemical elements are observed to form overabundance rings in the horizontal field regions as predicted by the theory and there are numerous examples of element accumulations in the vicinity of radial field zones, which cannot be explained by diffusion calculations.

Partial synchronization in diffusively time-delay coupled oscillator networks

NARCIS (Netherlands)

Steur, E.; Oguchi, T.; Leeuwen, van C.; Nijmeijer, H.

2012-01-01

We study networks of diffusively time-delay coupled oscillatory units and we show that networks with certain symmetries can exhibit a form of incomplete synchronization called partial synchronization. We present conditions for the existence and stability of partial synchronization modes in networks

Innovation diffusion on time-varying activity driven networks

Science.gov (United States)

Rizzo, Alessandro; Porfiri, Maurizio

2016-01-01

Since its introduction in the 1960s, the theory of innovation diffusion has contributed to the advancement of several research fields, such as marketing management and consumer behavior. The 1969 seminal paper by Bass [F.M. Bass, Manag. Sci. 15, 215 (1969)] introduced a model of product growth for consumer durables, which has been extensively used to predict innovation diffusion across a range of applications. Here, we propose a novel approach to study innovation diffusion, where interactions among individuals are mediated by the dynamics of a time-varying network. Our approach is based on the Bass' model, and overcomes key limitations of previous studies, which assumed timescale separation between the individual dynamics and the evolution of the connectivity patterns. Thus, we do not hypothesize homogeneous mixing among individuals or the existence of a fixed interaction network. We formulate our approach in the framework of activity driven networks to enable the analysis of the concurrent evolution of the interaction and individual dynamics. Numerical simulations offer a systematic analysis of the model behavior and highlight the role of individual activity on market penetration when targeted advertisement campaigns are designed, or a competition between two different products takes place.

Large Deviations for Two-Time-Scale Diffusions, with Delays

International Nuclear Information System (INIS)

Kushner, Harold J.

2010-01-01

We consider the problem of large deviations for a two-time-scale reflected diffusion process, possibly with delays in the dynamical terms. The Dupuis-Ellis weak convergence approach is used. It is perhaps the most intuitive and simplest for the problems of concern. The results have applications to the problem of approximating optimal controls for two-time-scale systems via use of the averaged equation.

Moving-boundary problems for the time-fractional diffusion equation

Directory of Open Access Journals (Sweden)

Sabrina D. Roscani

2017-02-01

Full Text Available We consider a one-dimensional moving-boundary problem for the time-fractional diffusion equation. The time-fractional derivative of order $\\alpha\\in (0,1$ is taken in the sense of Caputo. We study the asymptotic behaivor, as t tends to infinity, of a general solution by using a fractional weak maximum principle. Also, we give some particular exact solutions in terms of Wright functions.

Finite element approximation for time-dependent diffusion with measure-valued source

Czech Academy of Sciences Publication Activity Database

Seidman, T.; Gobbert, M.; Trott, D.; Kružík, Martin

2012-01-01

Roč. 122, č. 4 (2012), s. 709-723 ISSN 0029-599X R&D Projects: GA AV ČR IAA100750802 Institutional support: RVO:67985556 Keywords : measure-valued source * diffusion equation Subject RIV: BA - General Mathematics Impact factor: 1.329, year: 2012 http://library.utia.cas.cz/separaty/2012/MTR/kruzik-finite element approximation for time - dependent diffusion with measure-valued source.pdf

Aggressive time step selection for the time asymptotic velocity diffusion problem

International Nuclear Information System (INIS)

Hewett, D.W.; Krapchev, V.B.; Hizanidis, K.; Bers, A.

1984-12-01

An aggressive time step selector for an ADI algorithm is preseneted that is applied to the linearized 2-D Fokker-Planck equation including an externally imposed quasilinear diffusion term. This method provides a reduction in CPU requirements by factors of two or three compared to standard ADI. More important, the robustness of the procedure greatly reduces the work load of the user. The procedure selects a nearly optimal Δt with a minimum of intervention by the user thus relieving the need to supervise the algorithm. In effect, the algorithm does its own supervision by discarding time steps made with Δt too large

Slab-diffusion approximation from time-constant-like calculations

International Nuclear Information System (INIS)

Johnson, R.W.

1976-12-01

Two equations were derived which describe the quantity and any fluid diffused from a slab as a function of time. One equation is applicable to the initial stage of the process; the other to the final stage. Accuracy is 0.2 percent at the one point where both approximations apply and where accuracy of either approximation is the poorest. Characterizing other rate processes might be facilitated by the use of the concept of NOLOR (normal of the logarithm of the rate) and its time dependence

Stochastic interpretation of the advection-diffusion equation and its relevance to bed load transport

Science.gov (United States)

Ancey, C.; Bohorquez, P.; Heyman, J.

2015-12-01

The advection-diffusion equation is one of the most widespread equations in physics. It arises quite often in the context of sediment transport, e.g., for describing time and space variations in the particle activity (the solid volume of particles in motion per unit streambed area). Phenomenological laws are usually sufficient to derive this equation and interpret its terms. Stochastic models can also be used to derive it, with the significant advantage that they provide information on the statistical properties of particle activity. These models are quite useful when sediment transport exhibits large fluctuations (typically at low transport rates), making the measurement of mean values difficult. Among these stochastic models, the most common approach consists of random walk models. For instance, they have been used to model the random displacement of tracers in rivers. Here we explore an alternative approach, which involves monitoring the evolution of the number of particles moving within an array of cells of finite length. Birth-death Markov processes are well suited to this objective. While the topic has been explored in detail for diffusion-reaction systems, the treatment of advection has received no attention. We therefore look into the possibility of deriving the advection-diffusion equation (with a source term) within the framework of birth-death Markov processes. We show that in the continuum limit (when the cell size becomes vanishingly small), we can derive an advection-diffusion equation for particle activity. Yet while this derivation is formally valid in the continuum limit, it runs into difficulty in practical applications involving cells or meshes of finite length. Indeed, within our stochastic framework, particle advection produces nonlocal effects, which are more or less significant depending on the cell size and particle velocity. Albeit nonlocal, these effects look like (local) diffusion and add to the intrinsic particle diffusion (dispersal due

Efficient Estimation for Diffusions Sampled at High Frequency Over a Fixed Time Interval

DEFF Research Database (Denmark)

Jakobsen, Nina Munkholt; Sørensen, Michael

Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find easily verified conditions on approximate martingale...

Effects of time-dependent diffusion behaviors on the rumor spreading in social networks

Energy Technology Data Exchange (ETDEWEB)

Qiu, Xiaoyan [School of Management, Shanghai University, Shanghai 200444 (China); Zhao, Laijun, E-mail: ljzhao70@sjtu.edu.cn [Sino–US Global Logistics Institute, Shanghai Jiao Tong University, Shanghai 200030 (China); Antai College of Economics and Management, Shanghai Jiao Tong University, Shanghai 200052 (China); Wang, Jiajia [Sino–US Global Logistics Institute, Shanghai Jiao Tong University, Shanghai 200030 (China); Antai College of Economics and Management, Shanghai Jiao Tong University, Shanghai 200052 (China); Wang, Xiaoli [School of Management, Shanghai University of Engineering Science, Shanghai 201620 (China); Wang, Qin [College of Transport & Communications, Shanghai Maritime University, Shanghai 201306 (China)

2016-05-27

When considering roles of realistic external forces (e.g. authorities) and internal forces (e.g. the forgetting nature of human), diffusion behaviors like spreading, stifling and forgetting behaviors are time-dependent. They were incorporated in an SIR-like rumor spreading model to investigate the effects to rumor spreading dynamics. Mean-field equations were derived, and the steady state analysis was conducted. Simulations were carried out on different complex networks. We demonstrated that the combination of the three variable diffusion behaviors provides a faster and larger spreading expansion capacity. Network structure matters considerably in rumor spreading dynamics. - Highlights: • We incorporate time-dependent diffusion behaviors into a SIR-like rumor spreading model. • The combination of the three variable diffusion behaviors provides a faster and larger spreading expansion capacity. • Network structure matters considerably in rumor spreading dynamics.

Effects of time-dependent diffusion behaviors on the rumor spreading in social networks

International Nuclear Information System (INIS)

Qiu, Xiaoyan; Zhao, Laijun; Wang, Jiajia; Wang, Xiaoli; Wang, Qin

2016-01-01

When considering roles of realistic external forces (e.g. authorities) and internal forces (e.g. the forgetting nature of human), diffusion behaviors like spreading, stifling and forgetting behaviors are time-dependent. They were incorporated in an SIR-like rumor spreading model to investigate the effects to rumor spreading dynamics. Mean-field equations were derived, and the steady state analysis was conducted. Simulations were carried out on different complex networks. We demonstrated that the combination of the three variable diffusion behaviors provides a faster and larger spreading expansion capacity. Network structure matters considerably in rumor spreading dynamics. - Highlights: • We incorporate time-dependent diffusion behaviors into a SIR-like rumor spreading model. • The combination of the three variable diffusion behaviors provides a faster and larger spreading expansion capacity. • Network structure matters considerably in rumor spreading dynamics.

The first-passage time distribution for the diffusion model with variable drift

DEFF Research Database (Denmark)

Blurton, Steven Paul; Kesselmeier, Miriam; Gondan, Matthias

2017-01-01

across trials. This extra flexibility allows accounting for slow errors that often occur in response time experiments. So far, the predicted response time distributions were obtained by numerical evaluation as analytical solutions were not available. Here, we present an analytical expression...... for the cumulative first-passage time distribution in the diffusion model with normally distributed trial-to-trial variability in the drift. The solution is obtained with predefined precision, and its evaluation turns out to be extremely fast.......The Ratcliff diffusion model is now arguably the most widely applied model for response time data. Its major advantage is its description of both response times and the probabilities for correct as well as incorrect responses. The model assumes a Wiener process with drift between two constant...

An inverse problem for a one-dimensional time-fractional diffusion problem

KAUST Repository

Jin, Bangti; Rundell, William

2012-01-01

We study an inverse problem of recovering a spatially varying potential term in a one-dimensional time-fractional diffusion equation from the flux measurements taken at a single fixed time corresponding to a given set of input sources. The unique

First-Order Hyperbolic System Method for Time-Dependent Advection-Diffusion Problems

Science.gov (United States)

2014-03-01

accuracy, with rapid convergence over each physical time step, typically less than five Newton iter - ations. 1 Contents 1 Introduction 3 2 Hyperbolic...however, we employ the Gauss - Seidel (GS) relaxation, which is also an O(N) method for the discretization arising from hyperbolic advection-diffusion system...advection-diffusion scheme. The linear dependency of the iterations on Table 1: Boundary layer problem ( Convergence criteria: Residuals < 10−8.) log10Re

Time-dependent diffusive acceleration of test particles at shocks

Energy Technology Data Exchange (ETDEWEB)

Drury, L.O' C. (Dublin Inst. for Advanced Studies (Ireland))

1991-07-15

The acceleration of test particles at a steady plane non-relativistic shock is considered. Analytic expressions are found for the mean and the variance of the acceleration time distribution in the case where the diffusion coefficient has an arbitrary dependence on position and momentum. These expressions are used as the basis for an approximation scheme which is shown, by comparison with numerical solutions, to give an excellent representation of the time-dependent spectrum. (author).

Time-dependent diffusive acceleration of test particles at shocks

International Nuclear Information System (INIS)

Drury, L.O'C.

1991-01-01

The acceleration of test particles at a steady plane non-relativistic shock is considered. Analytic expressions are found for the mean and the variance of the acceleration time distribution in the case where the diffusion coefficient has an arbitrary dependence on position and momentum. These expressions are used as the basis for an approximation scheme which is shown, by comparison with numerical solutions, to give an excellent representation of the time-dependent spectrum. (author)

Long time diffusion in suspensions of interacting charged colloids

NARCIS (Netherlands)

Schepper, I.M. de; Cohen, E.G.D.; Pusey, P.N.; Lekkerkerker, H.N.W.

1989-01-01

A new expression is given for the long time diffusion coefficient DL(k) of charged interacting colloidal spheres in suspension, as a function of the wavenumber k, near k = km, where the static structure factor has a maximum. The expression is based on a physical analogy between a mode description

Diffusive and subdiffusive dynamics of indoor microclimate: a time series modeling.

Science.gov (United States)

Maciejewska, Monika; Szczurek, Andrzej; Sikora, Grzegorz; Wyłomańska, Agnieszka

2012-09-01

The indoor microclimate is an issue in modern society, where people spend about 90% of their time indoors. Temperature and relative humidity are commonly used for its evaluation. In this context, the two parameters are usually considered as behaving in the same manner, just inversely correlated. This opinion comes from observation of the deterministic components of temperature and humidity time series. We focus on the dynamics and the dependency structure of the time series of these parameters, without deterministic components. Here we apply the mean square displacement, the autoregressive integrated moving average (ARIMA), and the methodology for studying anomalous diffusion. The analyzed data originated from five monitoring locations inside a modern office building, covering a period of nearly one week. It was found that the temperature data exhibited a transition between diffusive and subdiffusive behavior, when the building occupancy pattern changed from the weekday to the weekend pattern. At the same time the relative humidity consistently showed diffusive character. Also the structures of the dependencies of the temperature and humidity data sets were different, as shown by the different structures of the ARIMA models which were found appropriate. In the space domain, the dynamics and dependency structure of the particular parameter were preserved. This work proposes an approach to describe the very complex conditions of indoor air and it contributes to the improvement of the representative character of microclimate monitoring.

Philosophy in contemporary time: Relevance vs. Public perception ...

African Journals Online (AJOL)

What is the relevance of philosophy in this contemporary time? Philosophy is viewed by many people as an irrelevant discipline- one of no social and/or practical significance. It is sometimes seen also as an abstract and drab enterprise fit only for the intellectuals. Overtime also, philosophy has come to be perceived as ...

Time-of-flight and vector polarization analysis for diffuse neutron scattering

International Nuclear Information System (INIS)

Schweika, W.

2003-01-01

The potential of pulsed neutron sources for diffuse scattering including time-of-flight (TOF) and polarization analysis is discussed in comparison to the capabilities of the present instrument diffuse neutron scattering at the research center Juelich. We present first results of a new method for full polarization analysis using precessing neutron polarization. A proposal is made for a new type of instrument at pulsed sources, which allows for vector polarization analysis in TOF instruments with multi-detectors

Interaction dynamics of two diffusing particles: contact times and influence of nearby surfaces.

Science.gov (United States)

Tränkle, B; Ruh, D; Rohrbach, A

2016-03-14

Interactions of diffusing particles are governed by hydrodynamics on different length and timescales. The local hydrodynamics can be influenced substantially by simple interfaces. Here, we investigate the interaction dynamics of two micron-sized spheres close to plane interfaces to mimic more complex biological systems or microfluidic environments. Using scanned line optical tweezers and fast 3D interferometric particle tracking, we are able to track the motion of each bead with precisions of a few nanometers and at a rate of 10 kilohertz. From the recorded trajectories, all spatial and temporal information is accessible. This way, we measure diffusion coefficients for two coupling particles at varying distances h to one or two glass interfaces. We analyze their coupling strength and length by cross-correlation analysis relative to h and find a significant decrease in the coupling length when a second particle diffuses nearby. By analysing the times the particles are in close contact, we find that the influence of nearby surfaces and interaction potentials reduce the diffusivity strongly, although we found that the diffusivity hardly affects the contact times and the binding probability between the particles. All experimental results are compared to a theoretical model, which is based on the number of possible diffusion paths following the Catalan numbers and a diffusion probability, which is biased by the spheres' surface potential. The theoretical and experimental results agree very well and therefore enable a better understanding of hydrodynamically coupled interaction processes.

The functional relevance of diffusion tensor imaging in comparison to conventional MRI in patients with cervical compressive myelopathy

Energy Technology Data Exchange (ETDEWEB)

Yang, Young-Mi; Oh, Jae-Keun; Song, Ji-Sun [Hallym University Sacred Heart Hospital, College of Medicine, Hallym University, Spine Center, Anyang-si, Gyeonggi-do (Korea, Republic of); Yoo, Woo-Kyoung [Hallym University Sacred Heart Hospital, College of Medicine, Hallym University, Department of Physical Medicine and Rehabilitation, Anyang-si (Korea, Republic of); Hallym University Sacred Heart Hospital, College of Medicine, Hallym University, Hallym Institute for Translational Genomics and Bioinformatics, Anyang-si (Korea, Republic of); Yoo, Je Hyun; Kwak, Yoon Hae [Hallym University Sacred Heart Hospital, College of Medicine, Hallym University, Department of Orthopaedic surgery, Anyang-si (Korea, Republic of); Kim, Seok Woo [Hallym University Sacred Heart Hospital, College of Medicine, Hallym University, Spine Center, Anyang-si, Gyeonggi-do (Korea, Republic of); Hallym University Sacred Heart Hospital, College of Medicine, Hallym University, Department of Orthopaedic surgery, Anyang-si (Korea, Republic of)

2017-11-15

To determine the functional relevance of diffusion tensor imaging (DTI) metrics and conventional MRI (signal intensity change in T2, compression ratio) by measuring the correlation of these parameters with clinical outcome measured by the modified Japanese Orthopedic Association (mJOA) score. A total of 20 cervical myelopathy (CM) patients participated in this prospective cohort study. The severities of CM were assessed using the mJOA score. Conventional MRIs (T2-weighted images) measuring the signal changes of spinal cords and the degree of compression at the lesion level and DTI metrics [fractional anisotropy (FA), apparent diffusion coefficient (ADC)] at each lesion and below each lesion (C7/T1) level were acquired using a 3-T Achieva MRI. These parameters were correlated with the mJOA scores to determine the functional relevance. Ninety percent of CM patients showed signal changes and 30 % of patients noted a more than 40% canal compression ratio in conventional MRIs at the lesion level; however, these findings were not correlated with the mJOA score (p < 0.05). In contrast, FA values on DTI showed high sensitivity to CM (100%), which was well correlated with the mJOA score (p = 0.034, r = 0.475) below the lesion level (C7/T1). This study showed a meaningful symptomatic correlation between mJOA scores and FA values below the lesion levels in CM patients. It could give us more understanding of the pathological changes in spinal cords matched with various clinical findings in CM patients than the results from conventional MRI. (orig.)

Continuous Time Random Walk and different diffusive regimes - doi: 10.4025/actascitechnol.v34i2.11521

Directory of Open Access Journals (Sweden)

Haroldo Valetin Ribeiro

2012-03-01

Full Text Available We investigate how it is possible to obtain different diffusive regimes from the Continuous Time Random Walk (CTRW approach performing suitable changes for the waiting time and jumping distributions in order to get two or more regimes for the same diffusive process. We also obtain diffusion-like equations related to these processes and investigate the connection of the results with anomalous diffusion. 

Large-time behavior of solutions to a reaction-diffusion system with distributed microstructure

NARCIS (Netherlands)

Muntean, A.

2009-01-01

Abstract We study the large-time behavior of a class of reaction-diffusion systems with constant distributed microstructure arising when modeling diffusion and reaction in structured porous media. The main result of this Note is the following: As t ¿ 8 the macroscopic concentration vanishes, while

Simultaneous inversion for the space-dependent diffusion coefficient and the fractional order in the time-fractional diffusion equation

International Nuclear Information System (INIS)

Li, Gongsheng; Zhang, Dali; Jia, Xianzheng; Yamamoto, Masahiro

2013-01-01

This paper deals with an inverse problem of simultaneously identifying the space-dependent diffusion coefficient and the fractional order in the 1D time-fractional diffusion equation with smooth initial functions by using boundary measurements. The uniqueness results for the inverse problem are proved on the basis of the inverse eigenvalue problem, and the Lipschitz continuity of the solution operator is established. A modified optimal perturbation algorithm with a regularization parameter chosen by a sigmoid-type function is put forward for the discretization of the minimization problem. Numerical inversions are performed for the diffusion coefficient taking on different functional forms and the additional data having random noise. Several factors which have important influences on the realization of the algorithm are discussed, including the approximate space of the diffusion coefficient, the regularization parameter and the initial iteration. The inversion solutions are good approximations to the exact solutions with stability and adaptivity demonstrating that the optimal perturbation algorithm with the sigmoid-type regularization parameter is efficient for the simultaneous inversion. (paper)

Extracting the relevant delays in time series modelling

DEFF Research Database (Denmark)

Goutte, Cyril

1997-01-01

selection, and more precisely stepwise forward selection. The method is compared to other forward selection schemes, as well as to a nonparametric tests aimed at estimating the embedding dimension of time series. The final application extends these results to the efficient estimation of FIR filters on some......In this contribution, we suggest a convenient way to use generalisation error to extract the relevant delays from a time-varying process, i.e. the delays that lead to the best prediction performance. We design a generalisation-based algorithm that takes its inspiration from traditional variable...

The Complete Solution of Fick's Second Law of Diffusion with Time-dependent Diffusion Coefficient and Surface Concentration

DEFF Research Database (Denmark)

Mejlbro, Leif

1996-01-01

Fick's Second Law of Diffusion with time-dependent diffusioncoefficient and surface concentration is solved. Mimicking the classicalsolution, special time-dependent surface concentration functions areconsidered. These models are used in giving estimates of the lifetimeof the structure, when...... the concrete cover is given, as well as estimatesof the thickness of the concrete cover, when the expected lifetime is given.*Note: Book tilte: Durability of Concrete in Saline Environment...

Time-resolved diffusion tomographic imaging in highly scattering turbid media

Science.gov (United States)

Alfano, Robert R. (Inventor); Cai, Wei (Inventor); Liu, Feng (Inventor); Lax, Melvin (Inventor); Das, Bidyut B. (Inventor)

1998-01-01

A method for imaging objects in highly scattering turbid media. According to one embodiment of the invention, the method involves using a plurality of intersecting source/detectors sets and time-resolving equipment to generate a plurality of time-resolved intensity curves for the diffusive component of light emergent from the medium. For each of the curves, the intensities at a plurality of times are then inputted into the following inverse reconstruction algorithm to form an image of the medium: X.sup.(k+1).spsp.T =?Y.sup.T W+X.sup.(k).spsp.T .LAMBDA.!?W.sup.T W+.LAMBDA.!.sup.-1 wherein W is a matrix relating output at detector position r.sub.d, at time t, to source at position r.sub.s, .LAMBDA. is a regularization matrix, chosen for convenience to be diagonal, but selected in a way related to the ratio of the noise, to fluctuations in the absorption (or diffusion) X.sub.j that we are trying to determine: .LAMBDA..sub.ij =.lambda..sub.j .delta..sub.ij with .lambda..sub.j =/ Here Y is the data collected at the detectors, and X.sup.k is the kth iterate toward the desired absoption information.

Similarity Solutions for Multiterm Time-Fractional Diffusion Equation

OpenAIRE

Elsaid, A.; Abdel Latif, M. S.; Maneea, M.

2016-01-01

Similarity method is employed to solve multiterm time-fractional diffusion equation. The orders of the fractional derivatives belong to the interval (0,1] and are defined in the Caputo sense. We illustrate how the problem is reduced from a multiterm two-variable fractional partial differential equation to a multiterm ordinary fractional differential equation. Power series solution is obtained for the resulting ordinary problem and the convergence of the series solution is discussed. Based on ...

Sensitivity analysis of an experimental methodology to determine radionuclide diffusion coefficients in granite

International Nuclear Information System (INIS)

Alonso, U.; Missana, T.; Garcia-Gutierrez, M.; Patelli, A.; Rigato, V.

2005-01-01

Full text of publication follows: The long-term quantitative analysis of the migration behaviour of the relevant radionuclides (RN) within the geological barrier of a radioactive waste repository requires, amongst other data, the introduction of reliable transport parameters, as diffusion coefficients. Since the determination of diffusion coefficients within crystalline rocks is complex and requires long experimental times even for non-sorbing radionuclides, the data available in the literature are very scarce. The nuclear ion beam technique RBS (Rutherford Backscattering Spectrometry) that is successfully used to determine diffusion profiles in thin film science is here examined as possible suitable technique to determine the diffusion coefficients of different RN within granite. As first step, the technique sensitivity and limitations to analyse diffusion coefficients in granite samples is evaluated, considering that the technique is especially sensitive to heavy elements. The required experimental conditions in terms of experimental times, concentration and methodology of analysis are discussed. The diffusants were selected accounting the RBS sensitivity but also trying to cover different behaviours of critical RN and a wide range of possible oxidation states. In particular, Cs(I) was chosen as representative fission product, while as relevant actinides or homologues, the diffusion of Th(IV), U(IV) and Eu (III) was studied. The diffusion of these above-mentioned cations is compared to the diffusion of Re, and I as representative of anionic species. The methodology allowed evaluating diffusion coefficients in the granite samples and, for most of the elements, the values obtained are in agreement with the values found in the literature. The diffusion coefficients calculated ranged from 10 -13 to 10 -16 m 2 /s. It is remarkable that the RBS technique is especially promising to determine diffusion coefficients of high-sorbing RN and it is applicable to a wide range

Quantifying brain microstructure with diffusion MRI

DEFF Research Database (Denmark)

Novikov, Dmitry S.; Jespersen, Sune N.; Kiselev, Valerij G.

2016-01-01

the potential to quantify the relevant length scales for neuronal tissue, such as the packing correlation length for neuronal fibers, the degree of neuronal beading, and compartment sizes. The second avenue corresponds to the long-time limit, when the observed signal can be approximated as a sum of multiple non......-exchanging anisotropic Gaussian components. Here the challenge lies in parameter estimation and in resolving its hidden degeneracies. The third avenue employs multiple diffusion encoding techniques, able to access information not contained in the conventional diffusion propagator. We conclude with our outlook...... on the future research directions which can open exciting possibilities for developing markers of pathology and development based on methods of studying mesoscopic transport in disordered systems....

The missing dimension: the relevance of people's conception of time.

Science.gov (United States)

Norgate, Sarah H; Davies, Nigel; Speed, Chris; Cherrett, Tom; Dickinson, Janet

2014-02-01

While a timely conceptual innovation for the digital age, the "map" proposed by Bentley et al. would benefit from strengthening through the inclusion of a non-clock-time perspective. In this way, there could be new hypotheses developed which could be applied and tested relevant to more diverse societies, cultures, and individuals.

Solutions to Time-Fractional Diffusion-Wave Equation in Cylindrical Coordinates

Directory of Open Access Journals (Sweden)

Povstenko YZ

2011-01-01

Full Text Available Nonaxisymmetric solutions to time-fractional diffusion-wave equation with a source term in cylindrical coordinates are obtained for an infinite medium. The solutions are found using the Laplace transform with respect to time , the Hankel transform with respect to the radial coordinate , the finite Fourier transform with respect to the angular coordinate , and the exponential Fourier transform with respect to the spatial coordinate . Numerical results are illustrated graphically.

The Rational Relevance of the Diffuse Paradigms

Directory of Open Access Journals (Sweden)

Marin Dinu

2006-01-01

Full Text Available Processes like the globalization consistency and learning about society are screened by diffuse concepts such as those taking the last steps of the industrial civilization and hierarchically ordered world through hegemony. This is why the meaning of globalization is given by deviant trends, like globalism, and the knowledge society is taken for the tools promoted by itself, such as the internet. This does not imply only approximations of meaning but rather the vanity of change, preserving the status quo represented by the pre-global world or the adversity principle. Historicism of paradigm cannot be avoided. Evolvement towards something else, announced by globalization is implacable, and the new ordinating principle, the one of competition, opens the opportunity horizon to global world.

The Rational Relevance of the Diffuse Paradigms

Directory of Open Access Journals (Sweden)

Marin Dinu

2006-03-01

Full Text Available Processes like the globalization consistency and learning about society are screened by diffuse concepts such as those taking the last steps of the industrial civilization and hierarchically ordered world through hegemony. This is why the meaning of globalization is given by deviant trends, like globalism, and the knowledge society is taken for the tools promoted by itself, such as the internet. This does not imply only approximations of meaning but rather the vanity of change, preserving the status quo represented by the pre-global world or the adversity principle. Historicism of paradigm cannot be avoided. Evolvement towards something else, announced by globalization is implacable, and the new ordinating principle, the one of competition, opens the opportunity horizon to global world

Diffusion-sensitive optical coherence tomography for real-time monitoring of mucus thinning treatments

Science.gov (United States)

Blackmon, Richard L.; Kreda, Silvia M.; Sears, Patrick R.; Ostrowski, Lawrence E.; Hill, David B.; Chapman, Brian S.; Tracy, Joseph B.; Oldenburg, Amy L.

2016-03-01

Mucus hydration (wt%) has become an increasingly useful metric in real-time assessment of respiratory health in diseases like cystic fibrosis and COPD, with higher wt% indicative of diseased states. However, available in vivo rheological techniques are lacking. Gold nanorods (GNRs) are attractive biological probes whose diffusion through tissue is sensitive to the correlation length of comprising biopolymers. Through employment of dynamic light scattering theory on OCT signals from GNRs, we find that weakly-constrained GNR diffusion predictably decreases with increasing wt% (more disease-like) mucus. Previously, we determined this method is robust against mucus transport on human bronchial epithelial (hBE) air-liquid interface cultures (R2=0.976). Here we introduce diffusion-sensitive OCT (DS-OCT), where we collect M-mode image ensembles, from which we derive depth- and temporally-resolved GNR diffusion rates. DS-OCT allows for real-time monitoring of changing GNR diffusion as a result of topically applied mucus-thinning agents, enabling monitoring of the dynamics of mucus hydration never before seen. Cultured human airway epithelial cells (Calu-3 cell) with a layer of endogenous mucus were doped with topically deposited GNRs (80x22nm), and subsequently treated with hypertonic saline (HS) or isotonic saline (IS). DS-OCT provided imaging of the mucus thinning response up to a depth of 600μm with 4.65μm resolution, over a total of 8 minutes in increments of >=3 seconds. For both IS and HS conditions, DS-OCT captured changes in the pattern of mucus hydration over time. DS-OCT opens a new window into understanding mechanisms of mucus thinning during treatment, enabling real-time efficacy feedback needed to optimize and tailor treatments for individual patients.

Analytical approximate solutions of the time-domain diffusion equation in layered slabs.

Science.gov (United States)

Martelli, Fabrizio; Sassaroli, Angelo; Yamada, Yukio; Zaccanti, Giovanni

2002-01-01

Time-domain analytical solutions of the diffusion equation for photon migration through highly scattering two- and three-layered slabs have been obtained. The effect of the refractive-index mismatch with the external medium is taken into account, and approximate boundary conditions at the interface between the diffusive layers have been considered. A Monte Carlo code for photon migration through a layered slab has also been developed. Comparisons with the results of Monte Carlo simulations showed that the analytical solutions correctly describe the mean path length followed by photons inside each diffusive layer and the shape of the temporal profile of received photons, while discrepancies are observed for the continuous-wave reflectance or transmittance.

Distribution of diffusion times determined by fluorescence (lifetime) correlation spectroscopy

Czech Academy of Sciences Publication Activity Database

Pánek, Jiří; Loukotová, Lenka; Hrubý, Martin; Štěpánek, Petr

2018-01-01

Roč. 51, č. 8 (2018), s. 2796-2804 ISSN 0024-9297 R&D Projects: GA MŠk(CZ) LO1507 Institutional support: RVO:61389013 Keywords : polymer solution * fluorescence correlation spectroscopy * diffusion time distribution Subject RIV: CD - Macromolecular Chemistry OBOR OECD: Polymer science Impact factor: 5.835, year: 2016

The use of diffusion theory to compute invasion effects for the pulsed neutron thermal decay time log

International Nuclear Information System (INIS)

Tittle, C.W.

1992-01-01

Diffusion theory has been successfully used to model the effect of fluid invasion into the formation for neutron porosity logs and for the gamma-gamma density log. The purpose of this paper is to present results of computations using a five-group time-dependent diffusion code on invasion effects for the pulsed neutron thermal decay time log. Previous invasion studies by the author involved the use of a three-dimensional three-group steady-state diffusion theory to model the dual-detector thermal neutron porosity log and the gamma-gamma density log. The five-group time-dependent code MGNDE (Multi-Group Neutron Diffusion Equation) used in this work was written by Ferguson. It has been successfully used to compute the intrinsic formation life-time correction for pulsed neutron thermal decay time logs. This application involves the effect of fluid invasion into the formation

A time-efficient acquisition protocol for multipurpose diffusion-weighted microstructural imaging at 7 Tesla.

Science.gov (United States)

Sepehrband, Farshid; O'Brien, Kieran; Barth, Markus

2017-12-01

Several diffusion-weighted MRI techniques have been developed and validated during the past 2 decades. While offering various neuroanatomical inferences, these techniques differ in their proposed optimal acquisition design, preventing clinicians and researchers benefiting from all potential inference methods, particularly when limited time is available. This study reports an optimal design that enables for a time-efficient diffusion-weighted MRI acquisition scheme at 7 Tesla. The primary audience of this article is the typical end user, interested in diffusion-weighted microstructural imaging at 7 Tesla. We tested b-values in the range of 700 to 3000 s/mm 2 with different number of angular diffusion-encoding samples, against a data-driven "gold standard." The suggested design is a protocol with b-values of 1000 and 2500 s/mm 2 , with 25 and 50 samples, uniformly distributed over two shells. We also report a range of protocols in which the results of fitting microstructural models to the diffusion-weighted data had high correlation with the gold standard. We estimated minimum acquisition requirements that enable diffusion tensor imaging, higher angular resolution diffusion-weighted imaging, neurite orientation dispersion, and density imaging and white matter tract integrity across whole brain with isotropic resolution of 1.8 mm in less than 11 min. Magn Reson Med 78:2170-2184, 2017. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

Enhanced diffusion with abnormal temperature dependence in underdamped space-periodic systems subject to time-periodic driving

Science.gov (United States)

Marchenko, I. G.; Marchenko, I. I.; Zhiglo, A. V.

2018-01-01

We present a study of the diffusion enhancement of underdamped Brownian particles in a one-dimensional symmetric space-periodic potential due to external symmetric time-periodic driving with zero mean. We show that the diffusivity can be enhanced by many orders of magnitude at an appropriate choice of the driving amplitude and frequency. The diffusivity demonstrates abnormal (decreasing) temperature dependence at the driving amplitudes exceeding a certain value. At any fixed driving frequency Ω normal temperature dependence of the diffusivity is restored at low enough temperatures, T oscillation frequency at the potential minimum, the diffusivity is shown to decrease with Ω according to a power law, with the exponent related to the transient superdiffusion exponent. This behavior is found similar for the cases of sinusoidal in time and piecewise constant periodic ("square") driving.

RKC time-stepping for advection-diffusion-reaction problems

International Nuclear Information System (INIS)

Verwer, J.G.; Sommeijer, B.P.; Hundsdorfer, W.

2004-01-01

The original explicit Runge-Kutta-Chebyshev (RKC) method is a stabilized second-order integration method for pure diffusion problems. Recently, it has been extended in an implicit-explicit manner to also incorporate highly stiff reaction terms. This implicit-explicit RKC method thus treats diffusion terms explicitly and the highly stiff reaction terms implicitly. The current paper deals with the incorporation of advection terms for the explicit method, thus aiming at the implicit-explicit RKC integration of advection-diffusion-reaction equations in a manner that advection and diffusion terms are treated simultaneously and explicitly and the highly stiff reaction terms implicitly

Dynamic Analysis for a Kaldor–Kalecki Model of Business Cycle with Time Delay and Diffusion Effect

Directory of Open Access Journals (Sweden)

Wenjie Hu

2018-01-01

Full Text Available The dynamics behaviors of Kaldor–Kalecki business cycle model with diffusion effect and time delay under the Neumann boundary conditions are investigated. First the conditions of time-independent and time-dependent stability are investigated. Then, we find that the time delay can give rise to the Hopf bifurcation when the time delay passes a critical value. Moreover, the normal form of Hopf bifurcations is obtained by using the center manifold theorem and normal form theory of the partial differential equation, which can determine the bifurcation direction and the stability of the periodic solutions. Finally, numerical results not only validate the obtained theorems, but also show that the diffusion coefficients play a key role in the spatial pattern. With the diffusion coefficients increasing, different patterns appear.

Knowledge diffusion in complex networks by considering time-varying information channels

Science.gov (United States)

Zhu, He; Ma, Jing

2018-03-01

In this article, based on a model of epidemic spreading, we explore the knowledge diffusion process with an innovative mechanism for complex networks by considering time-varying information channels. To cover the knowledge diffusion process in homogeneous and heterogeneous networks, two types of networks (the BA network and the ER network) are investigated. The mean-field theory is used to theoretically draw the knowledge diffusion threshold. Numerical simulation demonstrates that the knowledge diffusion threshold is almost linearly correlated with the mean of the activity rate. In addition, under the influence of the activity rate and distinct from the classic Susceptible-Infected-Susceptible (SIS) model, the density of knowers almost linearly grows with the spreading rate. Finally, in consideration of the ubiquitous mechanism of innovation, we further study the evolution of knowledge in our proposed model. The results suggest that compared with the effect of the spreading rate, the average knowledge version of the population is affected more by the innovation parameter and the mean of the activity rate. Furthermore, in the BA network, the average knowledge version of individuals with higher degree is always newer than those with lower degree.

Scaling of the first-passage time of biased diffusion on hierarchical comb structures

International Nuclear Information System (INIS)

Lin Zhifang; Tao Ruibao.

1989-12-01

Biased diffusion on hierarchical comb structures is studied within an exact renormalization group scheme. The scaling exponents of the moments of the first-passage time for random walks are obtained. It is found that the scaling properties of the diffusion depend only on the direction of bias. In this particular case, the presence of bias may give rise to a new multifractality. (author). 7 refs, 2 figs

The time dependent propensity function for acceleration of spatial stochastic simulation of reaction–diffusion systems

International Nuclear Information System (INIS)

Fu, Jin; Wu, Sheng; Li, Hong; Petzold, Linda R.

2014-01-01

The inhomogeneous stochastic simulation algorithm (ISSA) is a fundamental method for spatial stochastic simulation. However, when diffusion events occur more frequently than reaction events, simulating the diffusion events by ISSA is quite costly. To reduce this cost, we propose to use the time dependent propensity function in each step. In this way we can avoid simulating individual diffusion events, and use the time interval between two adjacent reaction events as the simulation stepsize. We demonstrate that the new algorithm can achieve orders of magnitude efficiency gains over widely-used exact algorithms, scales well with increasing grid resolution, and maintains a high level of accuracy

Measurement of time series variation of thermal diffusivity of magnetic fluid under magnetic field by forced Rayleigh scattering method

Energy Technology Data Exchange (ETDEWEB)

Motozawa, Masaaki, E-mail: motozawa.masaaki@shizuoka.ac.jp [Shizuoka University, 3-5-1 Johoku, Naka-ku, Hamamatsu-shi, Shizuoka 432-8561 (Japan); Muraoka, Takashi [Shizuoka University, 3-5-1 Johoku, Naka-ku, Hamamatsu-shi, Shizuoka 432-8561 (Japan); Motosuke, Masahiro, E-mail: mot@rs.tus.ac.jp [Tokyo University of Science, 6-3-1 Niijuku, Katsushika-ku, Tokyo 125-8585 (Japan); Fukuta, Mitsuhiro, E-mail: fukuta.mitsuhiro@shizuoka.ac.jp [Shizuoka University, 3-5-1 Johoku, Naka-ku, Hamamatsu-shi, Shizuoka 432-8561 (Japan)

2017-04-15

It can be expected that the thermal diffusivity of a magnetic fluid varies from time to time after applying a magnetic field because of the growth of the inner structure of a magnetic fluid such as chain-like clusters. In this study, time series variation of the thermal diffusivity of a magnetic fluid caused by applying a magnetic field was investigated experimentally. For the measurement of time series variation of thermal diffusivity, we attempted to apply the forced Rayleigh scattering method (FRSM), which has high temporal and high spatial resolution. We set up an optical system for the FRSM and measured the thermal diffusivity. A magnetic field was applied to a magnetic fluid in parallel and perpendicular to the heat flux direction, and the magnetic field intensity was 70 mT. The FRSM was successfully applied to measurement of the time series variation of the magnetic fluid from applying a magnetic field. The results show that a characteristic configuration in the time series variation of the thermal diffusivity of magnetic fluid was obtained in the case of applying a magnetic field parallel to the heat flux direction. In contrast, in the case of applying a magnetic field perpendicular to the heat flux, the thermal diffusivity of the magnetic fluid hardly changed during measurement. - Highlights: • Thermal diffusivity was measured by forced Rayleigh scattering method (FRSM). • FRSM has high temporal and high spatial resolutions for measurement. • We attempted to apply FRSM to magnetic fluid (MF). • Time series variation of thermal diffusivity of MF was successfully measured by FRSM. • Anisotropic thermal diffusivity of magnetic fluid was also successfully confirmed.

Similarity Solutions for Multiterm Time-Fractional Diffusion Equation

Directory of Open Access Journals (Sweden)

A. Elsaid

2016-01-01

Full Text Available Similarity method is employed to solve multiterm time-fractional diffusion equation. The orders of the fractional derivatives belong to the interval (0,1] and are defined in the Caputo sense. We illustrate how the problem is reduced from a multiterm two-variable fractional partial differential equation to a multiterm ordinary fractional differential equation. Power series solution is obtained for the resulting ordinary problem and the convergence of the series solution is discussed. Based on the obtained results, we propose a definition for a multiterm error function with generalized coefficients.

Diffuse reflectance spectroscopy : toward real-time quantification of steatosis in liver

NARCIS (Netherlands)

Evers, Daniel J.; Westerkamp, Andrie C.; Spliethoff, Jarich W.; Pully, Vishnu V.; Hompes, Daphne; Hendriks, Benno H. W.; Prevoo, Warner; van Velthuysen, Marie-Louise F.; Porte, Robert J.; Ruers, Theo J. M.

Assessment of fatty liver grafts during orthotopic liver transplantation is a challenge due to the lack of real-time analysis options during surgery. Diffuse reflectance spectroscopy (DRS) could be a new diagnostic tool to quickly assess steatosis. Eight hundred and seventy-eight optical

An instrument for small-animal imaging using time-resolved diffuse and fluorescence optical methods

International Nuclear Information System (INIS)

Montcel, Bruno; Poulet, Patrick

2006-01-01

We describe time-resolved optical methods that use diffuse near-infrared photons to image the optical properties of tissues and their inner fluorescent probe distribution. The assembled scanner uses picosecond laser diodes at 4 wavelengths, an 8-anode photo-multiplier tube and time-correlated single photon counting. Optical absorption and reduced scattering images as well as fluorescence emission images are computed from temporal profiles of diffuse photons. This method should improve the spatial resolution and the quantification of fluorescence signals. We used the diffusion approximation of the radiation transport equation and the finite element method to solve the forward problem. The inverse problem is solved with an optimization algorithm such as ART or conjugate gradient. The scanner and its performances are presented, together with absorption, scattering and fluorescent images obtained with it

Diffusion in membranes: Toward a two-dimensional diffusion map

Directory of Open Access Journals (Sweden)

Toppozini Laura

2015-01-01

Full Text Available For decades, quasi-elastic neutron scattering has been the prime tool for studying molecular diffusion in membranes over relevant nanometer distances. These experiments are essential to our current understanding of molecular dynamics of lipids, proteins and membrane-active molecules. Recently, we presented experimental evidence from X-ray diffraction and quasi-elastic neutron scattering demonstrating that ethanol enhances the permeability of membranes. At the QENS 2014/WINS 2014 conference we presented a novel technique to measure diffusion across membranes employing 2-dimensional quasi-elastic neutron scattering. We present results from our preliminary analysis of an experiment on the cold neutron multi-chopper spectrometer LET at ISIS, where we studied the self-diffusion of water molecules along lipid membranes and have the possibility of studying the diffusion in membranes. By preparing highly oriented membrane stacks and aligning them horizontally in the spectrometer, our aim is to distinguish between lateral and transmembrane diffusion. Diffusion may also be measured at different locations in the membranes, such as the water layer and the hydrocarbon membrane core. With a complete analysis of the data, 2-dimensional mapping will enable us to determine diffusion channels of water and ethanol molecules to quantitatively determine nanoscale membrane permeability.

Global exponential stability of reaction-diffusion recurrent neural networks with time-varying delays

International Nuclear Information System (INIS)

Liang Jinling; Cao Jinde

2003-01-01

Employing general Halanay inequality, we analyze the global exponential stability of a class of reaction-diffusion recurrent neural networks with time-varying delays. Several new sufficient conditions are obtained to ensure existence, uniqueness and global exponential stability of the equilibrium point of delayed reaction-diffusion recurrent neural networks. The results extend and improve the earlier publications. In addition, an example is given to show the effectiveness of the obtained result

Analysis of discrete reaction-diffusion equations for autocatalysis and continuum diffusion equations for transport

Energy Technology Data Exchange (ETDEWEB)

Wang, Chi-Jen [Iowa State Univ., Ames, IA (United States)

2013-01-01

In this thesis, we analyze both the spatiotemporal behavior of: (A) non-linear “reaction” models utilizing (discrete) reaction-diffusion equations; and (B) spatial transport problems on surfaces and in nanopores utilizing the relevant (continuum) diffusion or Fokker-Planck equations. Thus, there are some common themes in these studies, as they all involve partial differential equations or their discrete analogues which incorporate a description of diffusion-type processes. However, there are also some qualitative differences, as shall be discussed below.

Fluorescence diffuse optical tomography: benefits of using the time-resolved modality

International Nuclear Information System (INIS)

Ducros, Nicolas

2009-01-01

Fluorescence diffuse optical tomography enables the three-dimensional reconstruction of fluorescence markers injected within a biological tissue, with light in the near infrared range. The simple continuous modality uses steady excitation light and operates from the measurements at different positions of the attenuation of the incident beam. This technique is low-cost, non-ionizing, and easy to handle, but subject to low resolution for thick tissues due to diffusion. Hopefully, the time-resolved modality, which provides the time of flight of any detected photon, could overcome this limitation and pave the way to clinical applications. This thesis aims at determining the best way to exploit the time resolved information and at quantifying the advantages of this modality over the standard continuous wave one. Model deviations must be carefully limited when ill-posed problems as fluorescence diffuse optical tomography are considered. As a result, we have first addressed the modelling part of the problem. We have shown that the photons density models to good approximation the measurable quantity that is the quantity measured by an actual acquisition set-up. Then, the moment-based reconstruction scheme has been thoroughly evaluated by means of a theoretical analysis of the moments properties. It was found that the moment-based approach requires high photon counts to be profitable compared to the continuous wave modality. Last, a novel wavelet-based approach, which enables an improved reconstruction quality, has been introduced. This approach has shown good ability to exploit the temporal information at lower photon counts. (author) [fr

Diffusion archeology for diffusion progression history reconstruction.

Science.gov (United States)

Sefer, Emre; Kingsford, Carl

2016-11-01

Diffusion through graphs can be used to model many real-world processes, such as the spread of diseases, social network memes, computer viruses, or water contaminants. Often, a real-world diffusion cannot be directly observed while it is occurring - perhaps it is not noticed until some time has passed, continuous monitoring is too costly, or privacy concerns limit data access. This leads to the need to reconstruct how the present state of the diffusion came to be from partial diffusion data. Here, we tackle the problem of reconstructing a diffusion history from one or more snapshots of the diffusion state. This ability can be invaluable to learn when certain computer nodes are infected or which people are the initial disease spreaders to control future diffusions. We formulate this problem over discrete-time SEIRS-type diffusion models in terms of maximum likelihood. We design methods that are based on submodularity and a novel prize-collecting dominating-set vertex cover (PCDSVC) relaxation that can identify likely diffusion steps with some provable performance guarantees. Our methods are the first to be able to reconstruct complete diffusion histories accurately in real and simulated situations. As a special case, they can also identify the initial spreaders better than the existing methods for that problem. Our results for both meme and contaminant diffusion show that the partial diffusion data problem can be overcome with proper modeling and methods, and that hidden temporal characteristics of diffusion can be predicted from limited data.

Hierarchical Bayesian modeling of the space - time diffusion patterns of cholera epidemic in Kumasi, Ghana

NARCIS (Netherlands)

Osei, Frank B.; Osei, F.B.; Duker, Alfred A.; Stein, A.

2011-01-01

This study analyses the joint effects of the two transmission routes of cholera on the space-time diffusion dynamics. Statistical models are developed and presented to investigate the transmission network routes of cholera diffusion. A hierarchical Bayesian modelling approach is employed for a joint

The effects of ageing on mouse muscle microstructure: a comparative study of time-dependent diffusion MRI and histological assessment.

Science.gov (United States)

Porcari, Paola; Hall, Matt G; Clark, Chris A; Greally, Elizabeth; Straub, Volker; Blamire, Andrew M

2018-03-01

The investigation of age-related changes in muscle microstructure between developmental and healthy adult mice may help us to understand the clinical features of early-onset muscle diseases, such as Duchenne muscular dystrophy. We investigated the evolution of mouse hind-limb muscle microstructure using diffusion imaging of in vivo and in vitro samples from both actively growing and mature mice. Mean apparent diffusion coefficients (ADCs) of the gastrocnemius and tibialis anterior muscles were determined as a function of diffusion time (Δ), age (7.5, 22 and 44 weeks) and diffusion gradient direction, applied parallel or transverse to the principal axis of the muscle fibres. We investigated a wide range of diffusion times with the goal of probing a range of diffusion lengths characteristic of muscle microstructure. We compared the diffusion time-dependent ADC of hind-limb muscles with histology. ADC was found to vary as a function of diffusion time in muscles at all stages of maturation. Muscle water diffusivity was higher in younger (7.5 weeks) than in adult (22 and 44 weeks) mice, whereas no differences were observed between the older ages. In vitro data showed the same diffusivity pattern as in vivo data. The highlighted differences in diffusion properties between young and mature muscles suggested differences in underlying muscle microstructure, which were confirmed by histological assessment. In particular, although diffusion was more restricted in older muscle, muscle fibre size increased significantly from young to adult age. The extracellular space decreased with age by only ~1%. This suggests that the observed diffusivity differences between young and adult muscles may be caused by increased membrane permeability in younger muscle associated with properties of the sarcolemma. Copyright © 2018 John Wiley & Sons, Ltd.

Asymptotic equivalence of neutron diffusion and transport in time-independent reactor systems

International Nuclear Information System (INIS)

Borysiewicz, M.; Mika, J.; Spiga, G.

1982-01-01

Presented in this paper is the asymptotic analysis of the time-independent neutron transport equation in the second-order variational formulation. The small parameter introduced into the equation is an estimate of the ratio of absorption and leakage to scattering in the system considered. When the ratio tends to zero, the weak solution to the transport problem tends to the weak solution of the diffusion problem, including properly defined boundary conditions. A formula for the diffusion coefficient different from that based on averaging the transport mean-free-path is derived

Prediction of tablets disintegration times using near-infrared diffuse reflectance spectroscopy as a nondestructive method.

Science.gov (United States)

Donoso, M; Ghaly, Evone S

2005-01-01

The goals of this study are to user near-infrared reflectance (NIR) spectroscopy to measure the disintegration time of a series of tablets compacted at different compressional forces, calibrate NIR data vs. laboratory equipment data, develop a model equation, validate the model, and test the model's predictive ability. Seven theophylline tablet formulations of the same composition but with different disintegration time values (0.224, 1.141, 2.797, 5.492, 9.397, 16.8, and 30.092 min) were prepared along with five placebo tablet formulations with different disintegration times. Laboratory disintegration time was compared to near-infrared diffuse reflectance data. Linear regression, quadratic, cubic, and partial least square techniques were used to determine the relationship between disintegration time and near-infrared spectra. The results demonstrated that an increase in disintegration time produced an increase in near-infrared absorbance. Series of model equations, which depended on the mathematical technique used for regression, were developed from the calibration of disintegration time using laboratory equipment vs. the near-infrared diffuse reflectance for each formulation. The results of NIR disintegration time were similar to laboratory tests. The near-infrared diffuse reflectance spectroscopy method is an alternative nondestructive method for measurement of disintegration time of tablets.

Diffuse mirrors: 3D reconstruction from diffuse indirect illumination using inexpensive time-of-flight sensors

KAUST Repository

Heide, Felix

2014-06-01

The functional difference between a diffuse wall and a mirror is well understood: one scatters back into all directions, and the other one preserves the directionality of reflected light. The temporal structure of the light, however, is left intact by both: assuming simple surface reflection, photons that arrive first are reflected first. In this paper, we exploit this insight to recover objects outside the line of sight from second-order diffuse reflections, effectively turning walls into mirrors. We formulate the reconstruction task as a linear inverse problem on the transient response of a scene, which we acquire using an affordable setup consisting of a modulated light source and a time-of-flight image sensor. By exploiting sparsity in the reconstruction domain, we achieve resolutions in the order of a few centimeters for object shape (depth and laterally) and albedo. Our method is robust to ambient light and works for large room-sized scenes. It is drastically faster and less expensive than previous approaches using femtosecond lasers and streak cameras, and does not require any moving parts.

Diffuse mirrors: 3D reconstruction from diffuse indirect illumination using inexpensive time-of-flight sensors

KAUST Repository

Heide, Felix; Xiao, Lei; Heidrich, Wolfgang; Hullin, Matthias B.

2014-01-01

The functional difference between a diffuse wall and a mirror is well understood: one scatters back into all directions, and the other one preserves the directionality of reflected light. The temporal structure of the light, however, is left intact by both: assuming simple surface reflection, photons that arrive first are reflected first. In this paper, we exploit this insight to recover objects outside the line of sight from second-order diffuse reflections, effectively turning walls into mirrors. We formulate the reconstruction task as a linear inverse problem on the transient response of a scene, which we acquire using an affordable setup consisting of a modulated light source and a time-of-flight image sensor. By exploiting sparsity in the reconstruction domain, we achieve resolutions in the order of a few centimeters for object shape (depth and laterally) and albedo. Our method is robust to ambient light and works for large room-sized scenes. It is drastically faster and less expensive than previous approaches using femtosecond lasers and streak cameras, and does not require any moving parts.

Permeability estimation from NMR diffusion measurements in reservoir rocks.

Science.gov (United States)

Balzarini, M; Brancolini, A; Gossenberg, P

1998-01-01

It is well known that in restricted geometries, such as in porous media, the apparent diffusion coefficient (D) of the fluid depends on the observation time. From the time dependence of D, interesting information can be derived to characterise geometrical features of the porous media that are relevant in oil industry applications. In particular, the permeability can be related to the surface-to-volume ratio (S/V), estimated from the short time behaviour of D(t), and to the connectivity of the pore space, which is probed by the long time behaviour of D(t). The stimulated spin-echo pulse sequence, with pulsed magnetic field gradients, has been used to measure the diffusion coefficients on various homogeneous and heterogeneous sandstone samples. It is shown that the petrophysical parameters obtained by our measurements are in good agreement with those yielded by conventional laboratory techniques (gas permeability and electrical conductivity). Although the diffusing time is limited by T1, eventually preventing an observation of the real asymptotic behaviour, and the surface-to-volume ratio measured by nuclear magnetic resonance is different from the value obtained by BET because of the different length scales probed, the measurement remains reliable and low-time consuming.

Time reversibility of quantum diffusion in small-world networks

Science.gov (United States)

Han, Sung-Guk; Kim, Beom Jun

2012-02-01

We study the time-reversal dynamics of a tight-binding electron in the Watts-Strogatz (WS) small-world networks. The localized initial wave packet at time t = 0 diffuses as time proceeds until the time-reversal operation, together with the momentum perturbation of the strength η, is made at the reversal time T. The time irreversibility is measured by I = |Π( t = 2 T) - Π( t = 0)|, where Π is the participation ratio gauging the extendedness of the wavefunction and for convenience, t is measured forward even after the time reversal. When η = 0, the time evolution after T makes the wavefunction at t = 2 T identical to the one at t = 0, and we find I = 0, implying a null irreversibility or a complete reversibility. On the other hand, as η is increased from zero, the reversibility becomes weaker, and we observe enhancement of the irreversibility. We find that I linearly increases with increasing η in the weakly-perturbed region, and that the irreversibility is much stronger in the WS network than in the local regular network.

Brain Metabolite Diffusion from Ultra-Short to Ultra-Long Time Scales: What Do We Learn, Where Should We Go?

Directory of Open Access Journals (Sweden)

Julien Valette

2018-01-01

Full Text Available In vivo diffusion-weighted MR spectroscopy (DW-MRS allows measuring diffusion properties of brain metabolites. Unlike water, most metabolites are confined within cells. Hence, their diffusion is expected to purely reflect intracellular properties, opening unique possibilities to use metabolites as specific probes to explore cellular organization and structure. However, interpretation and modeling of DW-MRS, and more generally of intracellular diffusion, remains difficult. In this perspective paper, we will focus on the study of the time-dependency of brain metabolite apparent diffusion coefficient (ADC. We will see how measuring ADC over several orders of magnitude of diffusion times, from less than 1 ms to more than 1 s, allows clarifying our understanding of brain metabolite diffusion, by firmly establishing that metabolites are neither massively transported by active mechanisms nor massively confined in subcellular compartments or cell bodies. Metabolites appear to be instead diffusing in long fibers typical of neurons and glial cells such as astrocytes. Furthermore, we will evoke modeling of ADC time-dependency to evaluate the effect of, and possibly quantify, some structural parameters at various spatial scales, departing from a simple model of hollow cylinders and introducing additional complexity, either short-ranged (such as dendritic spines or long-ranged (such as cellular fibers ramification. Finally, we will discuss the experimental feasibility and expected benefits of extending the range of diffusion times toward even shorter and longer values.

Total variation regularization for a backward time-fractional diffusion problem

International Nuclear Information System (INIS)

Wang, Liyan; Liu, Jijun

2013-01-01

Consider a two-dimensional backward problem for a time-fractional diffusion process, which can be considered as image de-blurring where the blurring process is assumed to be slow diffusion. In order to avoid the over-smoothing effect for object image with edges and to construct a fast reconstruction scheme, the total variation regularizing term and the data residual error in the frequency domain are coupled to construct the cost functional. The well posedness of this optimization problem is studied. The minimizer is sought approximately using the iteration process for a series of optimization problems with Bregman distance as a penalty term. This iteration reconstruction scheme is essentially a new regularizing scheme with coupling parameter in the cost functional and the iteration stopping times as two regularizing parameters. We give the choice strategy for the regularizing parameters in terms of the noise level of measurement data, which yields the optimal error estimate on the iterative solution. The series optimization problems are solved by alternative iteration with explicit exact solution and therefore the amount of computation is much weakened. Numerical implementations are given to support our theoretical analysis on the convergence rate and to show the significant reconstruction improvements. (paper)

Whisper: Tracing the Spatiotemporal Process of Information Diffusion in Real Time.

Science.gov (United States)

Cao, Nan; Lin, Yu-Ru; Sun, Xiaohua; Lazer, D; Liu, Shixia; Qu, Huamin

2012-12-01

When and where is an idea dispersed? Social media, like Twitter, has been increasingly used for exchanging information, opinions and emotions about events that are happening across the world. Here we propose a novel visualization design, "Whisper", for tracing the process of information diffusion in social media in real time. Our design highlights three major characteristics of diffusion processes in social media: the temporal trend, social-spatial extent, and community response of a topic of interest. Such social, spatiotemporal processes are conveyed based on a sunflower metaphor whose seeds are often dispersed far away. In Whisper, we summarize the collective responses of communities on a given topic based on how tweets were retweeted by groups of users, through representing the sentiments extracted from the tweets, and tracing the pathways of retweets on a spatial hierarchical layout. We use an efficient flux line-drawing algorithm to trace multiple pathways so the temporal and spatial patterns can be identified even for a bursty event. A focused diffusion series highlights key roles such as opinion leaders in the diffusion process. We demonstrate how our design facilitates the understanding of when and where a piece of information is dispersed and what are the social responses of the crowd, for large-scale events including political campaigns and natural disasters. Initial feedback from domain experts suggests promising use for today's information consumption and dispersion in the wild.

Diffusion in the pore water of compacted crushed salt

Energy Technology Data Exchange (ETDEWEB)

Fluegge, Judith; Herr, Sebastian; Lauke, Thomas; Meleshyn, Artur; Miehe, Ruediger; Ruebel, Andre

2016-07-15

Diffusion of dissolved radionuclides in the pore water of compacted crushed salt in the long-term is the most relevant process for the release of radionuclides from a dedicated repository for high-level waste in a salt formation as has been shown in latest safety assessments and research projects /BUH 16/. So far, diffusion coefficients for free water have been applied for the diffusion in pore water in models for long-term safety assessments. This conservative assumption was used, because data on the diffusion coefficient of dissolved substances in crushed salt have been missing. Furthermore, the diffusion coefficient in the pore water was assumed to be constant and independent from the degree of compaction of the crushed salt. The work presented in this report was intended to contribute to fill this gap of knowledge about how the diffusion of radionuclides takes place in the compacted backfill of a repository in salt. For the first time, the pore diffusion coefficient as well as its dependence on the porosity of the crushed salt was determined experimentally by means of through-diffusion experiments using caesium as tracer. The results achieved in this project suggest that the diffusion in compacted crushed salt is not fully comparable to that in a homogeneous, temporally stable porous medium like sand or clay. The results obtained from four diffusion experiments show a remarkably different behaviour and all yield unique concentration versus time plots which includes highly temporal variable tracer fluxes with even full interruptions of the flux for longer periods of time. This effect cannot be explained by assuming a tracer transport by diffusion in a temporarily invariant pore space and / or under temporally invariant experimental conditions. From our point of view, a restructuring of the pore space seems to lead to closed areas of pore water in the sample which may open up again after some time, leading to a variable pore space and hence variable diffusive

Time-delayed fronts from biased random walks

International Nuclear Information System (INIS)

Fort, Joaquim; Pujol, Toni

2007-01-01

We generalize a previous model of time-delayed reaction-diffusion fronts (Fort and Mendez 1999 Phys. Rev. Lett. 82 867) to allow for a bias in the microscopic random walk of particles or individuals. We also present a second model which takes the time order of events (diffusion and reproduction) into account. As an example, we apply them to the human invasion front across the USA in the 19th century. The corrections relative to the previous model are substantial. Our results are relevant to physical and biological systems with anisotropic fronts, including particle diffusion in disordered lattices, population invasions, the spread of epidemics, etc

Homotopy decomposition method for solving one-dimensional time-fractional diffusion equation

Science.gov (United States)

Abuasad, Salah; Hashim, Ishak

2018-04-01

In this paper, we present the homotopy decomposition method with a modified definition of beta fractional derivative for the first time to find exact solution of one-dimensional time-fractional diffusion equation. In this method, the solution takes the form of a convergent series with easily computable terms. The exact solution obtained by the proposed method is compared with the exact solution obtained by using fractional variational homotopy perturbation iteration method via a modified Riemann-Liouville derivative.

Second order time evolution of the multigroup diffusion and P1 equations for radiation transport

International Nuclear Information System (INIS)

Olson, Gordon L.

2011-01-01

Highlights: → An existing multigroup transport algorithm is extended to be second-order in time. → A new algorithm is presented that does not require a grey acceleration solution. → The two algorithms are tested with 2D, multi-material problems. → The two algorithms have comparable computational requirements. - Abstract: An existing solution method for solving the multigroup radiation equations, linear multifrequency-grey acceleration, is here extended to be second order in time. This method works for simple diffusion and for flux-limited diffusion, with or without material conduction. A new method is developed that does not require the solution of an averaged grey transport equation. It is effective solving both the diffusion and P 1 forms of the transport equation. Two dimensional, multi-material test problems are used to compare the solution methods.

Spin-diffusions and diffusive molecular dynamics

Science.gov (United States)

Farmer, Brittan; Luskin, Mitchell; Plecháč, Petr; Simpson, Gideon

2017-12-01

Metastable configurations in condensed matter typically fluctuate about local energy minima at the femtosecond time scale before transitioning between local minima after nanoseconds or microseconds. This vast scale separation limits the applicability of classical molecular dynamics (MD) methods and has spurned the development of a host of approximate algorithms. One recently proposed method is diffusive MD which aims at integrating a system of ordinary differential equations describing the likelihood of occupancy by one of two species, in the case of a binary alloy, while quasistatically evolving the locations of the atoms. While diffusive MD has shown itself to be efficient and provide agreement with observations, it is fundamentally a model, with unclear connections to classical MD. In this work, we formulate a spin-diffusion stochastic process and show how it can be connected to diffusive MD. The spin-diffusion model couples a classical overdamped Langevin equation to a kinetic Monte Carlo model for exchange amongst the species of a binary alloy. Under suitable assumptions and approximations, spin-diffusion can be shown to lead to diffusive MD type models. The key assumptions and approximations include a well-defined time scale separation, a choice of spin-exchange rates, a low temperature approximation, and a mean field type approximation. We derive several models from different assumptions and show their relationship to diffusive MD. Differences and similarities amongst the models are explored in a simple test problem.

Study on neutron diffusion and time dependence heat ina fluidized bed nuclear reactor

International Nuclear Information System (INIS)

Vilhena, M.T. de.

1988-01-01

The purpose of this work is to model the neutron diffusion and heat transfer for a Fluidized Bed Nuclear Reactor and its solution by Laplace Transform Technique with numerical inversion using Fourier Series. Also Gaussian quadrature and residues techniques were applied for numerical inversion. The neutron transport, diffusion, and point Kinetic equation for this nuclear reactor concept are developed. A matricial and Taylor Series methods are proposed for the solution of the point Kinetic equation which is a time scale problem of Stiff type

Divergent series and memory of the initial condition in the long-time solution of some anomalous diffusion problems.

Science.gov (United States)

Yuste, S Bravo; Borrego, R; Abad, E

2010-02-01

We consider various anomalous d -dimensional diffusion problems in the presence of an absorbing boundary with radial symmetry. The motion of particles is described by a fractional diffusion equation. Their mean-square displacement is given by r(2) proportional, variant t(gamma)(0divergent series appear when the concentration or survival probabilities are evaluated via the method of separation of variables. While the solution for normal diffusion problems is, at most, divergent as t-->0 , the emergence of such series in the long-time domain is a specific feature of subdiffusion problems. We present a method to regularize such series, and, in some cases, validate the procedure by using alternative techniques (Laplace transform method and numerical simulations). In the normal diffusion case, we find that the signature of the initial condition on the approach to the steady state rapidly fades away and the solution approaches a single (the main) decay mode in the long-time regime. In remarkable contrast, long-time memory of the initial condition is present in the subdiffusive case as the spatial part Psi1(r) describing the long-time decay of the solution to the steady state is determined by a weighted superposition of all spatial modes characteristic of the normal diffusion problem, the weight being dependent on the initial condition. Interestingly, Psi1(r) turns out to be independent of the anomalous diffusion exponent gamma .

RESIDENCE TIMES OF PARTICLES IN DIFFUSIVE PROTOPLANETARY DISK ENVIRONMENTS. I. VERTICAL MOTIONS

International Nuclear Information System (INIS)

Ciesla, F. J.

2010-01-01

The chemical and physical evolution of primitive materials in protoplanetary disks are determined by the types of environments they are exposed to and their residence times within each environment. Here, a method for calculating representative paths of materials in diffusive protoplanetary disks is developed and applied to understanding how the vertical trajectories that particles take impact their overall evolution. The methods are general enough to be applied to disks with uniform diffusivity, the so-called constant-α cases, and disks with a spatially varying diffusivity, such as expected in 'layered-disks'. The average long-term dynamical evolution of small particles and gaseous molecules is independent of the specific form of the diffusivity in that they spend comparable fractions of their lifetimes at different heights in the disk. However, the paths that individual particles and molecules take depend strongly on the form of the diffusivity leading to a different range of behavior of particles in terms of deviations from the mean. As temperatures, gas densities, chemical abundances, and photon fluxes will vary with height in protoplanetary disks, the different paths taken by primitive materials will lead to differences in their chemical and physical evolution. Examples of differences in gas phase chemistry and photochemistry are explored here. The methods outlined here provide a powerful tool that can be integrated with chemical models to understand the formation and evolution of primitive materials in protoplanetary disks on timescales of 10 5 -10 6 years.

Diffusion of protein through the human cornea.

Science.gov (United States)

Charalel, Resmi A; Engberg, Kristin; Noolandi, Jaan; Cochran, Jennifer R; Frank, Curtis; Ta, Christopher N

2012-01-01

To determine the rate of diffusion of myoglobin and bovine serum albumin (BSA) through the human cornea. These small proteins have hydrodynamic diameters of approximately 4.4 and 7.2 nm, and molecular weights of 16.7 and 66 kDa, for myoglobin and BSA, respectively. Diffusion coefficients were measured using a diffusion chamber where the protein of interest and balanced salt solution were in different chambers separated by an ex vivo human cornea. Protein concentrations in the balanced salt solution chamber were measured over time. Diffusion coefficients were calculated using equations derived from Fick's law and conservation of mass in a closed system. Our experiments demonstrate that the diffusion coefficient of myoglobin is 5.5 ± 0.9 × 10(-8) cm(2)/s (n = 8; SD = 1.3 × 10(-8) cm(2)/s; 95% CI: 4.6 × 10(-8) to 6.4 × 10(-8) cm(2)/s) and the diffusion coefficient of BSA is 3.1 ± 1.0 × 10(-8) cm(2)/s (n = 8; SD = 1.4 × 10(-8) cm(2)/s; 95% CI: 2.1 × 10(-8) to 4.1 × 10(-8) cm(2)/s). Our study suggests that molecules as large as 7.2 nm may be able to passively diffuse through the human cornea. With applications in pharmacotherapy and the development of an artificial cornea, further experiments are warranted to fully understand the limits of human corneal diffusion and its clinical relevance. Copyright © 2012 S. Karger AG, Basel.

Time adaptivity in the diffusive wave approximation to the shallow water equations

KAUST Repository

Collier, Nathan; Radwan, Hany; Dalcí n, Lisandro D.; Calo, Victor M.

2013-01-01

We discuss the use of time adaptivity applied to the one dimensional diffusive wave approximation to the shallow water equations. A simple and computationally economical error estimator is discussed which enables time-step size adaptivity. This robust adaptive time discretization corrects the initial time step size to achieve a user specified bound on the discretization error and allows time step size variations of several orders of magnitude. In particular, the one dimensional results presented in this work feature a change of four orders of magnitudes for the time step over the entire simulation. © 2011 Elsevier B.V.

Time adaptivity in the diffusive wave approximation to the shallow water equations

KAUST Repository

Collier, Nathan

2013-05-01

We discuss the use of time adaptivity applied to the one dimensional diffusive wave approximation to the shallow water equations. A simple and computationally economical error estimator is discussed which enables time-step size adaptivity. This robust adaptive time discretization corrects the initial time step size to achieve a user specified bound on the discretization error and allows time step size variations of several orders of magnitude. In particular, the one dimensional results presented in this work feature a change of four orders of magnitudes for the time step over the entire simulation. © 2011 Elsevier B.V.

Single molecule diffusion and the solution of the spherically symmetric residence time equation.

Science.gov (United States)

Agmon, Noam

2011-06-16

The residence time of a single dye molecule diffusing within a laser spot is propotional to the total number of photons emitted by it. With this application in mind, we solve the spherically symmetric "residence time equation" (RTE) to obtain the solution for the Laplace transform of the mean residence time (MRT) within a d-dimensional ball, as a function of the initial location of the particle and the observation time. The solutions for initial conditions of potential experimental interest, starting in the center, on the surface or uniformly within the ball, are explicitly presented. Special cases for dimensions 1, 2, and 3 are obtained, which can be Laplace inverted analytically for d = 1 and 3. In addition, the analytic short- and long-time asymptotic behaviors of the MRT are derived and compared with the exact solutions for d = 1, 2, and 3. As a demonstration of the simplification afforded by the RTE, the Appendix obtains the residence time distribution by solving the Feynman-Kac equation, from which the MRT is obtained by differentiation. Single-molecule diffusion experiments could be devised to test the results for the MRT presented in this work. © 2011 American Chemical Society

Short-scan-time multi-slice diffusion MRI of the mouse cervical spinal cord using echo planar imaging.

Science.gov (United States)

Callot, Virginie; Duhamel, Guillaume; Cozzone, Patrick J; Kober, Frank

2008-10-01

Mouse spinal cord (SC) diffusion-weighted imaging (DWI) provides important information on tissue morphology and structural changes that may occur during pathologies such as multiple sclerosis or SC injury. The acquisition scheme of the commonly used DWI techniques is based on conventional spin-echo encoding, which is time-consuming. The purpose of this work was to investigate whether the use of echo planar imaging (EPI) would provide good-quality diffusion MR images of mouse SC, as well as accurate measurements of diffusion-derived metrics, and thus enable diffusion tensor imaging (DTI) and highly resolved DWI within reasonable scan times. A four-shot diffusion-weighted spin-echo EPI (SE-EPI) sequence was evaluated at 11.75 T on a group of healthy mice (n = 10). SE-EPI-derived apparent diffusion coefficients of gray and white matter were compared with those obtained using a conventional spin-echo sequence (c-SE) to validate the accuracy of the method. To take advantage of the reduction in acquisition time offered by the EPI sequence, multi-slice DTI acquisitions were performed covering the cervical segments (six slices, six diffusion-encoding directions, three b values) within 30 min (vs 2 h for c-SE). From these measurements, fractional anisotropy and mean diffusivities were calculated, and fiber tracking along the C1 to C6 cervical segments was performed. In addition, high-resolution images (74 x 94 microm(2)) were acquired within 5 min per direction. Clear delineation of gray and white matter and identical apparent diffusion coefficient values were obtained, with a threefold reduction in acquisition time compared with c-SE. While overcoming the difficulties associated with high spatially and temporally resolved DTI measurements, the present SE-EPI approach permitted identification of reliable quantitative parameters with a reproducibility compatible with the detection of pathologies. The SE-EPI method may be particularly valuable when multiple sets of images

Diffusing diffusivity: Rotational diffusion in two and three dimensions

Science.gov (United States)

Jain, Rohit; Sebastian, K. L.

2017-06-01

We consider the problem of calculating the probability distribution function (pdf) of angular displacement for rotational diffusion in a crowded, rearranging medium. We use the diffusing diffusivity model and following our previous work on translational diffusion [R. Jain and K. L. Sebastian, J. Phys. Chem. B 120, 3988 (2016)], we show that the problem can be reduced to that of calculating the survival probability of a particle undergoing Brownian motion, in the presence of a sink. We use the approach to calculate the pdf for the rotational motion in two and three dimensions. We also propose new dimensionless, time dependent parameters, αr o t ,2 D and αr o t ,3 D, which can be used to analyze the experimental/simulation data to find the extent of deviation from the normal behavior, i.e., constant diffusivity, and obtain explicit analytical expressions for them, within our model.

Time-resolved measurements of laser-induced diffusion of CO molecules on stepped Pt(111)-surfaces; Zeitaufgeloeste Untersuchung der laser-induzierten Diffusion von CO-Molekuelen auf gestuften Pt(111)-Oberflaechen

Energy Technology Data Exchange (ETDEWEB)

Lawrenz, M.

2007-10-30

In the present work the dynamics of CO-molecules on a stepped Pt(111)-surface induced by fs-laser pulses at low temperatures was studied by using laser spectroscopy. In the first part of the work, the laser-induced diffusion for the CO/Pt(111)-system could be demonstrated and modelled successfully for step diffusion. At first, the diffusion of CO-molecules from the step sites to the terrace sites on the surface was traced. The experimentally discovered energy transfer time of 500 fs for this process confirms the assumption of an electronically induced process. In the following it was explained how the experimental results were modelled. A friction coefficient which depends on the electron temperature yields a consistent model, whereas for the understanding of the fluence dependence and time-resolved measurements parallel the same set of parameters was used. Furthermore, the analysis was extended to the CO-terrace diffusion. Small coverages of CO were adsorbed to the terraces and the diffusion was detected as the temporal evolution of the occupation of the step sites acting as traps for the diffusing molecules. The additional performed two-pulse correlation measurements also indicate an electronically induced process. At the substrate temperature of 40 K the cross-correlation - where an energy transfer time of 1.8 ps was extracted - suggests also an electronically induced energy transfer mechanism. Diffusion experiments were performed for different substrate temperatures. (orig.)

Real-time transmission electron microscope observation of gold nanoclusters diffusing into silicon at room temperature

International Nuclear Information System (INIS)

Ishida, Tadashi; Nakajima, Yuuki; Fujita, Hiroyuki; Endo, Junji; Collard, Dominique

2009-01-01

Gold diffusion into silicon at room temperature was observed in real time with atomic resolution. Gold nanoclusters were formed on a silicon surface by an electrical discharge between a silicon tip and a gold coated tip inside an ultrahigh-vacuum transmission electron microscope (TEM) specimen chamber. At the moment of the gold nanocluster deposition, the gold nanoclusters had a crystalline structure. The crystalline structure gradually disappeared due to the interdiffusion between silicon and gold as observed after the deposition of gold nanoclusters. The shape of the nanocluster gradually changed due to the gold diffusion into the damaged silicon. The diffusion front between silicon and gold moved toward the silicon side. From the observations of the diffusion front, the gold diffusivity at room temperature was extracted. The extracted activation energy, 0.21 eV, matched the activation energy in bulk diffusion between damaged silicon and gold. This information is useful for optimizing the hybridization between solid-state and biological nanodevices in which gold is used as an adhesive layer between the two devices.

Access of energetic particles to storm time ring current through enhanced radial diffusion

International Nuclear Information System (INIS)

Lyons, L.R.; Schulz, M.

1989-01-01

Magnetic storms are distinguishable from other periods of geomagnetic activity by the injection of trapped electrons and ions to the 2 approx-lt L approx-lt 4 region. It has been proposed previously that this injection results from an inward displacement of the preexisting trapped-particle population by enhanced storm time electric fields. However, high-energy (approx-gt 40 keV) ring-current particles have drift periods that are typically shorter than the time of the main-phase development, and so the direct radial transport of these particles is restricted. The authors propose here that the transport of approx-gt 40 keV particles into the storm time ring current can result from enhanced stochastic radial transport driven by fluctuating electric fields during a storm's main phase. They estimate the effects of such electric fields by applying radial-diffusion theory, assuming a preexisting trapped-particle population as the initial conditions, and they demonstrate the feasibility of explaining observed flux increases of approx-gt 40-keV particles at L approx-lt 4 by enhanced radial diffusion. It is necessary that new particles be injected near the outer boundary of the trapping region so as to maintain the fluxes there as an outer boundary condition, and they estimate that the approx-gt 40-keV portion of the storm time ring current at L ∼ 3 consists of about 50% preexisting and about 50% new particles. They thus find that formation of the storm time ring current may be explainable via a combination of direct radial transport at energies approx-lt 40 keV and diffusive radial transport at higher energies

Numerical method for solving the three-dimensional time-dependent neutron diffusion equation

International Nuclear Information System (INIS)

Khaled, S.M.; Szatmary, Z.

2005-01-01

A numerical time-implicit method has been developed for solving the coupled three-dimensional time-dependent multi-group neutron diffusion and delayed neutron precursor equations. The numerical stability of the implicit computation scheme and the convergence of the iterative associated processes have been evaluated. The computational scheme requires the solution of large linear systems at each time step. For this purpose, the point over-relaxation Gauss-Seidel method was chosen. A new scheme was introduced instead of the usual source iteration scheme. (author)

Material Barriers to Diffusive Mixing

Science.gov (United States)

Haller, George; Karrasch, Daniel

2017-11-01

Transport barriers, as zero-flux surfaces, are ill-defined in purely advective mixing in which the flux of any passive scalar is zero through all material surfaces. For this reason, Lagrangian Coherent Structures (LCSs) have been argued to play the role of mixing barriers as most repelling, attracting or shearing material lines. These three kinematic concepts, however, can also be defined in different ways, both within rigorous mathematical treatments and within the realm of heuristic diagnostics. This has lead to a an ever-growing number of different LCS methods, each generally identifying different objects as transport barriers. In this talk, we examine which of these methods have actual relevance for diffusive transport barriers. The latter barriers are arguably the practically relevant inhibitors in the mixing of physically relevant tracers, such as temperature, salinity, vorticity or potential vorticity. We demonstrate the role of the most effective diffusion barriers in analytical examples and observational data. Supported in part by the DFG Priority Program on Turbulent Superstructures.

Real-time inference of word relevance from electroencephalogram and eye gaze

Science.gov (United States)

Wenzel, M. A.; Bogojeski, M.; Blankertz, B.

2017-10-01

Objective. Brain-computer interfaces can potentially map the subjective relevance of the visual surroundings, based on neural activity and eye movements, in order to infer the interest of a person in real-time. Approach. Readers looked for words belonging to one out of five semantic categories, while a stream of words passed at different locations on the screen. It was estimated in real-time which words and thus which semantic category interested each reader based on the electroencephalogram (EEG) and the eye gaze. Main results. Words that were subjectively relevant could be decoded online from the signals. The estimation resulted in an average rank of 1.62 for the category of interest among the five categories after a hundred words had been read. Significance. It was demonstrated that the interest of a reader can be inferred online from EEG and eye tracking signals, which can potentially be used in novel types of adaptive software, which enrich the interaction by adding implicit information about the interest of the user to the explicit interaction. The study is characterised by the following novelties. Interpretation with respect to the word meaning was necessary in contrast to the usual practice in brain-computer interfacing where stimulus recognition is sufficient. The typical counting task was avoided because it would not be sensible for implicit relevance detection. Several words were displayed at the same time, in contrast to the typical sequences of single stimuli. Neural activity was related with eye tracking to the words, which were scanned without restrictions on the eye movements.

Universal Earthquake-Occurrence Jumps, Correlations with Time, and Anomalous Diffusion

International Nuclear Information System (INIS)

Corral, Alvaro

2006-01-01

Spatiotemporal properties of seismicity are investigated for a worldwide (WW) catalog and for southern California in the stationary case (SC), showing a nearly universal scaling behavior. Distributions of distances between consecutive earthquakes (jumps) are magnitude independent and show two power-law regimes, separated by jump values about 200 (WW) and 15 km (SC). Distributions of waiting times conditioned to the value of jumps show that both variables are correlated, in general, but turn out to be independent when only short or long jumps are considered. Finally, diffusion profiles are found to be independent on the magnitude, contrary to what the waiting-time distributions suggest

Applicable or relevant and appropriate requirements (ARARs) for remedial actions at the Portsmouth Gaseous Diffusion Plant: A compendium of environmental laws and guidance

International Nuclear Information System (INIS)

Houlberg, L.M.; Eaton, L.A.; Martin, J.A.; McDonald, E.P.; Etnier, E.L.

1992-02-01

Section 121 of the Comprehensive Environmental Response, Compensation, and Liability Act of 1990 (CERCLA) specifies that remedial actions for cleanup of hazardous substances must comply with applicable or relevant and appropriate requirements (ARARs) or standards under federal and state environmental laws. Although the US Department of Energy (DOE) Portsmouth Gaseous Diffusion Plant (PORTS) has not at this time been proposed for inclusion on the US Environmental Protection Agency National Priorities List, under Sect. I of an administrative consent order signed by DOE and the US Environmental Protection Agency on September 29, 1989, effective October 4, 1989, any necessary response actions at PORTS stipulated in the administrative consent order must be performed in a manner consistent with the Resource Conservation and Recovery Act of 1976 and CERCLA. Section 121 of CERCLA calls for the preparation of a draft listing of all ARARs. This report supplies a preliminary list of available federal and state ARARs that might be considered for remedial response at PORTS. A description of the terms ''applicable'' and ''relevant and appropriate'' is provided, as well as definitions of chemical-, location-, and action-specific ARARs. ARARs promulgated by the federal government and by the state of Ohio are listed in tables. In addition, the major provisions of the Resource Conservation and Recovery Act, Safe Drinking Water Act, Clean Water Act, and other acts, as they apply to hazardous waste cleanup, are discussed

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM.

Science.gov (United States)

Singh, Brajesh K; Srivastava, Vineet K

2015-04-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations.

Localized diffusive motion on two different time scales in solid alkane nanoparticles

International Nuclear Information System (INIS)

Wang, S.-K.; Mamontov, Eugene; Bai, M.; Hansen, F.Y.; Taub, H.; Copley, J.R.D.; Garcia Sakai, V.; Gasparovic, Goran; Jenkins, Timothy; Tyagi, M.; Herwig, Kenneth W.; Neumann, D.A.; Montfrooij, W.; Volkmann, U.G.

2010-01-01

High-energy-resolution quasielastic neutron scattering on three complementary spectrometers has been used to investigate molecular diffusive motion in solid nano- to bulk-sized particles of the alkane n-C32H66. The crystalline-to-plastic and plastic-to-fluid phase transition temperatures are observed to decrease as the particle size decreases. In all samples, localized molecular diffusive motion in the plastic phase occurs on two different time scales: a 'fast' motion corresponding to uniaxial rotation about the long molecular axis; and a 'slow' motion attributed to conformational changes of the molecule. Contrary to the conventional interpretation in bulk alkanes, the fast uniaxial rotation begins in the low-temperature crystalline phase.

Calculation of force and time of contact formation at diffusion metal joining

Energy Technology Data Exchange (ETDEWEB)

Sukhanov, V E [Tsentral' nyj Nauchno-Issledovatel' skij Inst. Chernoj Metallurgii, Moscow (USSR); Grushevskij, A V [Moskovskij Stankoinstrumental' nyj Inst., Moscow (USSR); Surovtsev, A P

1989-03-01

An analytical model of contact for mation at diffusion joining is suggested. It is based on the introduction of a rough surface with roughnesses in the form of absolutely rigid spherical segnunts into a smooth laminar body. Mathematical expressions, permitting to calculate maximum welding force (pressure) providing close contact of the surfaces welded and time for contact formation between rough surfaces joined, are obtained. Divergence of calculational and experimental data does not exceed 20%. It is confirmed that the most intensive formation of joining occurs in the initial period of welding -the stage of formation of a physical contact, when deformation processes proceed in tensively. Finite formation of a strength joint occurs at the stage of diffusion interaction.

Single-molecule diffusion and conformational dynamics by spatial integration of temporal fluctuations

KAUST Repository

Serag, Maged F.

2014-10-06

Single-molecule localization and tracking has been used to translate spatiotemporal information of individual molecules to map their diffusion behaviours. However, accurate analysis of diffusion behaviours and including other parameters, such as the conformation and size of molecules, remain as limitations to the method. Here, we report a method that addresses the limitations of existing single-molecular localization methods. The method is based on temporal tracking of the cumulative area occupied by molecules. These temporal fluctuations are tied to molecular size, rates of diffusion and conformational changes. By analysing fluorescent nanospheres and double-stranded DNA molecules of different lengths and topological forms, we demonstrate that our cumulative-area method surpasses the conventional single-molecule localization method in terms of the accuracy of determined diffusion coefficients. Furthermore, the cumulative-area method provides conformational relaxation times of structurally flexible chains along with diffusion coefficients, which together are relevant to work in a wide spectrum of scientific fields.

Single-molecule diffusion and conformational dynamics by spatial integration of temporal fluctuations

KAUST Repository

Serag, Maged F.; Abadi, Maram; Habuchi, Satoshi

2014-01-01

Single-molecule localization and tracking has been used to translate spatiotemporal information of individual molecules to map their diffusion behaviours. However, accurate analysis of diffusion behaviours and including other parameters, such as the conformation and size of molecules, remain as limitations to the method. Here, we report a method that addresses the limitations of existing single-molecular localization methods. The method is based on temporal tracking of the cumulative area occupied by molecules. These temporal fluctuations are tied to molecular size, rates of diffusion and conformational changes. By analysing fluorescent nanospheres and double-stranded DNA molecules of different lengths and topological forms, we demonstrate that our cumulative-area method surpasses the conventional single-molecule localization method in terms of the accuracy of determined diffusion coefficients. Furthermore, the cumulative-area method provides conformational relaxation times of structurally flexible chains along with diffusion coefficients, which together are relevant to work in a wide spectrum of scientific fields.

Coherent quantum transport in disordered systems: II. Temperature dependence of carrier diffusion coefficients from the time-dependent wavepacket diffusion method

International Nuclear Information System (INIS)

Zhong, Xinxin; Zhao, Yi; Cao, Jianshu

2014-01-01

The time-dependent wavepacket diffusion method for carrier quantum dynamics (Zhong and Zhao 2013 J. Chem. Phys. 138 014111), a truncated version of the stochastic Schrödinger equation/wavefunction approach that approximately satisfies the detailed balance principle and scales well with the size of the system, is applied to investigate the carrier transport in one-dimensional systems including both the static and dynamic disorders on site energies. The predicted diffusion coefficients with respect to temperature successfully bridge from band-like to hopping-type transport. As demonstrated in paper I (Moix et al 2013 New J. Phys. 15 085010), the static disorder tends to localize the carrier, whereas the dynamic disorder induces carrier dynamics. For the weak dynamic disorder, the diffusion coefficients are temperature-independent (band-like property) at low temperatures, which is consistent with the prediction from the Redfield equation, and a linear dependence of the coefficient on temperature (hopping-type property) only appears at high temperatures. In the intermediate regime of dynamic disorder, the transition from band-like to hopping-type transport can be easily observed at relatively low temperatures as the static disorder increases. When the dynamic disorder becomes strong, the carrier motion can follow the hopping-type mechanism even without static disorder. Furthermore, it is found that the memory time of dynamic disorder is an important factor in controlling the transition from the band-like to hopping-type motions. (paper)

Lie and conditional symmetries of the three-component diffusive Lotka–Volterra system

International Nuclear Information System (INIS)

Cherniha, Roman; Davydovych, Vasyl’

2013-01-01

Lie and Q-conditional symmetries of the classical three-component diffusive Lotka–Volterra system in the case of one space variable are studied. The group-classification problems for finding Lie symmetries and Q-conditional symmetries of the first type are completely solved. Notably, non-Lie symmetries (Q-conditional symmetry operators) for a multi-component nonlinear reaction–diffusion system are constructed for the first time. The results are compared with those derived for the two-component diffusive Lotka–Volterra system. The conditional symmetry obtained for the non-Lie reduction of the three-component system used for modeling competition between three species in population dynamics is applied and the relevant exact solutions are found. Particularly, the exact solution describing different scenarios of competition between three species is constructed. (paper)

Time domain diffuse Raman spectrometer based on a TCSPC camera for the depth analysis of diffusive media.

Science.gov (United States)

Konugolu Venkata Sekar, S; Mosca, S; Tannert, S; Valentini, G; Martelli, F; Binzoni, T; Prokazov, Y; Turbin, E; Zuschratter, W; Erdmann, R; Pifferi, A

2018-05-01

We present a time domain diffuse Raman spectrometer for depth probing of highly scattering media. The system is based on, to the best of our knowledge, a novel time-correlated single-photon counting (TCSPC) camera that simultaneously acquires both spectral and temporal information of Raman photons. A dedicated non-contact probe was built, and time domain Raman measurements were performed on a tissue mimicking bilayer phantom. The fluorescence contamination of the Raman signal was eliminated by early time gating (0-212 ps) the Raman photons. Depth sensitivity is achieved by time gating Raman photons at different delays with a gate width of 106 ps. Importantly, the time domain can provide time-dependent depth sensitivity leading to a high contrast between two layers of Raman signal. As a result, an enhancement factor of 2170 was found for our bilayer phantom which is much higher than the values obtained by spatial offset Raman spectroscopy (SORS), frequency offset Raman spectroscopy (FORS), or hybrid FORS-SORS on a similar phantom.

Robust and fast nonlinear optimization of diffusion MRI microstructure models.

Science.gov (United States)

Harms, R L; Fritz, F J; Tobisch, A; Goebel, R; Roebroeck, A

2017-07-15

run time, fit, accuracy and precision. Parameter initialization approaches were found to be relevant especially for more complex models, such as those involving several fiber orientations per voxel. For these, a fitting cascade initializing or fixing parameter values in a later optimization step from simpler models in an earlier optimization step further improved run time, fit, accuracy and precision compared to a single step fit. This establishes and makes available standards by which robust fit and accuracy can be achieved in shorter run times. This is especially relevant for the use of diffusion microstructure modeling in large group or population studies and in combining microstructure parameter maps with tractography results. Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.

Towards the use of bioresorbable fibers in time-domain diffuse optics.

Science.gov (United States)

Di Sieno, Laura; Boetti, Nadia G; Dalla Mora, Alberto; Pugliese, Diego; Farina, Andrea; Konugolu Venkata Sekar, Sanathana; Ceci-Ginistrelli, Edoardo; Janner, Davide; Pifferi, Antonio; Milanese, Daniel

2018-01-01

In the last years bioresorbable materials are gaining increasing interest for building implantable optical components for medical devices. In this work we show the fabrication of bioresorbable optical fibers designed for diffuse optics applications, featuring large core diameter (up to 200 μm) and numerical aperture (0.17) to maximize the collection efficiency of diffused light. We demonstrate the suitability of bioresorbable fibers for time-domain diffuse optical spectroscopy firstly checking the intrinsic performances of the setup by acquiring the instrument response function. We then validate on phantoms the use of bioresorbable fibers by applying the MEDPHOT protocol to assess the performance of the system in measuring optical properties (namely, absorption and scattering coefficients) of homogeneous media. Further, we show an ex-vivo validation on a chicken breast by measuring the absorption and scattering spectra in the 500-1100 nm range using interstitially inserted bioresorbable fibers. This work represents a step toward a new way to look inside the body using optical fibers that can be implanted in patients. These fibers could be useful either for diagnostic (e. g. for monitoring the evolution after surgical interventions) or treatment (e. g. photodynamic therapy) purposes. Picture: Microscopy image of the 100 μm core bioresorbable fiber. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

From conservative to reactive transport under diffusion-controlled conditions

Science.gov (United States)

Babey, Tristan; de Dreuzy, Jean-Raynald; Ginn, Timothy R.

2016-05-01

We assess the possibility to use conservative transport information, such as that contained in transit time distributions, breakthrough curves and tracer tests, to predict nonlinear fluid-rock interactions in fracture/matrix or mobile/immobile conditions. Reference simulated data are given by conservative and reactive transport simulations in several diffusive porosity structures differing by their topological organization. Reactions includes nonlinear kinetically controlled dissolution and desorption. Effective Multi-Rate Mass Transfer models (MRMT) are calibrated solely on conservative transport information without pore topology information and provide concentration distributions on which effective reaction rates are estimated. Reference simulated reaction rates and effective reaction rates evaluated by MRMT are compared, as well as characteristic desorption and dissolution times. Although not exactly equal, these indicators remain very close whatever the porous structure, differing at most by 0.6% and 10% for desorption and dissolution. At early times, this close agreement arises from the fine characterization of the diffusive porosity close to the mobile zone that controls fast mobile-diffusive exchanges. At intermediate to late times, concentration gradients are strongly reduced by diffusion, and reactivity can be captured by a very limited number of rates. We conclude that effective models calibrated solely on conservative transport information like MRMT can accurately estimate monocomponent kinetically controlled nonlinear fluid-rock interactions. Their relevance might extend to more advanced biogeochemical reactions because of the good characterization of conservative concentration distributions, even by parsimonious models (e.g., MRMT with 3-5 rates). We propose a methodology to estimate reactive transport from conservative transport in mobile-immobile conditions.

The effect of payback time on solar hot water systems diffusion: the case of Greece

International Nuclear Information System (INIS)

Sidiras, Dimitrios K.; Koukios, Emmanuel G.

2005-01-01

The effect of the payback time on the spectacular diffusion of solar hot water systems (SHWS) in Greece was investigated in this work. The time pattern of the diffusion of flat plate solar collectors since its first appearance in 1974 shows that the diffusion rate grew exponentially at first, with the annual sales figure reaching 185,000 m 2 in the mid-80s. A rapid decline of the growth rate, down to the present annual sales level followed. By the year 2000, more than 2,000,000 m 2 of collectors had been installed. The economic behaviour of the main type of users (households and hotels) was found to have undergone two stages: in one of them, 1978-2002, the change of sales is in agreement with a change in economic feasibility, measured by payback time, while in the other, the early growth stage, 1974-1977, the demand grew despite a negative economic trend, obviously because of non-economic factors. The role of tax deduction, which is the most influential incentive, has been rather instrumental in the growth period 1978-1989, but lost its significance thereafter. This incentive has been withdrawn since the beginning of 1993

The effect of payback time on solar hot water systems diffusion: the case of Greece

International Nuclear Information System (INIS)

Sidiras, D.K.; Koukios, E.G.

2005-01-01

The effect of the payback time on the spectacular diffusion of solar hot water systems (SHWS) in Greece was investigated in this work. The time pattern of the diffusion of flat plate solar collectors since its first appearance in 1974 shows that the diffusion rate grew exponentially at first, with the annual sales figure reaching 185,000 m 2 in the mid-80s. A rapid decline of the growth rate, down to the present annual sales level followed. By the year 2000, more than 2,000,000 m 2 of collectors had been installed. The economic behaviour of the main type of users (households and hotels) was found to have undergone two stages: in one of them, 1978-2002, the change of sales is in agreement with a change in economic feasibility, measured by payback time, while in the other, the early growth stage, 1974-1977, the demand grew despite a negative economic trend, obviously because of non-economic factors. The role of tax deduction, which is the most influential incentive, has been rather instrumental in the growth period 1978-1989, but lost its significance thereafter. This incentive has been withdrawn since the beginning of 1993. [Author

Microsurgical anatomy of the ventral callosal radiations: new destination, correlations with diffusion tensor imaging fiber-tracking, and clinical relevance.

Science.gov (United States)

Peltier, Johann; Verclytte, Sébastien; Delmaire, Christine; Deramond, Hervé; Pruvo, Jean-Pierre; Le Gars, Daniel; Godefroy, Olivier

2010-03-01

In the current literature, there is a lack of a detailed map of the origin, course, and connections of the ventral callosal radiations of the human brain. The authors used an older dissection technique based on a freezing process as well as diffusion tensor imaging to investigate this area of the human brain. The authors demonstrated interconnections between areas 11, 12, and 25 for the callosal radiations of the trunk and rostrum of the corpus callosum; between areas 9, 10, and 32 for the genu; and between areas 6, 8, and 9 for the ventral third of the body. The authors identified new ventral callosal connections crossing the rostrum between both temporal poles and coursing within the temporal stem, and they named these connections the "callosal radiations of Peltier." They found that the breadth of the callosal radiations slightly increases along their course from the rostrum to the first third of the body of the corpus callosum. The fiber dissection and diffusion tensor imaging techniques are complementary not only in their application to the study of the commissural system in the human brain, but also in their practical use for diagnosis and surgical planning. Further investigations, neurocognitive tests, and other contributions will permit elucidation of the functional relevance of the newly identified callosal radiations in patients with disease involving the ventral corpus callosum.

Exploiting the time-dynamics of news diffusion on the Internet through a generalized Susceptible-Infected model

Science.gov (United States)

De Martino, Giuseppe; Spina, Serena

2015-11-01

We construct a news spreading model with a time dependent contact rate which generalizes the classical Susceptible-Infected model of epidemiology. In particular, we are interested on the time-dynamics of the sharing and diffusion process of news on the Internet. We focus on the counting process describing the number of connections to a given website, characterizing the cumulative density function of its inter-arrival times. Moreover, starting from the general form of the finite dimensional distribution of the process, we determine a formula for the time-variable rate of the connections and establish its relationship with the probability density function of the interarrival times. We finally show the effectiveness of our theoretical framework analyzing a real-world dataset, the Memetracker dataset, whose parameters characterizing the diffusion process are determined.

A diffusion model-free framework with echo time dependence for free-water elimination and brain tissue microstructure characterization.

Science.gov (United States)

Molina-Romero, Miguel; Gómez, Pedro A; Sperl, Jonathan I; Czisch, Michael; Sämann, Philipp G; Jones, Derek K; Menzel, Marion I; Menze, Bjoern H

2018-03-23

The compartmental nature of brain tissue microstructure is typically studied by diffusion MRI, MR relaxometry or their correlation. Diffusion MRI relies on signal representations or biophysical models, while MR relaxometry and correlation studies are based on regularized inverse Laplace transforms (ILTs). Here we introduce a general framework for characterizing microstructure that does not depend on diffusion modeling and replaces ill-posed ILTs with blind source separation (BSS). This framework yields proton density, relaxation times, volume fractions, and signal disentanglement, allowing for separation of the free-water component. Diffusion experiments repeated for several different echo times, contain entangled diffusion and relaxation compartmental information. These can be disentangled by BSS using a physically constrained nonnegative matrix factorization. Computer simulations, phantom studies, together with repeatability and reproducibility experiments demonstrated that BSS is capable of estimating proton density, compartmental volume fractions and transversal relaxations. In vivo results proved its potential to correct for free-water contamination and to estimate tissue parameters. Formulation of the diffusion-relaxation dependence as a BSS problem introduces a new framework for studying microstructure compartmentalization, and a novel tool for free-water elimination. © 2018 International Society for Magnetic Resonance in Medicine.

In vivo time-gated diffuse correlation spectroscopy at quasi-null source-detector separation.

Science.gov (United States)

Pagliazzi, M; Sekar, S Konugolu Venkata; Di Sieno, L; Colombo, L; Durduran, T; Contini, D; Torricelli, A; Pifferi, A; Mora, A Dalla

2018-06-01

We demonstrate time domain diffuse correlation spectroscopy at quasi-null source-detector separation by using a fast time-gated single-photon avalanche diode without the need of time-tagging electronics. This approach allows for increased photon collection, simplified real-time instrumentation, and reduced probe dimensions. Depth discriminating, quasi-null distance measurement of blood flow in a human subject is presented. We envision the miniaturization and integration of matrices of optical sensors of increased spatial resolution and the enhancement of the contrast of local blood flow changes.

An exact and efficient first passage time algorithm for reaction–diffusion processes on a 2D-lattice

International Nuclear Information System (INIS)

Bezzola, Andri; Bales, Benjamin B.; Alkire, Richard C.; Petzold, Linda R.

2014-01-01

We present an exact and efficient algorithm for reaction–diffusion–nucleation processes on a 2D-lattice. The algorithm makes use of first passage time (FPT) to replace the computationally intensive simulation of diffusion hops in KMC by larger jumps when particles are far away from step-edges or other particles. Our approach computes exact probability distributions of jump times and target locations in a closed-form formula, based on the eigenvectors and eigenvalues of the corresponding 1D transition matrix, maintaining atomic-scale resolution of resulting shapes of deposit islands. We have applied our method to three different test cases of electrodeposition: pure diffusional aggregation for large ranges of diffusivity rates and for simulation domain sizes of up to 4096×4096 sites, the effect of diffusivity on island shapes and sizes in combination with a KMC edge diffusion, and the calculation of an exclusion zone in front of a step-edge, confirming statistical equivalence to standard KMC simulations. The algorithm achieves significant speedup compared to standard KMC for cases where particles diffuse over long distances before nucleating with other particles or being captured by larger islands

An exact and efficient first passage time algorithm for reaction–diffusion processes on a 2D-lattice

Energy Technology Data Exchange (ETDEWEB)

Bezzola, Andri, E-mail: andri.bezzola@gmail.com [Mechanical Engineering Department, University of California, Santa Barbara, CA 93106 (United States); Bales, Benjamin B., E-mail: bbbales2@gmail.com [Mechanical Engineering Department, University of California, Santa Barbara, CA 93106 (United States); Alkire, Richard C., E-mail: r-alkire@uiuc.edu [Department of Chemical Engineering, University of Illinois, Urbana, IL 61801 (United States); Petzold, Linda R., E-mail: petzold@engineering.ucsb.edu [Mechanical Engineering Department and Computer Science Department, University of California, Santa Barbara, CA 93106 (United States)

2014-01-01

We present an exact and efficient algorithm for reaction–diffusion–nucleation processes on a 2D-lattice. The algorithm makes use of first passage time (FPT) to replace the computationally intensive simulation of diffusion hops in KMC by larger jumps when particles are far away from step-edges or other particles. Our approach computes exact probability distributions of jump times and target locations in a closed-form formula, based on the eigenvectors and eigenvalues of the corresponding 1D transition matrix, maintaining atomic-scale resolution of resulting shapes of deposit islands. We have applied our method to three different test cases of electrodeposition: pure diffusional aggregation for large ranges of diffusivity rates and for simulation domain sizes of up to 4096×4096 sites, the effect of diffusivity on island shapes and sizes in combination with a KMC edge diffusion, and the calculation of an exclusion zone in front of a step-edge, confirming statistical equivalence to standard KMC simulations. The algorithm achieves significant speedup compared to standard KMC for cases where particles diffuse over long distances before nucleating with other particles or being captured by larger islands.

Time domain diffuse optical spectroscopy: In vivo quantification of collagen in breast tissue

Science.gov (United States)

Taroni, Paola; Pifferi, Antonio; Quarto, Giovanna; Farina, Andrea; Ieva, Francesca; Paganoni, Anna Maria; Abbate, Francesca; Cassano, Enrico; Cubeddu, Rinaldo

2015-05-01

Time-resolved diffuse optical spectroscopy provides non-invasively the optical characterization of highly diffusive media, such as biological tissues. Light pulses are injected into the tissue and the effects of light propagation on re-emitted pulses are interpreted with the diffusion theory to assess simultaneously tissue absorption and reduced scattering coefficients. Performing spectral measurements, information on tissue composition and structure is derived applying the Beer law to the measured absorption and an empiric approximation to Mie theory to the reduced scattering. The absorption properties of collagen powder were preliminarily measured in the range of 600-1100 nm using a laboratory set-up for broadband time-resolved diffuse optical spectroscopy. Optical projection images were subsequently acquired in compressed breast geometry on 218 subjects, either healthy or bearing breast lesions, using a portable instrument for optical mammography that operates at 7 wavelengths selected in the range 635-1060 nm. For all subjects, tissue composition was estimated in terms of oxy- and deoxy-hemoglobin, water, lipids, and collagen. Information on tissue microscopic structure was also derived. Good correlation was obtained between mammographic breast density (a strong risk factor for breast cancer) and an optical index based on collagen content and scattering power (that accounts mostly for tissue collagen). Logistic regression applied to all optically derived parameters showed that subjects at high risk for developing breast cancer for their high breast density can effectively be identified based on collagen content and scattering parameters. Tissue composition assessed in breast lesions with a perturbative approach indicated that collagen and hemoglobin content are significantly higher in malignant lesions than in benign ones.

Diffusion slowdown in the nanostructured liquid Ga-Sn alloy

International Nuclear Information System (INIS)

Podorozhkin, Dmitri Y.; Charnaya, Elena V.; Lee, Min Kai; Chang, Lieh-Jeng; Haase, Juergen; Michel, Dieter; Kumzerov, Yurii A.; Fokin, Alexsandr V.

2015-01-01

The diffusion of gallium in liquid Ga-Sn alloy embedded into different porous silica matrices was studied by NMR. Spin relaxation was measured for two gallium isotopes, 71 Ga and 69 Ga, at two magnetic fields. Pronounced rise of quadrupole contribution to relaxation was observed for the nanostructured alloy which increased with decreasing the pore size. The correlation time of atomic mobility was evaluated and found to be much larger than in the relevant bulk melt which evidenced a pronounced diffusion slowdown in the Ga-Sn alloy under nanoconfinement. It is shown that the diffusion was slower by a factor of 30 for the alloy within 7 nm pores. The spectral densities of electric field gradients at zero frequency were found to double for the finest pores. The Knight shift was found to decrease but slightly for the nanostructured alloy. (copyright 2015 by WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Diffusion of Botulinum Toxins

Directory of Open Access Journals (Sweden)

Matthew A. Brodsky

2012-08-01

Full Text Available Background: It is generally agreed that diffusion of botulinum toxin occurs, but the extent of the spread and its clinical importance are disputed. Many factors have been suggested to play a role but which have the most clinical relevance is a subject of much discussion.Methods: This review discusses the variables affecting diffusion, including protein composition and molecular size as well as injection factors (e.g., volume, dose, injection method. It also discusses data on diffusion from comparative studies in animal models and human clinical trials that illustrate differences between the available botulinum toxin products (onabotulinumtoxinA, abobotulinumtoxinA, incobotulinumtoxinA, and rimabotulinumtoxinB.Results: Neither molecular weight nor the presence of complexing proteins appears to affect diffusion; however, injection volume, concentration, and dose all play roles and are modifiable. Both animal and human studies show that botulinum toxin products are not interchangeable, and that some products are associated with greater diffusion and higher rates of diffusion-related adverse events than others.Discussion: Each of the botulinum toxins is a unique pharmacologic entity. A working knowledge of the different serotypes is essential to avoid unwanted diffusion-related adverse events. In addition, clinicians should be aware that the factors influencing diffusion may range from properties intrinsic to the drug to accurate muscle selection as well as dilution, volume, and dose injected.

Elucidating fluctuating diffusivity in center-of-mass motion of polymer models with time-averaged mean-square-displacement tensor

Science.gov (United States)

Miyaguchi, Tomoshige

2017-10-01

There have been increasing reports that the diffusion coefficient of macromolecules depends on time and fluctuates randomly. Here a method is developed to elucidate this fluctuating diffusivity from trajectory data. Time-averaged mean-square displacement (MSD), a common tool in single-particle-tracking (SPT) experiments, is generalized to a second-order tensor with which both magnitude and orientation fluctuations of the diffusivity can be clearly detected. This method is used to analyze the center-of-mass motion of four fundamental polymer models: the Rouse model, the Zimm model, a reptation model, and a rigid rodlike polymer. It is found that these models exhibit distinctly different types of magnitude and orientation fluctuations of diffusivity. This is an advantage of the present method over previous ones, such as the ergodicity-breaking parameter and a non-Gaussian parameter, because with either of these parameters it is difficult to distinguish the dynamics of the four polymer models. Also, the present method of a time-averaged MSD tensor could be used to analyze trajectory data obtained in SPT experiments.

On the analytical solutions of the system of conformable time-fractional Robertson equations with 1-D diffusion

International Nuclear Information System (INIS)

Iyiola, O.S.; Tasbozan, O.; Kurt, A.; Çenesiz, Y.

2017-01-01

In this paper, we consider the system of conformable time-fractional Robertson equations with one-dimensional diffusion having widely varying diffusion coefficients. Due to the mismatched nature of the initial and boundary conditions associated with Robertson equation, there are spurious oscillations appearing in many computational algorithms. Our goal is to obtain an approximate solutions of this system of equations using the q-homotopy analysis method (q-HAM) and examine the widely varying diffusion coefficients and the fractional order of the derivative.

Expression for time travel based on diffusive wave theory: applicability and considerations

Science.gov (United States)

Aguilera, J. C.; Escauriaza, C. R.; Passalacqua, P.; Gironas, J. A.

2017-12-01

Prediction of hydrological response is of utmost importance when dealing with urban planning, risk assessment, or water resources management issues. With the advent of climate change, special care must be taken with respect to variations in rainfall and runoff due to rising temperature averages. Nowadays, while typical workstations have adequate power to run distributed routing hydrological models, it is still not enough for modeling on-the-fly, a crucial ability in a natural disaster context, where rapid decisions must be made. Semi-distributed time travel models, which compute a watershed's hydrograph without explicitly solving the full shallow water equations, appear as an attractive approach to rainfall-runoff modeling since, like fully distributed models, also superimpose a grid on the watershed, and compute runoff based on cell parameter values. These models are heavily dependent on the travel time expression for an individual cell. Many models make use of expressions based on kinematic wave theory, which is not applicable in cases where watershed storage is important, such as mild slopes. This work presents a new expression for concentration times in overland flow, based on diffusive wave theory, which considers not only the effects of storage but also the effects on upstream contribution. Setting upstream contribution equal to zero gives an expression consistent with previous work on diffusive wave theory; on the other hand, neglecting storage effects (i.e.: diffusion,) is shown to be equivalent to kinematic wave theory, currently used in many spatially distributed time travel models. The newly found expression is shown to be dependent on plane discretization, particularly when dealing with very non-kinematic cases. This is shown to be the result of upstream contribution, which gets larger downstream, versus plane length. This result also provides some light on the limits on applicability of the expression: when a certain kinematic threshold is reached, the

Morphology, topography, and hardness of diffusion bonded sialon to AISI 420 at different bonding time

Science.gov (United States)

Ibrahim, Nor Nurulhuda Md.; Hussain, Patthi; Awang, Mokhtar

2015-07-01

Sialon and AISI 420 martensitic stainless steel were diffusion bonded in order to study the effect of bonding time on reaction layer's growth. Joining of these materials was conducted at 1200°C under a uniaxial pressure of 17 MPa in a vacuum ranging from 5.0 to 8.0×10-6 Torr with bonding time varied for 0.5, 2, and 3 h. Thicker reaction layer was formed in longer bonded sample since the elements from sialon could diffuse further into the steel. Sialon retained its microstructure but it was affected at the initial contact with the steel to form the new interface layer. Diffusion layer grew toward the steel and it was segregated with the parent steel as a result of the difference in properties between these regions. The segregation formed a stream-like structure and its depth decreased when the bonding time was increased. The microstructure of the steel transformed into large grain size with precipitates. Prolonging the bonding time produced more precipitates in the steel and reduced the steel thickness as well. Interdiffusions of elements occurred between the joined materials and the concentrations were decreasing toward the steel and vice versa. Silicon easily diffused into the steel because it possessed lower ionization potential compared to nitrogen. Formation of silicide and other compounds such as carbides were detected in the interface layer and steel grain boundary, respectively. These compounds were harmful due to silicide brittleness and precipitation of carbides in the grain boundary might cause intergranular corrosion cracking. Sialon retained its hardness but it dropped very low at the interface layer. The absence of crack at the joint in all samples could be contributed from the ductility characteristic of the reaction layer which compensated the residual stress that was formed upon the cooling process.

Lévy flight with absorption: A model for diffusing diffusivity with long tails

Science.gov (United States)

Jain, Rohit; Sebastian, K. L.

2017-03-01

We consider diffusion of a particle in rearranging environment, so that the diffusivity of the particle is a stochastic function of time. In our previous model of "diffusing diffusivity" [Jain and Sebastian, J. Phys. Chem. B 120, 3988 (2016), 10.1021/acs.jpcb.6b01527], it was shown that the mean square displacement of particle remains Fickian, i.e., ∝T at all times, but the probability distribution of particle displacement is not Gaussian at all times. It is exponential at short times and crosses over to become Gaussian only in a large time limit in the case where the distribution of D in that model has a steady state limit which is exponential, i.e., πe(D ) ˜e-D /D0 . In the present study, we model the diffusivity of a particle as a Lévy flight process so that D has a power-law tailed distribution, viz., πe(D ) ˜D-1 -α with 0 <α <1 . We find that in the short time limit, the width of displacement distribution is proportional to √{T }, implying that the diffusion is Fickian. But for long times, the width is proportional to T1 /2 α which is a characteristic of anomalous diffusion. The distribution function for the displacement of the particle is found to be a symmetric stable distribution with a stability index 2 α which preserves its shape at all times.

Clinical relevance of and risk factors associated with medication administration time errors

NARCIS (Netherlands)

Teunissen, R.; Bos, J.; Pot, H.; Pluim, M.; Kramers, C.

2013-01-01

PURPOSE: The clinical relevance of and risk factors associated with errors related to medication administration time were studied. METHODS: In this explorative study, 66 medication administration rounds were studied on two wards (surgery and neurology) of a hospital. Data on medication errors were

On an adaptive time stepping strategy for solving nonlinear diffusion equations

International Nuclear Information System (INIS)

Chen, K.; Baines, M.J.; Sweby, P.K.

1993-01-01

A new time step selection procedure is proposed for solving non- linear diffusion equations. It has been implemented in the ASWR finite element code of Lorenz and Svoboda [10] for 2D semiconductor process modelling diffusion equations. The strategy is based on equi-distributing the local truncation errors of the numerical scheme. The use of B-splines for interpolation (as well as for the trial space) results in a banded and diagonally dominant matrix. The approximate inverse of such a matrix can be provided to a high degree of accuracy by another banded matrix, which in turn can be used to work out the approximate finite difference scheme corresponding to the ASWR finite element method, and further to calculate estimates of the local truncation errors of the numerical scheme. Numerical experiments on six full simulation problems arising in semiconductor process modelling have been carried out. Results show that our proposed strategy is more efficient and better conserves the total mass. 18 refs., 6 figs., 2 tabs

Diffusion archeology for diffusion progression history reconstruction

OpenAIRE

Sefer, Emre; Kingsford, Carl

2015-01-01

Diffusion through graphs can be used to model many real-world processes, such as the spread of diseases, social network memes, computer viruses, or water contaminants. Often, a real-world diffusion cannot be directly observed while it is occurring — perhaps it is not noticed until some time has passed, continuous monitoring is too costly, or privacy concerns limit data access. This leads to the need to reconstruct how the present state of the diffusion came to be from partial d...

Reaction time for trimolecular reactions in compartment-based reaction-diffusion models

Science.gov (United States)

Li, Fei; Chen, Minghan; Erban, Radek; Cao, Yang

2018-05-01

Trimolecular reaction models are investigated in the compartment-based (lattice-based) framework for stochastic reaction-diffusion modeling. The formulae for the first collision time and the mean reaction time are derived for the case where three molecules are present in the solution under periodic boundary conditions. For the case of reflecting boundary conditions, similar formulae are obtained using a computer-assisted approach. The accuracy of these formulae is further verified through comparison with numerical results. The presented derivation is based on the first passage time analysis of Montroll [J. Math. Phys. 10, 753 (1969)]. Montroll's results for two-dimensional lattice-based random walks are adapted and applied to compartment-based models of trimolecular reactions, which are studied in one-dimensional or pseudo one-dimensional domains.

DASH-FP, Multicomponent Time-Dependent Concentration Diffusion

International Nuclear Information System (INIS)

Apperson, C.E. Jr.; Carruthers, L.M.; Shinn, J.F.; Lee, C.E.

1995-01-01

1 - Description of program or function: The program DASH-FP calculates the transient concentration of multiple diffusing species with radioactive decay. 2 - Method of solution: Uses finite difference and exponential operator techniques

Diffusion of calcium and fluride ions in bovine enamel

NARCIS (Netherlands)

Flim, Gerrit Jan

1976-01-01

This thesis deals with the diffusion of calcium and fluoride ions in bovine enamel, Special attention was given to the mechanism of this diffusion, The experiments were carried out with radioactive labeled ions. The information obtained is relevant with respect to de- and remineralization processes

Solution of the atmospheric diffusion equation with a realistic diffusion coefficient and time dependent mixing height

International Nuclear Information System (INIS)

Mayhoub, A.B.; Etman, S.M.

1997-01-01

One dimensional model for the dispersion of a passive atmospheric contaminant (neglecting chemical reactions) in the atmospheric boundary layer is introduced. The differential equation representing the dispersion of pollutants is solved on the basis of gradient-transfer theory (K- theory). The present approach deals with a more appropriate and realistic profile for the diffusion coefficient K, which is expressed in terms of the friction velocity U, the vertical coordinate z and the depth of the mixing layer h, which is taken time dependent. After some mathematical simplification, the equation analytic obtained solution can be easily applied to case study concerning atmospheric dispersion of pollutants

Diffusion in condensed matter methods, materials, models

CERN Document Server

Kärger, Jörg

2005-01-01

Diffusion as the process of particle transport due to stochastic movement is a phenomenon of crucial relevance for a large variety of processes and materials. This comprehensive, handbook- style survey of diffusion in condensed matter gives detailed insight into diffusion as the process of particle transport due to stochastic movement. Leading experts in the field describe in 23 chapters the different aspects of diffusion, covering microscopic and macroscopic experimental techniques and exemplary results for various classes of solids, liquids and interfaces as well as several theoretical concepts and models. Students and scientists in physics, chemistry, materials science, and biology will benefit from this detailed compilation.

Repeated diffusion MRI reveals earliest time point for stratification of radiotherapy response in brain metastases

DEFF Research Database (Denmark)

Mahmood, Faisal; Johannesen, Helle H; Geertsen, Poul

2017-01-01

An imaging biomarker for early prediction of treatment response potentially provides a non-invasive tool for better prognostics and individualized management of the disease. Radiotherapy (RT) response is generally related to changes in gross tumor volume manifesting months later. In this prospect......An imaging biomarker for early prediction of treatment response potentially provides a non-invasive tool for better prognostics and individualized management of the disease. Radiotherapy (RT) response is generally related to changes in gross tumor volume manifesting months later....... In this prospective study we investigated the apparent diffusion coefficient (ADC), perfusion fraction and pseudo diffusion coefficient derived from diffusion weighted MRI as potential early biomarkers for radiotherapy response of brain metastases. It was a particular aim to assess the optimal time point...

Strong Maximum Principle for Multi-Term Time-Fractional Diffusion Equations and its Application to an Inverse Source Problem

OpenAIRE

Liu, Yikan

2015-01-01

In this paper, we establish a strong maximum principle for fractional diffusion equations with multiple Caputo derivatives in time, and investigate a related inverse problem of practical importance. Exploiting the solution properties and the involved multinomial Mittag-Leffler functions, we improve the weak maximum principle for the multi-term time-fractional diffusion equation to a stronger one, which is parallel to that for its single-term counterpart as expected. As a direct application, w...

[Relevant factors of early puberty timing in urban primary schools in Chongqing].

Science.gov (United States)

Luo, Yan; Liu, Qin; Wen, Yi; Liu, Shudan; Lei, Xun; Wang, Hong

2016-05-01

To investigate the status of puberty timing and relevant factors of early puberty timing in children from grade one to four in urban primary schools of Chongqing. According to the purposive sample method, four urban primary schools in Chongqing were selected and of which 1471 children from grade one to four who have obtained informed consent were recruited. Questionnaire survey on social-demographic characteristics and family environment (e.g., age, parents' relationship, diet and lifestyle, etc), and Pubertal Development Scale (PDS) survey and physical examination (measurements of height, weight, pubertal development status, etc) were conducted. P25, P50, P75 ages of each important pubertal event were calculated by probit regression. Univariate and multivariate analysis were used to analyze relevant factors. The detection rate of early puberty timing was 17.7%, and the median ages of the onset of breast and testicular development were 10.77 and 11.48 years old, respectively. Multivariate logistic regression showed that early puberty timing occurred more likely in girls than in boys (OR = 0.561, 95% CI 0.406-0.774), and bad relationship between parents (OR = 1.320, 95% CI 1.007-1.729) and hair-products-use (OR = 1.685, 95%, CI 1.028-2.762) were risk factors of early puberty timing. Early onset of puberty in urban Chongqing is still exist. Gender, parents' relationship, and hair-products-use have an essential impact on early puberty timing.

Diffusion properties of conventional and calcium-sensitive MRI contrast agents in the rat cerebral cortex.

Science.gov (United States)

Hagberg, Gisela E; Mamedov, Ilgar; Power, Anthony; Beyerlein, Michael; Merkle, Hellmut; Kiselev, Valerij G; Dhingra, Kirti; Kubìček, Vojtĕch; Angelovski, Goran; Logothetis, Nikos K

2014-01-01

Calcium-sensitive MRI contrast agents can only yield quantitative results if the agent concentration in the tissue is known. The agent concentration could be determined by diffusion modeling, if relevant parameters were available. We have established an MRI-based method capable of determining diffusion properties of conventional and calcium-sensitive agents. Simulations and experiments demonstrate that the method is applicable both for conventional contrast agents with a fixed relaxivity value and for calcium-sensitive contrast agents. The full pharmacokinetic time-course of gadolinium concentration estimates was observed by MRI before, during and after intracerebral administration of the agent, and the effective diffusion coefficient D* was determined by voxel-wise fitting of the solution to the diffusion equation. The method yielded whole brain coverage with a high spatial and temporal sampling. The use of two types of MRI sequences for sampling of the diffusion time courses was investigated: Look-Locker-based quantitative T(1) mapping, and T(1) -weighted MRI. The observation times of the proposed MRI method is long (up to 20 h) and consequently the diffusion distances covered are also long (2-4 mm). Despite this difference, the D* values in vivo were in agreement with previous findings using optical measurement techniques, based on observation times of a few minutes. The effective diffusion coefficient determined for the calcium-sensitive contrast agents may be used to determine local tissue concentrations and to design infusion protocols that maintain the agent concentration at a steady state, thereby enabling quantitative sensing of the local calcium concentration. Copyright © 2014 John Wiley & Sons, Ltd.

Thermodynamics, diffusion and the Kirkendall effect in solids

CERN Document Server

Paul, Aloke; Vuorinen, Vesa; Divinski, Sergiy V

2014-01-01

Covering both basic and advanced thermodynamic and phase  principles,  as well as providing stability diagrams relevant for diffusion studies, Thermodynamics, Diffusion and the Kirkendall Effect in Solids maximizes reader insights into Fick’s laws of diffusion, atomic mechanisms, interdiffusion, intrinsic diffusion, tracer diffusion and the Kirkendall effect. Recent advances in the area of interdiffusion will be introduced, while the many practical examples and large number of illustrations given will serve to aid researches working in this area in learning the practical evaluation of various diffusion parameters from experimental results. With a unique approach to the two main focal points in solid state transformations, energetics (thermodynamics) and kinetics (interdiffusion) are extensively studied and their combined use in practise is discussed. Recent developments in the area of Kirkendall effect, grain boundary diffusion and multicomponent diffusion are also covered extensively. This book will appe...

Position-dependent radiative transfer as a tool for studying Anderson localization: Delay time, time-reversal and coherent backscattering

Science.gov (United States)

van Tiggelen, B. A.; Skipetrov, S. E.; Page, J. H.

2017-05-01

Previous work has established that the localized regime of wave transport in open media is characterized by a position-dependent diffusion coefficient. In this work we study how the concept of position-dependent diffusion affects the delay time, the transverse confinement, the coherent backscattering, and the time reversal of waves. Definitions of energy transport velocity of localized waves are proposed. We start with a phenomenological model of radiative transfer and then present a novel perturbational approach based on the self-consistent theory of localization. The latter allows us to obtain results relevant for realistic experiments in disordered quasi-1D wave guides and 3D slabs.

An analytic algorithm for the space-time fractional reaction-diffusion equation

Directory of Open Access Journals (Sweden)

M. G. Brikaa

2015-11-01

Full Text Available In this paper, we solve the space-time fractional reaction-diffusion equation by the fractional homotopy analysis method. Solutions of different examples of the reaction term will be computed and investigated. The approximation solutions of the studied models will be put in the form of convergent series to be easily computed and simulated. Comparison with the approximation solution of the classical case of the studied modeled with their approximation errors will also be studied.

Global Regularity and Time Decay for the 2D Magnetohydrodynamic Equations with Fractional Dissipation and Partial Magnetic Diffusion

Science.gov (United States)

Dong, Bo-Qing; Jia, Yan; Li, Jingna; Wu, Jiahong

2018-05-01

This paper focuses on a system of the 2D magnetohydrodynamic (MHD) equations with the kinematic dissipation given by the fractional operator (-Δ )^α and the magnetic diffusion by partial Laplacian. We are able to show that this system with any α >0 always possesses a unique global smooth solution when the initial data is sufficiently smooth. In addition, we make a detailed study on the large-time behavior of these smooth solutions and obtain optimal large-time decay rates. Since the magnetic diffusion is only partial here, some classical tools such as the maximal regularity property for the 2D heat operator can no longer be applied. A key observation on the structure of the MHD equations allows us to get around the difficulties due to the lack of full Laplacian magnetic diffusion. The results presented here are the sharpest on the global regularity problem for the 2D MHD equations with only partial magnetic diffusion.

An inverse diffusivity problem for the helium production–diffusion equation

International Nuclear Information System (INIS)

Bao, Gang; Xu, Xiang

2012-01-01

Thermochronology is a technique for the extraction of information about the thermal history of rocks. Such information is crucial for determining the depth below the surface at which rocks were located at a given time (Bao G et al 2011 Commun. Comput. Phys. 9 129). Mathematically, extracting the time–temperature path can be formulated as an inverse diffusivity problem for the helium production–diffusion equation which is the underlying process of thermochronology. In this paper, to reconstruct the diffusivity which depends on space only and accounts for the structural information of rocks, a local Hölder conditional stability is obtained by a Carleman estimate. A uniqueness result is also proven for extracting the thermal history, i.e. identifying the time-dependant part of the diffusion coefficient, provided that it is analytical with respect to time. Numerical examples are presented to illustrate the validity and effectiveness of the proposed regularization scheme. (paper)

Speckle-scale focusing in the diffusive regime with time reversal of variance-encoded light (TROVE)

Science.gov (United States)

Judkewitz, Benjamin; Wang, Ying Min; Horstmeyer, Roarke; Mathy, Alexandre; Yang, Changhuei

2013-04-01

Focusing of light in the diffusive regime inside scattering media has long been considered impossible. Recently, this limitation has been overcome with time reversal of ultrasound-encoded light (TRUE), but the resolution of this approach is fundamentally limited by the large number of optical modes within the ultrasound focus. Here, we introduce a new approach, time reversal of variance-encoded light (TROVE), which demixes these spatial modes by variance encoding to break the resolution barrier imposed by the ultrasound. By encoding individual spatial modes inside the scattering sample with unique variances, we effectively uncouple the system resolution from the size of the ultrasound focus. This enables us to demonstrate optical focusing and imaging with diffuse light at an unprecedented, speckle-scale lateral resolution of ~5 µm.

Speckle-scale focusing in the diffusive regime with time-reversal of variance-encoded light (TROVE).

Science.gov (United States)

Judkewitz, Benjamin; Wang, Ying Min; Horstmeyer, Roarke; Mathy, Alexandre; Yang, Changhuei

2013-04-01

Focusing of light in the diffusive regime inside scattering media has long been considered impossible. Recently, this limitation has been overcome with time reversal of ultrasound-encoded light (TRUE), but the resolution of this approach is fundamentally limited by the large number of optical modes within the ultrasound focus. Here, we introduce a new approach, time reversal of variance-encoded light (TROVE), which demixes these spatial modes by variance-encoding to break the resolution barrier imposed by the ultrasound. By encoding individual spatial modes inside the scattering sample with unique variances, we effectively uncouple the system resolution from the size of the ultrasound focus. This enables us to demonstrate optical focusing and imaging with diffuse light at unprecedented, speckle-scale lateral resolution of ~ 5 μm.

Development of high time-resolution laser flash equipment for thermal diffusivity measurements using miniature-size specimens

International Nuclear Information System (INIS)

Shikama, Tatsuo; Namba, Chusei; Kosuda, Michinori; Maeda, Yukio.

1994-01-01

For measurements of thermal diffusivity of miniature-size specimens heavily irradiated by neutrons, a new Q-switched laser-flash instrument was developed. In the present instrument the time-resolution was improved to 0.1 ms by using a laser-pulse width of 25 ns. The realization of high time-resolution made it possible to measure the thermal diffusivity of thin specimens. It is expected that copper of 0.7 mm thick, and SUS 304 of 0.1 mm could be used for the measurements. In case of ATJ graphite, 0.5 mm thick specimen could be used for the reliable measurement in the temperature range of 300-1300 K. (author)

Diffusion relaxation times of nonequilibrium isolated small bodies and their solid phase ensembles to equilibrium states

Science.gov (United States)

Tovbin, Yu. K.

2017-08-01

The possibility of obtaining analytical estimates in a diffusion approximation of the times needed by nonequilibrium small bodies to relax to their equilibrium states based on knowledge of the mass transfer coefficient is considered. This coefficient is expressed as the product of the self-diffusion coefficient and the thermodynamic factor. A set of equations for the diffusion transport of mixture components is formulated, characteristic scales of the size of microheterogeneous phases are identified, and effective mass transfer coefficients are constructed for them. Allowing for the developed interface of coexisting and immiscible phases along with the porosity of solid phases is discussed. This approach can be applied to the diffusion equalization of concentrations of solid mixture components in many physicochemical systems: the mutual diffusion of components in multicomponent systems (alloys, semiconductors, solid mixtures of inert gases) and the mass transfer of an absorbed mobile component in the voids of a matrix consisting of slow components or a mixed composition of mobile and slow components (e.g., hydrogen in metals, oxygen in oxides, and the transfer of molecules through membranes of different natures, including polymeric).

A combined kinetic and diffusion model for pyrite oxidation in tailings - a change in controls with time

International Nuclear Information System (INIS)

Elberling, B.; Nicholson, R.V.; Scharer, J.M.

1994-01-01

Acidic drainage from the oxidation of mine tailing wastes is an important environmental problem. The purpose of this paper is to develop a model (1) to simulate the rate of oxidation of pyrite over time, (2) to verify the importance of chemical kinetic control and diffusion control on the oxidation rate with time and, (3) to evaluate the sensitivity of the model to critical parameters of the tailings, such as grain size, pyrite content and the effective diffusion coefficient. The source code comprises four main modules including parameter allocation (kinetics, transport), sulphide oxidation (shrinking particle), oxygen transport and pyrite mass balance. The results show that high oxidation rates are observed in the initial time after tailings deposition. During this initial period of high rates, an apparent shift occurs from kinetic to diffusional control over a period of time that depends on the composition and properties of the tailings. Based on the simulation results, it is evident that the overall rate of oxidation after a few years will be controlled dominantly by the diffusion of oxygen rather than by biological or non-biological kinetics in the tailings

SYNTH-C, Steady-State and Time-Dependent 3-D Neutron Diffusion with Thermohydraulic Feedback

Energy Technology Data Exchange (ETDEWEB)

Brega, E [ENEL-CRTN, Bastioni di Porta Volta 10, Milan (Italy); Salina, E [A.R.S. Spa, Viale Maino 35, Milan (Italy)

1980-04-01

1 - Description of problem or function: SYNTH-C-STEADY and SYNTH-C- TRANS solve respectively the steady-state and time-dependent few- group neutron diffusion equations in three dimensions x,y,z in the presence of fuel temperature and thermal-hydraulic feedback. The neutron diffusion and delayed precursor equations are approximated by a space-time (z,t) synthesis method with axially discontinuous trial functions. Three thermal-hydraulic and fuel heat transfer models are available viz. COBRA-3C/MIT model, lumped parameter (WIGL) model and adiabatic fuel heat-up model. 2 - Method of solution: The steady-state and time-dependent synthesis equations are solved respectively by the Wielandt's power method and by the theta-difference method (in time), both coupled with a block factorization technique and double precision arithmetic. The thermal-hydraulic model equations are solved by fully implicit finite differences (WIGL) or explicit-implicit difference techniques with iterations (COBRA-EC/MIT). 3 - Restrictions on the complexity of the problem: Except for the few- group limitation, the programs have no other fixed limitation so the ability to run a problem depends only on the available computer storage.

Generalized Runge-Kutta method for two- and three-dimensional space-time diffusion equations with a variable time step

International Nuclear Information System (INIS)

Aboanber, A.E.; Hamada, Y.M.

2008-01-01

An extensive knowledge of the spatial power distribution is required for the design and analysis of different types of current-generation reactors, and that requires the development of more sophisticated theoretical methods. Therefore, the need to develop new methods for multidimensional transient reactor analysis still exists. The objective of this paper is to develop a computationally efficient numerical method for solving the multigroup, multidimensional, static and transient neutron diffusion kinetics equations. A generalized Runge-Kutta method has been developed for the numerical integration of the stiff space-time diffusion equations. The method is fourth-order accurate, using an embedded third-order solution to arrive at an estimate of the truncation error for automatic time step control. In addition, the A(α)-stability properties of the method are investigated. The analyses of two- and three-dimensional benchmark problems as well as static and transient problems, demonstrate that very accurate solutions can be obtained with assembly-sized spatial meshes. Preliminary numerical evaluations using two- and three-dimensional finite difference codes showed that the presented generalized Runge-Kutta method is highly accurate and efficient when compared with other optimized iterative numerical and conventional finite difference methods

Reduction of Poisson noise in measured time-resolved data for time-domain diffuse optical tomography.

Science.gov (United States)

Okawa, S; Endo, Y; Hoshi, Y; Yamada, Y

2012-01-01

A method to reduce noise for time-domain diffuse optical tomography (DOT) is proposed. Poisson noise which contaminates time-resolved photon counting data is reduced by use of maximum a posteriori estimation. The noise-free data are modeled as a Markov random process, and the measured time-resolved data are assumed as Poisson distributed random variables. The posterior probability of the occurrence of the noise-free data is formulated. By maximizing the probability, the noise-free data are estimated, and the Poisson noise is reduced as a result. The performances of the Poisson noise reduction are demonstrated in some experiments of the image reconstruction of time-domain DOT. In simulations, the proposed method reduces the relative error between the noise-free and noisy data to about one thirtieth, and the reconstructed DOT image was smoothed by the proposed noise reduction. The variance of the reconstructed absorption coefficients decreased by 22% in a phantom experiment. The quality of DOT, which can be applied to breast cancer screening etc., is improved by the proposed noise reduction.

Uniqueness and reconstruction of an unknown semilinear term in a time-fractional reaction–diffusion equation

KAUST Repository

Luchko, Yuri

2013-05-30

In this paper, we consider a reaction-diffusion problem with an unknown nonlinear source function that has to be determined from overposed data. The underlying model is in the form of a time-fractional reaction-diffusion equation and the work generalizes some known results for the inverse problems posed for PDEs of parabolic type. For the inverse problem under consideration, a uniqueness result is proved and a numerical algorithm with some theoretical qualification is presented in the one-dimensional case. The key both to the uniqueness result and to the numerical algorithm relies on the maximum principle which has recently been shown to hold for the fractional diffusion equation. In order to show the effectiveness of the proposed method, results of numerical simulations are presented. © 2013 IOP Publishing Ltd.

Toward the existence of ultrafast diffusion paths in Cu with a gradient microstructure: Room temperature diffusion of Ni

Science.gov (United States)

Wang, Z. B.; Lu, K.; Wilde, G.; Divinski, S.

2008-09-01

Room temperature diffusion of Ni63 in Cu with a gradient microstructure prepared by surface mechanical attrition treatment (SMAT) was investigated by applying the radiotracer technique. The results reveal significant penetration of Ni into the nanostructured layer. The relevant diffusivity is higher than that along the conventional high-angle grain boundaries by about six orders of magnitude. This behavior is associated with a higher energy state of internal interfaces produced via plastic deformation. The diffusivity in the top surface layer is somewhat smaller than that in the subsurface layer. This fact is related to nanotwin formation in the former during SMAT.

Magnetic diffuse scattering: a theorist's perspective

International Nuclear Information System (INIS)

Long, M.W.

1996-01-01

We attempt to show that magnetic diffuse scattering is the natural probe for frustrated antiferromagnetism. Comparison between nuclear and magnetic diffuse scattering compares the range of atomic clustering with the range of the magnetic impurity. At low temperature frustration is expected to lead to large differences which are a natural signature for the relevance of such frustration effects. We provide some elementary examples in first-row transition metals which display fairly dramatic effects. (author) 11 figs., tabs., 8 refs

Computational Diffusion MRI : MICCAI Workshop

CERN Document Server

Grussu, Francesco; Ning, Lipeng; Tax, Chantal; Veraart, Jelle

2018-01-01

This volume presents the latest developments in the highly active and rapidly growing field of diffusion MRI. The reader will find numerous contributions covering a broad range of topics, from the mathematical foundations of the diffusion process and signal generation, to new computational methods and estimation techniques for the in-vivo recovery of microstructural and connectivity features, as well as frontline applications in neuroscience research and clinical practice. These proceedings contain the papers presented at the 2017 MICCAI Workshop on Computational Diffusion MRI (CDMRI’17) held in Québec, Canada on September 10, 2017, sharing new perspectives on the most recent research challenges for those currently working in the field, but also offering a valuable starting point for anyone interested in learning computational techniques in diffusion MRI. This book includes rigorous mathematical derivations, a large number of rich, full-colour visualisations and clinically relevant results. As such, it wil...

Thermal diffuse scattering in time-of-flight neutron diffraction studied on SBN single crystals

International Nuclear Information System (INIS)

Prokert, F.; Savenko, B.N.; Balagurov, A.M.

1994-01-01

At time-of-flight (TOF) diffractometer D N-2, installed at the pulsed reactor IBR-2 in Dubna, Sr x Ba 1-x Nb 2 O 6 mixed single crystals (SBN-x) of different compositions (0.50 < x< 0.75) were investigated between 15 and 773 K. The diffraction patterns were found to be strongly influenced by the thermal diffuse scattering (TDS). The appearance of the TDS from the long wavelength acoustic models of vibration in single crystals is characterized by the ratio of the velocity of sound to the velocity of neutron. Due to the nature of the TOF Laue diffraction technique used on D N-2, the TDS around Bragg peaks has rather a complex profile. An understanding of the TDS close to Bragg peaks is essential in allowing the extraction of the diffuse scattering occurring at the diffuse ferroelectric phase transition in SBN crystals. 11 refs.; 9 figs.; 1 tab. (author)

Diffusion tensor optical coherence tomography

Science.gov (United States)

Marks, Daniel L.; Blackmon, Richard L.; Oldenburg, Amy L.

2018-01-01

In situ measurements of diffusive particle transport provide insight into tissue architecture, drug delivery, and cellular function. Analogous to diffusion-tensor magnetic resonance imaging (DT-MRI), where the anisotropic diffusion of water molecules is mapped on the millimeter scale to elucidate the fibrous structure of tissue, here we propose diffusion-tensor optical coherence tomography (DT-OCT) for measuring directional diffusivity and flow of optically scattering particles within tissue. Because DT-OCT is sensitive to the sub-resolution motion of Brownian particles as they are constrained by tissue macromolecules, it has the potential to quantify nanoporous anisotropic tissue structure at micrometer resolution as relevant to extracellular matrices, neurons, and capillaries. Here we derive the principles of DT-OCT, relating the detected optical signal from a minimum of six probe beams with the six unique diffusion tensor and three flow vector components. The optimal geometry of the probe beams is determined given a finite numerical aperture, and a high-speed hardware implementation is proposed. Finally, Monte Carlo simulations are employed to assess the ability of the proposed DT-OCT system to quantify anisotropic diffusion of nanoparticles in a collagen matrix, an extracellular constituent that is known to become highly aligned during tumor development.

An in situ method for real-time monitoring of soil gas diffusivity

Science.gov (United States)

Laemmel, Thomas; Maier, Martin; Schack-Kirchner, Helmer; Lang, Friederike

2016-04-01

of soil water infiltration deeper into the soil on soil gas diffusivity could be observed during the following hours. Our new DS determination device can be quickly and easily installed and allows for monitoring continuously soil gas transport over a long time. It allows following modifications of soil gas diffusivity due to rain events. In addition it enables the analysis of non-diffusive soil gas transport processes.

EEG dynamical correlates of focal and diffuse causes of coma.

Science.gov (United States)

Kafashan, MohammadMehdi; Ryu, Shoko; Hargis, Mitchell J; Laurido-Soto, Osvaldo; Roberts, Debra E; Thontakudi, Akshay; Eisenman, Lawrence; Kummer, Terrance T; Ching, ShiNung

2017-11-15

Rapidly determining the causes of a depressed level of consciousness (DLOC) including coma is a common clinical challenge. Quantitative analysis of the electroencephalogram (EEG) has the potential to improve DLOC assessment by providing readily deployable, temporally detailed characterization of brain activity in such patients. While used commonly for seizure detection, EEG-based assessment of DLOC etiology is less well-established. As a first step towards etiological diagnosis, we sought to distinguish focal and diffuse causes of DLOC through assessment of temporal dynamics within EEG signals. We retrospectively analyzed EEG recordings from 40 patients with DLOC with consensus focal or diffuse culprit pathology. For each recording, we performed a suite of time-series analyses, then used a statistical framework to identify which analyses (features) could be used to distinguish between focal and diffuse cases. Using cross-validation approaches, we identified several spectral and non-spectral EEG features that were significantly different between DLOC patients with focal vs. diffuse etiologies, enabling EEG-based classification with an accuracy of 76%. Our findings suggest that DLOC due to focal vs. diffuse injuries differ along several electrophysiological parameters. These results may form the basis of future classification strategies for DLOC and coma that are more etiologically-specific and therefore therapeutically-relevant.

Lie Symmetry of the Diffusive Lotka–Volterra System with Time-Dependent Coefficients

Directory of Open Access Journals (Sweden)

Vasyl’ Davydovych

2018-02-01

Full Text Available Lie symmetry classification of the diffusive Lotka–Volterra system with time-dependent coefficients in the case of a single space variable is studied. A set of such symmetries in an explicit form is constructed. A nontrivial ansatz reducing the Lotka–Volterra system with correctly-specified coefficients to the system of ordinary differential equations (ODEs and an example of the exact solution with a biological interpretation are found.

Analysis and correction of gradient nonlinearity bias in apparent diffusion coefficient measurements.

Science.gov (United States)

Malyarenko, Dariya I; Ross, Brian D; Chenevert, Thomas L

2014-03-01

Gradient nonlinearity of MRI systems leads to spatially dependent b-values and consequently high non-uniformity errors (10-20%) in apparent diffusion coefficient (ADC) measurements over clinically relevant field-of-views. This work seeks practical correction procedure that effectively reduces observed ADC bias for media of arbitrary anisotropy in the fewest measurements. All-inclusive bias analysis considers spatial and time-domain cross-terms for diffusion and imaging gradients. The proposed correction is based on rotation of the gradient nonlinearity tensor into the diffusion gradient frame where spatial bias of b-matrix can be approximated by its Euclidean norm. Correction efficiency of the proposed procedure is numerically evaluated for a range of model diffusion tensor anisotropies and orientations. Spatial dependence of nonlinearity correction terms accounts for the bulk (75-95%) of ADC bias for FA = 0.3-0.9. Residual ADC non-uniformity errors are amplified for anisotropic diffusion. This approximation obviates need for full diffusion tensor measurement and diagonalization to derive a corrected ADC. Practical scenarios are outlined for implementation of the correction on clinical MRI systems. The proposed simplified correction algorithm appears sufficient to control ADC non-uniformity errors in clinical studies using three orthogonal diffusion measurements. The most efficient reduction of ADC bias for anisotropic medium is achieved with non-lab-based diffusion gradients. Copyright © 2013 Wiley Periodicals, Inc.

A meshless method for solving two-dimensional variable-order time fractional advection-diffusion equation

Science.gov (United States)

Tayebi, A.; Shekari, Y.; Heydari, M. H.

2017-07-01

Several physical phenomena such as transformation of pollutants, energy, particles and many others can be described by the well-known convection-diffusion equation which is a combination of the diffusion and advection equations. In this paper, this equation is generalized with the concept of variable-order fractional derivatives. The generalized equation is called variable-order time fractional advection-diffusion equation (V-OTFA-DE). An accurate and robust meshless method based on the moving least squares (MLS) approximation and the finite difference scheme is proposed for its numerical solution on two-dimensional (2-D) arbitrary domains. In the time domain, the finite difference technique with a θ-weighted scheme and in the space domain, the MLS approximation are employed to obtain appropriate semi-discrete solutions. Since the newly developed method is a meshless approach, it does not require any background mesh structure to obtain semi-discrete solutions of the problem under consideration, and the numerical solutions are constructed entirely based on a set of scattered nodes. The proposed method is validated in solving three different examples including two benchmark problems and an applied problem of pollutant distribution in the atmosphere. In all such cases, the obtained results show that the proposed method is very accurate and robust. Moreover, a remarkable property so-called positive scheme for the proposed method is observed in solving concentration transport phenomena.

Effect of holding time on the microstructure and strength of tungsten/ferritic steel joints diffusion bonded with a nickel interlayer

International Nuclear Information System (INIS)

Zhong Zhihong; Hinoki, Tatsuya; Kohyama, Akira

2009-01-01

The microstructural development and mechanical properties of a tungsten/ferritic steel diffusion joint with a Ni interlayer, bonded at 900 deg. C under vacuum for 0.5-2 h, were investigated. Cross-sectional images of the W/Ni diffusion zone indicate the presence of a Ni-rich solid solution, Ni(W), for holding times up to 1.5 h. However, an intermetallic compound Ni 4 W grew as a distinguishable layer between the W and Ni(W) when the holding time was increased to 2 h. The growth behavior of diffusion layers and their growth mechanism is discussed. On the other hand, smooth changes in concentration of various elements across the Ni/steel interface were observed for the joints annealed at the holding time studied. An average bond strength of 215 MPa was obtained for the joint bonded for 1 h; this bond strength decreased as holding time increased. Variations in the strength of the joints was significantly related to the microstructural development of the diffusion zone. The formation of Ni 4 W and a solid solution phase enhanced hardness at the interfaces but reduced strength of the joints.

Preconditioned iterative methods for space-time fractional advection-diffusion equations

Science.gov (United States)

Zhao, Zhi; Jin, Xiao-Qing; Lin, Matthew M.

2016-08-01

In this paper, we propose practical numerical methods for solving a class of initial-boundary value problems of space-time fractional advection-diffusion equations. First, we propose an implicit method based on two-sided Grünwald formulae and discuss its stability and consistency. Then, we develop the preconditioned generalized minimal residual (preconditioned GMRES) method and preconditioned conjugate gradient normal residual (preconditioned CGNR) method with easily constructed preconditioners. Importantly, because resulting systems are Toeplitz-like, fast Fourier transform can be applied to significantly reduce the computational cost. We perform numerical experiments to demonstrate the efficiency of our preconditioners, even in cases with variable coefficients.

An inverse problem for a one-dimensional time-fractional diffusion problem

KAUST Repository

Jin, Bangti

2012-06-26

We study an inverse problem of recovering a spatially varying potential term in a one-dimensional time-fractional diffusion equation from the flux measurements taken at a single fixed time corresponding to a given set of input sources. The unique identifiability of the potential is shown for two cases, i.e. the flux at one end and the net flux, provided that the set of input sources forms a complete basis in L 2(0, 1). An algorithm of the quasi-Newton type is proposed for the efficient and accurate reconstruction of the coefficient from finite data, and the injectivity of the Jacobian is discussed. Numerical results for both exact and noisy data are presented. © 2012 IOP Publishing Ltd.

A critical comparison of constant and pulsed flow systems exploiting gas diffusion.

Science.gov (United States)

Silva, Claudineia Rodrigues; Henriquez, Camelia; Frizzarin, Rejane Mara; Zagatto, Elias Ayres Guidetti; Cerda, Victor

2016-02-01

Considering the beneficial aspects arising from the implementation of pulsed flows in flow analysis, and the relevance of in-line gas diffusion as an analyte separation/concentration step, influence of flow pattern in flow systems with in-line gas diffusion was critically investigated. To this end, constant or pulsed flows delivered by syringe or solenoid pumps were exploited. For each flow pattern, two variants involving different interaction times of the donor with the acceptor streams were studied. In the first one, both the acceptor and donor streams were continuously flowing, whereas in the second one, the acceptor was stopped during the gas diffusion step. Four different volatile species (ammonia, ethanol, carbon dioxide and hydrogen sulfide) were selected as models. For the flow patterns and variants studied, the efficiencies of mass transport in the gas diffusion process were compared, and sensitivity, repeatability, sampling frequency and recorded peak shape were evaluated. Analysis of the results revealed that sensitivity is strongly dependent on the implemented variant, and that flow pattern is an important feature in flow systems with in-line gas diffusion. Copyright © 2015 Elsevier B.V. All rights reserved.

Noninvasive observation of skeletal muscle contraction using near-infrared time-resolved reflectance and diffusing-wave spectroscopy

Science.gov (United States)

Belau, Markus; Ninck, Markus; Hering, Gernot; Spinelli, Lorenzo; Contini, Davide; Torricelli, Alessandro; Gisler, Thomas

2010-09-01

We introduce a method for noninvasively measuring muscle contraction in vivo, based on near-infrared diffusing-wave spectroscopy (DWS). The method exploits the information about time-dependent shear motions within the contracting muscle that are contained in the temporal autocorrelation function g(1)(τ,t) of the multiply scattered light field measured as a function of lag time, τ, and time after stimulus, t. The analysis of g(1)(τ,t) measured on the human M. biceps brachii during repetitive electrical stimulation, using optical properties measured with time-resolved reflectance spectroscopy, shows that the tissue dynamics giving rise to the speckle fluctuations can be described by a combination of diffusion and shearing. The evolution of the tissue Cauchy strain e(t) shows a strong correlation with the force, indicating that a significant part of the shear observed with DWS is due to muscle contraction. The evolution of the DWS decay time shows quantitative differences between the M. biceps brachii and the M. gastrocnemius, suggesting that DWS allows to discriminate contraction of fast- and slow-twitch muscle fibers.

Pseudospectral operational matrix for numerical solution of single and multiterm time fractional diffusion equation

OpenAIRE

GHOLAMI, SAEID; BABOLIAN, ESMAIL; JAVIDI, MOHAMMAD

2016-01-01

This paper presents a new numerical approach to solve single and multiterm time fractional diffusion equations. In this work, the space dimension is discretized to the Gauss$-$Lobatto points. We use the normalized Grunwald approximation for the time dimension and a pseudospectral successive integration matrix for the space dimension. This approach shows that with fewer numbers of points, we can approximate the solution with more accuracy. Some examples with numerical results in tables and fig...

On positive periodic solution of periodic competition Lotka-Volterra system with time delay and diffusion

International Nuclear Information System (INIS)

Sun Wen; Chen Shihua; Hong Zhiming; Wang Changping

2007-01-01

A two-species periodic competition Lotka-Volterra system with time delay and diffusion is investigated. Some sufficient conditions of the existence of positive periodic solution are established for the system by using the continuation theorem of coincidence degree theory

Stability of The Synchronization Manifold in An All-To-All Time LAG- Diffusively Coupled Oscillators

Directory of Open Access Journals (Sweden)

Adu A.M. Wasike

2009-06-01

Full Text Available we consider a lattice system of identical oscillators that are all coupled to one another with a diffusive coupling that has a time lag. We use the natural splitting of the system into synchronized manifold and transversal manifold to estimate the value of the time lag for which the stability of the system follows from that without a time lag. Each oscillator has a unique periodic solution that is attracting.

In situ measurement of diffusivity

International Nuclear Information System (INIS)

Berne, F.; Pocachard, J.

2004-01-01

The mechanism of molecular diffusion controls the migration of contaminants in very low-permeability porous media, like underground facilities for the storage of hazardous waste. Determining of relevant diffusion coefficients is therefore of prime importance. A few techniques exist for in situ measurement of the quantity, but they suffer from many handicaps (duration, complexity and cost of the experiments). We propose here two innovative methods that have some potential to improve the situation. So far, we have found them feasible on the basis of design calculations and laboratory experiments. This work is presently protected by a patent. (author)

In situ measurement of diffusivity

International Nuclear Information System (INIS)

Berne, Ph.; Pocachard, J.

2005-01-01

The mechanism of molecular diffusion controls the migration of contaminants in very low-permeability porous media, like underground facilities for the storage of hazardous waste. Determining the relevant diffusion coefficients is, therefore, of prime importance. A few techniques exist for the in situ measurement of that quantity, but they suffer from many handicaps (duration, complexity and cost of the experiments). We propose here two innovative methods that have some potential to improve this situation. So far, we have found them feasible on the basis of design calculations and laboratory experiments. This work is presently protected by a patent. (author)

Real-Time Emulation of Nonstationary Channels in Safety-Relevant Vehicular Scenarios

Directory of Open Access Journals (Sweden)

Golsa Ghiaasi

2018-01-01

Full Text Available This paper proposes and discusses the architecture for a real-time vehicular channel emulator capable of reproducing the input/output behavior of nonstationary time-variant radio propagation channels in safety-relevant vehicular scenarios. The vehicular channel emulator architecture aims at a hardware implementation which requires minimal hardware complexity for emulating channels with the varying delay-Doppler characteristics of safety-relevant vehicular scenarios. The varying delay-Doppler characteristics require real-time updates to the multipath propagation model for each local stationarity region. The vehicular channel emulator is used for benchmarking the packet error performance of commercial off-the-shelf (COTS vehicular IEEE 802.11p modems and a fully software-defined radio-based IEEE 802.11p modem stack. The packet error ratio (PER estimated from temporal averaging over a single virtual drive and the packet error probability (PEP estimated from ensemble averaging over repeated virtual drives are evaluated and compared for the same vehicular scenario. The proposed architecture is realized as a virtual instrument on National Instruments™ LabVIEW. The National Instrument universal software radio peripheral with reconfigurable input-output (USRP-Rio 2953R is used as the software-defined radio platform for implementation; however, the results and considerations reported are of general purpose and can be applied to other platforms. Finally, we discuss the PER performance of the modem for two categories of vehicular channel models: a vehicular nonstationary channel model derived for urban single lane street crossing scenario of the DRIVEWAY’09 measurement campaign and the stationary ETSI models.

Global exponential stability of BAM neural networks with time-varying delays and diffusion terms

International Nuclear Information System (INIS)

Wan Li; Zhou Qinghua

2007-01-01

The stability property of bidirectional associate memory (BAM) neural networks with time-varying delays and diffusion terms are considered. By using the method of variation parameter and inequality technique, the delay-independent sufficient conditions to guarantee the uniqueness and global exponential stability of the equilibrium solution of such networks are established

Global exponential stability of BAM neural networks with time-varying delays and diffusion terms

Science.gov (United States)

Wan, Li; Zhou, Qinghua

2007-11-01

The stability property of bidirectional associate memory (BAM) neural networks with time-varying delays and diffusion terms are considered. By using the method of variation parameter and inequality technique, the delay-independent sufficient conditions to guarantee the uniqueness and global exponential stability of the equilibrium solution of such networks are established.

Flux-gradient relationships and soil-water diffusivity from curves of water content versus time

Energy Technology Data Exchange (ETDEWEB)

Nofziger, D.L.; Ahuja, L.R.; Swartzendruber, D.

Direct analysis of a family of curves of soil-water content vs. time at different fixed positions enables assessment of the flux-gradient relationship prior to the calculations of soil-water diffusivity. The method is evaluated on both smooth and random-error data generated from the solution of the horizontal soil-water intake problem with a known diffusivity function. Interpolation, differentiation, and intergration are carried out by least-squares curve fitting based on the 2 recently developed techniques of parabolic splines and sliding parabolas, with all computations performed by computer. Results are excellent for both smooth and random-error input data, whether in terms of recovering the original known diffusivity function, assessing the nature of the flux-gradient relationship, or in making the numerous checks and validations at various intermediate stages of computation. The method applies for any horizontal soil-wetting process independently of the specific boundary conditions, including water entry through a nonzero inlet resistance. It should be adaptable to horizontal dewatering, and extendable to vertical flow. (11 refs.)

Molecular dynamics on diffusive time scales from the phase-field-crystal equation.

Science.gov (United States)

Chan, Pak Yuen; Goldenfeld, Nigel; Dantzig, Jon

2009-03-01

We extend the phase-field-crystal model to accommodate exact atomic configurations and vacancies by requiring the order parameter to be non-negative. The resulting theory dictates the number of atoms and describes the motion of each of them. By solving the dynamical equation of the model, which is a partial differential equation, we are essentially performing molecular dynamics simulations on diffusive time scales. To illustrate this approach, we calculate the two-point correlation function of a fluid.

Now consider diffusion

International Nuclear Information System (INIS)

Dungey, J.W.

1984-01-01

The authors want to talk about future work, but first he will reply to Stan Cowley's comment on his naivety in believing in the whole story to 99% confidence in '65, when he knew about Fairfield's results. Does it matter whether you make the right judgment about theories? Yes, it does, particularly for experimentalists perhaps, but also for theorists. The work you do later depends on the judgment you've made on previous work. People have wasted a lot of time developing on insecure or even wrong foundations. Now for future work. One mild surprise the authors have had is that they haven't heard more about diffusion, in two contexts. Gordon Rostoker is yet to come and he may talk about particles getting into the magnetosphere by diffusion. Lots of noise is observed and so diffusion must happen. If time had not been short, the authors were planning to discuss in a handwaving way what sort of diffusion mechanisms one might consider. The other aspect of diffusion he was going to talk about is at the other end of things and is velocity diffusion, which is involved in anomalous resistivity

Dependence of Exciton Diffusion Length and Diffusion Coefficient on Photophysical Parameters in Bulk Heterojunction Organic Solar Cells

Science.gov (United States)

Yeboah, Douglas; Singh, Jai

2017-11-01

Recently, the dependence of exciton diffusion length (LD ) on some photophysical parameters of organic solids has been experimentally demonstrated, however no systematic theoretical analysis of this phenomenon has been carried out. We have conducted a theoretical study by using the Förster resonance energy transfer and Dexter carrier transfer mechanisms together with the Einstein-Smoluchowski diffusion equation to derive analytical models for the diffusion lengths (LD ) and diffusion coefficients (D) of singlet (S) and triplet (T) excitons in organic solids as functions of spectral overlap integral (J) , photoluminescence (PL) quantum yield (φD ) , dipole moment (μT ) and refractive index (n) of the photoactive material. The exciton diffusion lengths and diffusion coefficients in some selected organic solids were calculated, and we found that the singlet exciton diffusion length (LDS ) increases with φD and J, and decreases with n. Also, the triplet exciton diffusion length (LDT ) increases with φD and decreases with μT . These may be achieved through doping the organic solids into broad optical energy gap host materials as observed in previous experiments. The calculated exciton diffusion lengths are compared with experimental values and a reasonably good agreement is found between them. The results presented are expected to provide insight relevant to the synthesis of new organic solids for fabrication of bulk heterojunction organic solar cells characterized by better power conversion efficiency.

Magnetic diffuse scattering: a theorist`s perspective

Energy Technology Data Exchange (ETDEWEB)

Long, M W [Birmingham Univ., School of Physics, Birmingham (United Kingdom)

1996-11-01

We attempt to show that magnetic diffuse scattering is the natural probe for frustrated antiferromagnetism. Comparison between nuclear and magnetic diffuse scattering compares the range of atomic clustering with the range of the magnetic impurity. At low temperature frustration is expected to lead to large differences which are a natural signature for the relevance of such frustration effects. We provide some elementary examples in first-row transition metals which display fairly dramatic effects. (author) 11 figs., tabs., 8 refs.

Electron mobilities of n-type organic semiconductors from time-dependent wavepacket diffusion method: pentacenequinone derivatives.

Science.gov (United States)

Zhang, WeiWei; Zhong, XinXin; Zhao, Yi

2012-11-26

The electron mobilities of two n-type pentacenequinone derivative organic semiconductors, 5,7,12,14-tetraaza-6,13-pentacenequinone (TAPQ5) and 1,4,8,11-tetraaza-6,13-pentacenequinone (TAPQ7), are investigated with use of the methods of electronic structure and quantum dynamics. The electronic structure calculations reveal that the two key parameters for the control of electron transfer, reorganization energy and electronic coupling, are similar for these two isomerization systems, and the charge carriers essentially display one-dimensional transport properties. The mobilities are then calculated by using the time-dependent wavepacket diffusion approach in which the dynamic fluctuations of the electronic couplings are incorporated via their correlation functions obtained from molecular dynamics simulations. The predicted mobility of TAPQ7 crystal is about six times larger than that of TAPQ5 crystal. Most interestingly, Fermi's golden rule predicts the mobilities very close to those from the time-dependent wavepacket diffusion method, even though the electronic couplings are explicitly large enough to make the perturbation theory invalid. The possible reason is analyzed from the dynamic fluctuations.

Computation of short-time diffusion using the particle simulation method

International Nuclear Information System (INIS)

Janicke, L.

1983-01-01

The method of particle simulation allows a correct description of turbulent diffusion even in areas near the source and the computation of overall average values (anticipated values). The model is suitable for dealing with complex situation. It is derived from the K-model which describes the dispersion of noxious matter using the diffusion formula. (DG) [de

First passage time for a diffusive process under a geometric constraint

International Nuclear Information System (INIS)

Tateishi, A A; Michels, F S; Dos Santos, M A F; Lenzi, E K; Ribeiro, H V

2013-01-01

We investigate the solutions, survival probability, and first passage time for a two-dimensional diffusive process subjected to the geometric constraints of a backbone structure. We consider this process governed by a fractional Fokker–Planck equation by taking into account the boundary conditions ρ(0,y;t) = ρ(∞,y;t) = 0, ρ(x, ± ∞;t) = 0, and an arbitrary initial condition. Our results show an anomalous spreading and, consequently, a nonusual behavior for the survival probability and for the first passage time distribution that may be characterized by different regimes. In addition, depending on the choice of the parameters present in the fractional Fokker–Planck equation, the survival probability indicates that part of the system may be trapped in the branches of the backbone structure. (paper)

Time scales of transient enhanced diffusion: Free and clustered interstitials

Science.gov (United States)

Cowern, N. E. B.; Huizing, H. G. A.; Stolk, P. A.; Visser, C. C. G.; de Kruif, R. C. M.; Kyllesbech Larsen, K.; Privitera, V.; Nanver, L. K.; Crans, W.

1996-12-01

Transient enhanced diffusion (TED) and electrical activation after nonamorphizing Si implantations into lightly B-doped Si multilayers shows two distinct timescales, each related to a different class of interstitial defect. At 700°C, ultrafast TED occurs within the first 15 s with a B diffusivity enhancement of > 2 × 10 5. Immobile clustered B is present at low concentration levels after the ultrafast transient and persists for an extended period (˜ 10 2-10 3 s). The later phase of TED exhibits a near-constant diffusivity enhancement of ≈ 1 × 10 4, consistent with interstitial injection controlled by dissolving {113} interstitial clusters. The relative contributions of the ultrafast and regular TED regimes to the final diffusive broadening of the B profile depends on the proportion of interstitials that escape capture by {113} clusters growing within the implant damage region upon annealing. Our results explain the ultrafast TED recently observed after medium-dose B implantation. In that case there are enough B atoms to trap a large proportion of interstitials in SiB clusters, and the remaining interstitials contribute to TED without passing through an intermediate {113} defect stage. The data on the ultrafast TED pulse allows us to extract lower limits for the diffusivities of the Si interstitial ( DI > 2 × 10 -10 cm 2s -1) and the B interstitial(cy) defect ( DBi > 2 × 10 -13 cm 2s -1) at 700°C.

Time-to-failure analysis of 5 nm amorphous Ru(P) as a copper diffusion barrier

International Nuclear Information System (INIS)

Henderson, Lucas B.; Ekerdt, John G.

2009-01-01

Evaluation of chemical vapor deposited amorphous ruthenium-phosphorous alloy as a copper interconnect diffusion barrier is reported. Approximately 5 nm-thick Ru(P) and TaN films in Cu/Ru(P)/SiO 2 /p-Si and Cu/TaN/SiO 2 /p-Si stacks are subjected to bias-temperature stress at electric fields from 2.0 MV/cm to 4.0 MV/cm and temperatures from 200 deg. C to 300 deg. C . Time-to-failure measurements suggest that chemical vapor deposited Ru(P) is comparable to physical vapor deposited TaN in preventing Cu diffusion. The activation energy of failure for stacks using Ru(P) as a liner is determined to be 1.83 eV in the absence of an electric field. Multiple models of dielectric failure, including the E and Schottky-type √E models indicate that Ru(P) is acceptable for use as a diffusion barrier at conditions likely in future technology generations

Flux-limited diffusion coefficients in reactor physics applications

International Nuclear Information System (INIS)

Pounders, J.; Rahnema, F.; Szilard, R.

2007-01-01

Flux-limited diffusion theory has been successfully applied to problems in radiative transfer and radiation hydrodynamics, but its relevance to reactor physics has not yet been explored. The current investigation compares the performance of a flux-limited diffusion coefficient against the traditionally defined transport cross section. A one-dimensional BWR benchmark problem is examined at both the assembly and full-core level with varying degrees of heterogeneity. (authors)

Rhodium SPND's Error Reduction using Extended Kalman Filter combined with Time Dependent Neutron Diffusion Equation

International Nuclear Information System (INIS)

Lee, Jeong Hun; Park, Tong Kyu; Jeon, Seong Su

2014-01-01

The Rhodium SPND is accurate in steady-state conditions but responds slowly to changes in neutron flux. The slow response time of Rhodium SPND precludes its direct use for control and protection purposes specially when nuclear power plant is used for load following. To shorten the response time of Rhodium SPND, there were some acceleration methods but they could not reflect neutron flux distribution in reactor core. On the other hands, some methods for core power distribution monitoring could not consider the slow response time of Rhodium SPND and noise effect. In this paper, time dependent neutron diffusion equation is directly used to estimate reactor power distribution and extended Kalman filter method is used to correct neutron flux with Rhodium SPND's and to shorten the response time of them. Extended Kalman filter is effective tool to reduce measurement error of Rhodium SPND's and even simple FDM to solve time dependent neutron diffusion equation can be an effective measure. This method reduces random errors of detectors and can follow reactor power level without cross-section change. It means monitoring system may not calculate cross-section at every time steps and computing time will be shorten. To minimize delay of Rhodium SPND's conversion function h should be evaluated in next study. Neutron and Rh-103 reaction has several decay chains and half-lives over 40 seconds causing delay of detection. Time dependent neutron diffusion equation will be combined with decay chains. Power level and distribution change corresponding movement of control rod will be tested with more complicated reference code as well as xenon effect. With these efforts, final result is expected to be used as a powerful monitoring tool of nuclear reactor core

Rhodium SPND's Error Reduction using Extended Kalman Filter combined with Time Dependent Neutron Diffusion Equation

Energy Technology Data Exchange (ETDEWEB)

Lee, Jeong Hun; Park, Tong Kyu; Jeon, Seong Su [FNC Technology Co., Ltd., Yongin (Korea, Republic of)

2014-05-15

The Rhodium SPND is accurate in steady-state conditions but responds slowly to changes in neutron flux. The slow response time of Rhodium SPND precludes its direct use for control and protection purposes specially when nuclear power plant is used for load following. To shorten the response time of Rhodium SPND, there were some acceleration methods but they could not reflect neutron flux distribution in reactor core. On the other hands, some methods for core power distribution monitoring could not consider the slow response time of Rhodium SPND and noise effect. In this paper, time dependent neutron diffusion equation is directly used to estimate reactor power distribution and extended Kalman filter method is used to correct neutron flux with Rhodium SPND's and to shorten the response time of them. Extended Kalman filter is effective tool to reduce measurement error of Rhodium SPND's and even simple FDM to solve time dependent neutron diffusion equation can be an effective measure. This method reduces random errors of detectors and can follow reactor power level without cross-section change. It means monitoring system may not calculate cross-section at every time steps and computing time will be shorten. To minimize delay of Rhodium SPND's conversion function h should be evaluated in next study. Neutron and Rh-103 reaction has several decay chains and half-lives over 40 seconds causing delay of detection. Time dependent neutron diffusion equation will be combined with decay chains. Power level and distribution change corresponding movement of control rod will be tested with more complicated reference code as well as xenon effect. With these efforts, final result is expected to be used as a powerful monitoring tool of nuclear reactor core.

Diffusion, quantum theory, and radically elementary mathematics (MN-47)

CERN Document Server

Faris, William G

2014-01-01

Diffusive motion--displacement due to the cumulative effect of irregular fluctuations--has been a fundamental concept in mathematics and physics since Einstein''s work on Brownian motion. It is also relevant to understanding various aspects of quantum theory. This book explains diffusive motion and its relation to both nonrelativistic quantum theory and quantum field theory. It shows how diffusive motion concepts lead to a radical reexamination of the structure of mathematical analysis. The book''s inspiration is Princeton University mathematics professor Edward Nelson''s influential work in

Determination of the diffusion coefficient of salts in non-Newtonian liquids by the Taylor dispersion method

Energy Technology Data Exchange (ETDEWEB)

Mey, Paula; Varges, Priscilla R.; Mendes, Paulo R. de Souza [Dept. of Mechanical Engineering. Pontificia Universidade Catolica do RJ (PUC-Rio), RJ (Brazil)], e-mails: prvarges@puc-rio.br, pmendes@puc-rio.br

2010-07-01

This research looked for a method to determine the binary diffusion coefficient D of salts in liquids (especially in drilling fluids) not only accurately, but in a reasonable time. We chose to use the Taylor Dispersion Method. This technique has been used for measuring binary diffusion coefficients in gaseous, liquid and supercritical fluids, due to its simplicity and accuracy. In the method, the diffusion coefficient is determined by the analysis of the dispersion of a pulse of soluble material in a solvent flowing laminarly through a tube. This work describes the theoretical basis and the experimental requirements for the application of the Taylor Dispersion Method, emphasizing the description of our experiment. A mathematical formulation for both Newtonian and non-Newtonian fluids is presented. The relevant sources of errors are discussed. The experimental procedure and associated analysis are validated by applying the method in well known systems, such as NaCl in water.D of salts in liquids (especially in drilling fluids) not only accurately, but in a reasonable time. We chose to use the Taylor Dispersion Method. This technique has been used for measuring binary diffusion coefficients in gaseous, liquid and supercritical fluids, due to its simplicity and accuracy. In the method, the diffusion coefficient is determined by the analysis of the dispersion of a pulse of soluble material in a solvent flowing laminarly through a tube. This work describes the theoretical basis and the experimental requirements for the application of the Taylor Dispersion Method, emphasizing the description of our experiment. A mathematical formulation for both Newtonian and non-Newtonian fluids is presented. The relevant sources of errors are discussed. The experimental procedure and associated analysis are validated by applying the method in well known systems, such as NaCl in water. (author)

Infinite set of relevant operators for an exact solution of the time-dependent Jaynes-Cummings Hamiltonian

International Nuclear Information System (INIS)

Gruver, J.L.; Aliaga, J.; Cerdeira, H.A.; Proto, A.N.

1995-03-01

The dynamics and thermodynamics of a quantum time-dependent field coupled to a two-level system, well known as the Jaynes-Cummings Hamiltonian, is studied, using the maximum entropy principle. In the framework of this approach we found three different infinite sets of relevant operators that describe the dynamics of the system for any temporal dependence. These sets of relevant operators are connected by isomorphisms, which allow us to consider the case of mixed initial conditions. A consistent set of initial conditions is established using the maximum entropy principle density operator, obtaining restrictions to the physically feasible initial conditions of the system. The behaviour of the population inversion is shown for different time dependencies of the Hamiltonian and initial conditions. For the time-independent case, an explicit solution for the population inversion in terms of the relevant operators of one of the sets is given. It is also shown how the well-known formulas for the population inversion are recovered for the special cases where the initial conditions correspond to a pure, coherent, and thermal field. (author). 35 refs, 9 figs

CROSS DIFFUSION AND NONLINEAR DIFFUSION PREVENTING BLOW UP IN THE KELLER–SEGEL MODEL

KAUST Repository

CARRILLO, JOSÉ ANTONIO

2012-12-01

A parabolic-parabolic (Patlak-)Keller-Segel model in up to three space dimensions with nonlinear cell diffusion and an additional nonlinear cross-diffusion term is analyzed. The main feature of this model is that there exists a new entropy functional, yielding gradient estimates for the cell density and chemical concentration. For arbitrarily small cross-diffusion coefficients and for suitable exponents of the nonlinear diffusion terms, the global-in-time existence of weak solutions is proved, thus preventing finite-time blow up of the cell density. The global existence result also holds for linear and fast diffusion of the cell density in a certain parameter range in three dimensions. Furthermore, we show L∞ bounds for the solutions to the parabolic-elliptic system. Sufficient conditions leading to the asymptotic stability of the constant steady state are given for a particular choice of the nonlinear diffusion exponents. Numerical experiments in two and three space dimensions illustrate the theoretical results. © 2012 World Scientific Publishing Company.

A NEM diffusion code for fuel management and time average core calculation

International Nuclear Information System (INIS)

Mishra, Surendra; Ray, Sherly; Kumar, A.N.

2005-01-01

A computer code based on Nodal expansion method has been developed for solving two groups three dimensional diffusion equation. This code can be used for fuel management and time average core calculation. Explicit Xenon and fuel temperature estimation are also incorporated in this code. TAPP-4 phase-B physics experimental results were analyzed using this code and a code based on FD method. This paper gives the comparison of the observed data and the results obtained with this code and FD code. (author)

Time-Resolved Diffuse Optical Spectroscopy and Imaging Using Solid-State Detectors: Characteristics, Present Status, and Research Challenges.

Science.gov (United States)

Alayed, Mrwan; Deen, M Jamal

2017-09-14

Diffuse optical spectroscopy (DOS) and diffuse optical imaging (DOI) are emerging non-invasive imaging modalities that have wide spread potential applications in many fields, particularly for structural and functional imaging in medicine. In this article, we review time-resolved diffuse optical imaging (TR-DOI) systems using solid-state detectors with a special focus on Single-Photon Avalanche Diodes (SPADs) and Silicon Photomultipliers (SiPMs). These TR-DOI systems can be categorized into two types based on the operation mode of the detector (free-running or time-gated). For the TR-DOI prototypes, the physical concepts, main components, figures-of-merit of detectors, and evaluation parameters are described. The performance of TR-DOI prototypes is evaluated according to the parameters used in common protocols to test DOI systems particularly basic instrumental performance (BIP). In addition, the potential features of SPADs and SiPMs to improve TR-DOI systems and expand their applications in the foreseeable future are discussed. Lastly, research challenges and future developments for TR-DOI are discussed for each component in the prototype separately and also for the entire system.

Cosmic ray acceleration by shock waves in a diffusion medium. Research of high energies

International Nuclear Information System (INIS)

Lagage, P.O.

1982-06-01

The problem of galactic cosmic-ray acceleration is presented with the study of a new acceleration mechanism by supernova shock waves in a diffusive medium. The question is: do supernova shocks have enough time to accelerate cosmic rays beyond 10 4 -10 5 GeV. A firm upper limit to the energy that can be acquired by particles is established and it is considered that the mean free path of the particle has its lowest possible value and the most favorable model of supernova evolution. The diffusion coefficients which are relevant for the determination of the high energy cut off are investigated. The effect of the spatial dependence of the diffusion coefficient on the rate of acceleration of particles is examined. A more realistic cut off energy is calculated. We find E max = 2 10 4 GeV [fr

Adsorption and diffusion of hydrogen in Zircaloy-4

International Nuclear Information System (INIS)

Torres, E.; Desquines, J.; Baietto, M.C.; Coret, M.; Wehling, F.; Blat-Yrieix, M.; Ambard, A.

2015-01-01

Hydrogen in zirconium alloys is considered in many nuclear safety issues. Below 500 Celsius degrees, rather limited knowledge is available on the combined hydrogen adsorption at the sample surface and diffusion in the metal. A modeling of hydrogen gaseous charging has been established starting with a set of relevant laws and parameters derived from open literature. Simulating the hydrogen charging process requires simultaneous analysis of gaseous surface adsorption, hydrogen solid-solution diffusion and precipitation, when exceeding the material solubility limit. The modeling has been extended to reproduce the solid-gas exchange. Gaseous charging experiments have been performed at 420 C. degrees on Stress Relieved Annealed (SRA) Zircaloy-4 cladding samples to validate the model. The sample hydrogen content has been systematically measured after charging and compared to the calculated value thus providing a validation of the adsorption modeling. Complementary tests have been carried out on Recrystallized Annealed (RXA) Zircaloy-4 rods to characterize the combined diffusion and adsorption process. The hydrogen concentration distribution has been characterized using an inverse technique based on destructive analyses of the samples. This additional set of data was relevant for the validation of the hydrogen combined adsorption/diffusion modeling up to 420 C. degrees. (authors)

Real-time nonlinear feedback control of pattern formation in (bio)chemical reaction-diffusion processes: a model study.

Science.gov (United States)

Brandt-Pollmann, U; Lebiedz, D; Diehl, M; Sager, S; Schlöder, J

2005-09-01

Theoretical and experimental studies related to manipulation of pattern formation in self-organizing reaction-diffusion processes by appropriate control stimuli become increasingly important both in chemical engineering and cellular biochemistry. In a model study, we demonstrate here exemplarily the application of an efficient nonlinear model predictive control (NMPC) algorithm to real-time optimal feedback control of pattern formation in a bacterial chemotaxis system modeled by nonlinear partial differential equations. The corresponding drift-diffusion model type is representative for many (bio)chemical systems involving nonlinear reaction dynamics and nonlinear diffusion. We show how the computed optimal feedback control strategy exploits the system inherent physical property of wave propagation to achieve desired control aims. We discuss various applications of our approach to optimal control of spatiotemporal dynamics.

Time-dependent free boundary equilibrium and resistive diffusion in a tokamak plasma

International Nuclear Information System (INIS)

Selig, G.

2012-12-01

In a Tokamak, in order to create the necessary conditions for nuclear fusion to occur, a plasma is maintained by applying magnetic fields. Under the hypothesis of an axial symmetry of the tokamak, the study of the magnetic configuration at equilibrium is done in two dimensions, and is deduced from the poloidal flux function. This function is solution of a non linear partial differential equation system, known as equilibrium problem. This thesis presents the time dependent free boundary equilibrium problem, where the circuit equations in the tokamak coils and passive conductors are solved together with the Grad-Shafranov equation to produce a dynamic simulation of the plasma. In this framework, the Finite Element equilibrium code CEDRES has been improved in order to solve the aforementioned dynamic problem. Consistency tests and comparisons with the DINA-CH code on an ITER vertical instability case have validated the results. Then, the resistive diffusion of the plasma current density has been simulated using a coupling between CEDRES and the averaged one-dimensional diffusion equation, and it has been successfully compared with the integrated modeling code CRONOS. (author)

Entropy as a measure of diffusion

International Nuclear Information System (INIS)

Aghamohammadi, Amir; Fatollahi, Amir H.; Khorrami, Mohammad; Shariati, Ahmad

2013-01-01

The time variation of entropy, as an alternative to the variance, is proposed as a measure of the diffusion rate. It is shown that for linear and time-translationally invariant systems having a large-time limit for the density, at large times the entropy tends exponentially to a constant. For systems with no stationary density, at large times the entropy is logarithmic with a coefficient specifying the speed of the diffusion. As an example, the large-time behaviors of the entropy and the variance are compared for various types of fractional-derivative diffusions.

Entropy as a measure of diffusion

Energy Technology Data Exchange (ETDEWEB)

Aghamohammadi, Amir, E-mail: mohamadi@alzahra.ac.ir; Fatollahi, Amir H., E-mail: fath@alzahra.ac.ir; Khorrami, Mohammad, E-mail: mamwad@mailaps.org; Shariati, Ahmad, E-mail: shariati@mailaps.org

2013-10-15

The time variation of entropy, as an alternative to the variance, is proposed as a measure of the diffusion rate. It is shown that for linear and time-translationally invariant systems having a large-time limit for the density, at large times the entropy tends exponentially to a constant. For systems with no stationary density, at large times the entropy is logarithmic with a coefficient specifying the speed of the diffusion. As an example, the large-time behaviors of the entropy and the variance are compared for various types of fractional-derivative diffusions.

DSA-guided embolization in establishing different canine spinal cord ischemia models and relevant diffusion-weighted imaging study

International Nuclear Information System (INIS)

Zhang Jingsong; Sun Lijun; Huan Yi; He Hongde; Zhang Xuexin; Zhao Haitao; Zhang Jing; Zhang Xijing

2006-01-01

Objective: To evaluate DSA-guided embolization in establishing different spinal cord ischemia models of canine and relevant diffusion-weighted imaging (DWI) application. Methods: Nine canines were randomly divided into three groups with different matching of lipiodol and diatrizoate meglumine which were injected into bilateral intercostal arteries at 9-11 level guided by DSA monitor. Then observe the changes of motor function and pathologic findings, especially perform routine MRI and DWI by a 1.5 T MR system. Results: Except one case, 8 embolization models were established successfully. Among three groups, slight-group got slight injury and muscle power was about 3-5 grade and range of injury was about two vertebra distance; medium-group presented obvious paraplegia and muscle power was 0-1 grade and range of injury was between 3-4 vertebra distance; severe-group showed greater severity and larger range of injury. All lesions presented high signals at routine MRI and DWI. Conclusion: Using different matching of lipiodol and diatrizoate meglumine can establish different spinal cord ischemia models of canine by DSA- guided embolization and DWI can be performed successfully by 1.5 T MR system, which may be a good method for advanced study of spinal cord ischemia. (authors)

Time-resolved diffusion tomographic 2D and 3D imaging in highly scattering turbid media

Science.gov (United States)

Alfano, Robert R. (Inventor); Cai, Wei (Inventor); Gayen, Swapan K. (Inventor)

2000-01-01

A method for imaging objects in highly scattering turbid media. According to one embodiment of the invention, the method involves using a plurality of intersecting source/detectors sets and time-resolving equipment to generate a plurality of time-resolved intensity curves for the diffusive component of light emergent from the medium. For each of the curves, the intensities at a plurality of times are then inputted into the following inverse reconstruction algorithm to form an image of the medium: wherein W is a matrix relating output at source and detector positions r.sub.s and r.sub.d, at time t, to position r, .LAMBDA. is a regularization matrix, chosen for convenience to be diagonal, but selected in a way related to the ratio of the noise, to fluctuations in the absorption (or diffusion) X.sub.j that we are trying to determine: .LAMBDA..sub.ij =.lambda..sub.j .delta..sub.ij with .lambda..sub.j =/ Y is the data collected at the detectors, and X.sup.k is the kth iterate toward the desired absorption information. An algorithm, which combines a two dimensional (2D) matrix inversion with a one-dimensional (1D) Fourier transform inversion is used to obtain images of three dimensional hidden objects in turbid scattering media.

Two-Dimensional Space-Time Dependent Multi-group Diffusion Equation with SLOR Method

International Nuclear Information System (INIS)

Yulianti, Y.; Su'ud, Z.; Waris, A.; Khotimah, S. N.

2010-01-01

The research of two-dimensional space-time diffusion equations with SLOR (Successive-Line Over Relaxation) has been done. SLOR method is chosen because this method is one of iterative methods that does not required to defined whole element matrix. The research is divided in two cases, homogeneous case and heterogeneous case. Homogeneous case has been inserted by step reactivity. Heterogeneous case has been inserted by step reactivity and ramp reactivity. In general, the results of simulations are agreement, even in some points there are differences.

Wright-Fisher diffusion bridges.

Science.gov (United States)

Griffiths, Robert C; Jenkins, Paul A; Spanò, Dario

2017-10-06

The trajectory of the frequency of an allele which begins at x at time 0 and is known to have frequency z at time T can be modelled by the bridge process of the Wright-Fisher diffusion. Bridges when x=z=0 are particularly interesting because they model the trajectory of the frequency of an allele which appears at a time, then is lost by random drift or mutation after a time T. The coalescent genealogy back in time of a population in a neutral Wright-Fisher diffusion process is well understood. In this paper we obtain a new interpretation of the coalescent genealogy of the population in a bridge from a time t∈(0,T). In a bridge with allele frequencies of 0 at times 0 and T the coalescence structure is that the population coalesces in two directions from t to 0 and t to T such that there is just one lineage of the allele under consideration at times 0 and T. The genealogy in Wright-Fisher diffusion bridges with selection is more complex than in the neutral model, but still with the property of the population branching and coalescing in two directions from time t∈(0,T). The density of the frequency of an allele at time t is expressed in a way that shows coalescence in the two directions. A new algorithm for exact simulation of a neutral Wright-Fisher bridge is derived. This follows from knowing the density of the frequency in a bridge and exact simulation from the Wright-Fisher diffusion. The genealogy of the neutral Wright-Fisher bridge is also modelled by branching Pólya urns, extending a representation in a Wright-Fisher diffusion. This is a new very interesting representation that relates Wright-Fisher bridges to classical urn models in a Bayesian setting. Copyright © 2017 Elsevier Inc. All rights reserved.

Thermal diffusivity of a metallic thin layer using the time-domain thermo reflectance technique

International Nuclear Information System (INIS)

Battaglia, J-L; Kusiak, A; Rossignol, C; Chigarev, N

2007-01-01

The time domain thermo reflectance (TDTR) is widely used in the field of acoustic and thermal characterization of thin layers at the nano and micro scale. In this paper, we propose to derive a simple analytical expression of the thermal diffusivity of the layer. This relation is based on the analytical solution of one-dimensional heat transfer in the medium using integral transforms. For metals, the two-temperature model shows that the capacitance effect at the short times is essentially governed by the electronic contribution

Strategies for Solving Potential Problems Associated with Laboratory Diffusion and Batch Experiments - Part 1: An Overview of Conventional Test Methods

International Nuclear Information System (INIS)

Zhang, M.; Takeda, M.; Nakajima, H.

2006-01-01

Laboratory diffusion testing as well as batch experiments are well established and widely adopted techniques for characterizing the diffusive and adsorptive properties of geological, geotechnical, and synthetic materials in both scientific and applied fields, including geological disposal of radioactive waste. Although several types of diffusion test, such as the through- diffusion test, in-diffusion test, out-diffusion test, and column test, are currently available, different methods may have different advantages and disadvantages. In addition, traditional methods may have limitations, such as the need for relatively long test times, cumbersome test procedures, and the possibility of errors due to differences between analytical assumptions and actual test conditions. Furthermore, traditional batch experiments using mineral powders are known to overestimate the sorption coefficient. In part 1 of this report, we present a brief overview of laboratory diffusion and batch experiments. The advantages, disadvantages, limitations, and/or potential problems associated with individual tests were compared and summarized. This comprehensive report will provide practical references for reviewing the results obtained from relevant experiments, especially from the viewpoint of regulation. To solve and/or eliminate the potential problems associated with conventional methods, and to obtain the diffusion coefficient and rock capacity factor from a laboratory test both rapidly and accurately, part 2 of this study discusses possible strategies involving the development of rigorous solutions to some relevant test methods, and sensitivity analyses for the related tests that may be helpful to judge the accuracy of the two parameters to be determined from individual tests. (authors)

Whole-head functional brain imaging of neonates at cot-side using time-resolved diffuse optical tomography

Science.gov (United States)

Dempsey, Laura A.; Cooper, Robert J.; Powell, Samuel; Edwards, Andrea; Lee, Chuen-Wai; Brigadoi, Sabrina; Everdell, Nick; Arridge, Simon; Gibson, Adam P.; Austin, Topun; Hebden, Jeremy C.

2015-07-01

We present a method for acquiring whole-head images of changes in blood volume and oxygenation from the infant brain at cot-side using time-resolved diffuse optical tomography (TR-DOT). At UCL, we have built a portable TR-DOT device, known as MONSTIR II, which is capable of obtaining a whole-head (1024 channels) image sequence in 75 seconds. Datatypes extracted from the temporal point spread functions acquired by the system allow us to determine changes in absorption and reduced scattering coefficients within the interrogated tissue. This information can then be used to define clinically relevant measures, such as oxygen saturation, as well as to reconstruct images of relative changes in tissue chromophore concentration, notably those of oxy- and deoxyhaemoglobin. Additionally, the effective temporal resolution of our system is improved with spatio-temporal regularisation implemented through a Kalman filtering approach, allowing us to image transient haemodynamic changes. By using this filtering technique with intensity and mean time-of-flight datatypes, we have reconstructed images of changes in absorption and reduced scattering coefficients in a dynamic 2D phantom. These results demonstrate that MONSTIR II is capable of resolving slow changes in tissue optical properties within volumes that are comparable to the preterm head. Following this verification study, we are progressing to imaging a 3D dynamic phantom as well as the neonatal brain at cot-side. Our current study involves scanning healthy babies to demonstrate the quality of recordings we are able to achieve in this challenging patient population, with the eventual goal of imaging functional activation and seizures.

A variable timestep generalized Runge-Kutta method for the numerical integration of the space-time diffusion equations

International Nuclear Information System (INIS)

Aviles, B.N.; Sutton, T.M.; Kelly, D.J. III.

1991-09-01

A generalized Runge-Kutta method has been employed in the numerical integration of the stiff space-time diffusion equations. The method is fourth-order accurate, using an embedded third-order solution to arrive at an estimate of the truncation error for automatic timestep control. The efficiency of the Runge-Kutta method is enhanced by a block-factorization technique that exploits the sparse structure of the matrix system resulting from the space and energy discretized form of the time-dependent neutron diffusion equations. Preliminary numerical evaluation using a one-dimensional finite difference code shows the sparse matrix implementation of the generalized Runge-Kutta method to be highly accurate and efficient when compared to an optimized iterative theta method. 12 refs., 5 figs., 4 tabs

Diffusion between evolving interfaces

International Nuclear Information System (INIS)

Juntunen, Janne; Merikoski, Juha

2010-01-01

Diffusion in an evolving environment is studied by continuous-time Monte Carlo simulations. Diffusion is modeled by continuous-time random walkers on a lattice, in a dynamic environment provided by bubbles between two one-dimensional interfaces driven symmetrically towards each other. For one-dimensional random walkers constrained by the interfaces, the bubble size distribution dominates diffusion. For two-dimensional random walkers, it is also controlled by the topography and dynamics of the interfaces. The results of the one-dimensional case are recovered in the limit where the interfaces are strongly driven. Even with simple hard-core repulsion between the interfaces and the particles, diffusion is found to depend strongly on the details of the dynamical rules of particles close to the interfaces.

Multiphase Microfluidics The Diffuse Interface Model

CERN Document Server

2012-01-01

Multiphase flows are typically described assuming that the different phases are separated by a sharp interface, with appropriate boundary conditions. This approach breaks down whenever the lengthscale of the phenomenon that is being studied is comparable with the real interface thickness, as it happens, for example, in the coalescence and breakup of bubbles and drops, the wetting and dewetting of solid surfaces and, in general, im micro-devices. The diffuse interface model resolves these probems by assuming that all quantities can vary continuously, so that interfaces have a non-zero thickness, i.e. they are "diffuse". The contributions in this book review the theory and describe some relevant applications of the diffuse interface model for one-component, two-phase fluids and for liquid binary mixtures, to model multiphase flows in confined geometries.

Miniaturized pulsed laser source for time-domain diffuse optics routes to wearable devices.

Science.gov (United States)

Di Sieno, Laura; Nissinen, Jan; Hallman, Lauri; Martinenghi, Edoardo; Contini, Davide; Pifferi, Antonio; Kostamovaara, Juha; Mora, Alberto Dalla

2017-08-01

We validate a miniaturized pulsed laser source for use in time-domain (TD) diffuse optics, following rigorous and shared protocols for performance assessment of this class of devices. This compact source (12×6  mm2) has been previously developed for range finding applications and is able to provide short, high energy (∼100  ps, ∼0.5  nJ) optical pulses at up to 1 MHz repetition rate. Here, we start with a basic level laser characterization with an analysis of suitability of this laser for the diffuse optics application. Then, we present a TD optical system using this source and its performances in both recovering optical properties of tissue-mimicking homogeneous phantoms and in detecting localized absorption perturbations. Finally, as a proof of concept of in vivo application, we demonstrate that the system is able to detect hemodynamic changes occurring in the arm of healthy volunteers during a venous occlusion. Squeezing the laser source in a small footprint removes a key technological bottleneck that has hampered so far the realization of a miniaturized TD diffuse optics system, able to compete with already assessed continuous-wave devices in terms of size and cost, but with wider performance potentialities, as demonstrated by research over the last two decades. (2017) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE).

Fully implicit solution of large-scale non-equilibrium radiation diffusion with high order time integration

International Nuclear Information System (INIS)

Brown, Peter N.; Shumaker, Dana E.; Woodward, Carol S.

2005-01-01

We present a solution method for fully implicit radiation diffusion problems discretized on meshes having millions of spatial zones. This solution method makes use of high order in time integration techniques, inexact Newton-Krylov nonlinear solvers, and multigrid preconditioners. We explore the advantages and disadvantages of high order time integration methods for the fully implicit formulation on both two- and three-dimensional problems with tabulated opacities and highly nonlinear fusion source terms

The Galerkin Finite Element Method for A Multi-term Time-Fractional Diffusion equation

OpenAIRE

Jin, Bangti; Lazarov, Raytcho; Liu, Yikan; Zhou, Zhi

2014-01-01

We consider the initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space semidiscrete scheme based on the standard Galerkin finite element method using continuous piecewise linear functions. Nearly optimal error estimates for both cases of initial data and inhomogeneous term are derived, which cover both smooth and nonsmooth data. Further we develop a fully discrete scheme based on a finite...

Accurate and precise measurement of oxygen isotopic fractions and diffusion profiles by selective attenuation of secondary ions (SASI).

Science.gov (United States)

Téllez, Helena; Druce, John; Hong, Jong-Eun; Ishihara, Tatsumi; Kilner, John A

2015-03-03

The accuracy and precision of isotopic analysis in Time-of-Flight secondary ion mass spectrometry (ToF-SIMS) relies on the appropriate reduction of the dead-time and detector saturation effects, especially when analyzing species with high ion yields or present in high concentrations. Conventional approaches to avoid these problems are based on Poisson dead-time correction and/or an overall decrease of the total secondary ion intensity by reducing the target current. This ultimately leads to poor detection limits for the minor isotopes and high uncertainties of the measured isotopic ratios. An alternative strategy consists of the attenuation of those specific secondary ions that saturate the detector, providing an effective extension of the linear dynamic range. In this work, the selective attenuation of secondary ion signals (SASI) approach is applied to the study of oxygen transport properties in electroceramic materials by isotopic labeling with stable (18)O tracer and ToF-SIMS depth profiling. The better analytical performance in terms of accuracy and precision allowed a more reliable determination of the oxygen surface exchange and diffusion coefficients while maintaining good mass resolution and limits of detection for other minor secondary ion species. This improvement is especially relevant to understand the ionic transport mechanisms and properties of solid materials, such as the parallel diffusion pathways (e.g., oxygen diffusion through bulk, grain boundary, or dislocations) in electroceramic materials with relevant applications in energy storage and conversion devices.

Combined measurement of surface, grain boundary and lattice diffusion coefficients on olivine bi-crystals

Science.gov (United States)

Marquardt, Katharina; Dohmen, Ralf; Wagner, Johannes

2014-05-01

Diffusion along interface and grain boundaries provides an efficient pathway and may control chemical transport in rocks as well as their mechanical strength. Besides the significant relevance of these diffusion processes for various geologic processes, experimental data are still very limited (e.g., Dohmen & Milke, 2010). Most of these data were measured using polycrystalline materials and the formalism of LeClaire (1951) to fit integrated concentration depth profiles. To correctly apply this formalism, certain boundary conditions of the diffusion problem need to be fulfilled, e.g., surface diffusion is ignored, and furthermore the lattice diffusion coefficient has to be known from other studies or is an additional fitting parameter, which produces some ambiguity in the derived grain boundary diffusion coefficients. We developed an experimental setup where we can measure the lattice and grain boundary diffusion coefficients simultaneously but independent and demonstrate the relevance of surface diffusion for typical grain boundary diffusion experiments. We performed Mg2SiO4 bicrystal diffusion experiments, where a single grain boundary is covered by a thin-film of pure Ni2SiO4 acting as diffusant source, produced by pulsed laser deposition. The investigated grain boundary is a 60° (011)/[100]. This specific grain boundary configuration was modeled using molecular dynamics for comparison with the experimental observations in the transmission electron microscope (TEM). Both, experiment and model are in good agreement regarding the misorientation, whereas there are still some disagreements regarding the strain fields along the grain boundary that are of outmost importance for the strengths of the material. The subsequent diffusion experiments were carried out in the temperature range between 800° and 1450° C. The inter diffusion profiles were measured using the TEMs energy dispersive x-ray spectrometer standardized using the Cliff-Lorimer equation and EMPA

Diffusion of 99TcO4- in compacted bentonite: Effect of pH, concentration, density and contact time

International Nuclear Information System (INIS)

Xiangke Wang; Forschungszentrum Karlsruhe; Zuyi Tao

2004-01-01

In order to assess radionuclide diffusion and transport properties in compacted bentonite, the 'in-diffusion' method based on bentonite filled capillaries is used. The effect of 99 TcO 4 - concentration and pH value of the solution, the contact time and the dry density of compacted bentonite on the apparent diffusion coefficient (D a ) and on the distribution coefficient (K d ) values obtained from the capillary test was studied. The D a and K d values decrease with increasing of the bulk dry density of compacted bentonite. Ion exclusion influences the diffusion of 99 TcO 4 - 4 in the same substance. As compared to literature data, the K d values obtained from capillary tests are in most cases lower than those from batch tests, the difference between the two K d values is a strong function of dry density of the compacted bentonite. (author)

Two-photon time-lapse microscopy of BODIPY-cholesterol reveals anomalous sterol diffusion in chinese hamster ovary cells

Directory of Open Access Journals (Sweden)

Lund Frederik W

2012-10-01

Full Text Available Abstract Background Cholesterol is an important membrane component, but our knowledge about its transport in cells is sparse. Previous imaging studies using dehydroergosterol (DHE, an intrinsically fluorescent sterol from yeast, have established that vesicular and non-vesicular transport modes contribute to sterol trafficking from the plasma membrane. Significant photobleaching, however, limits the possibilities for in-depth analysis of sterol dynamics using DHE. Co-trafficking studies with DHE and the recently introduced fluorescent cholesterol analog BODIPY-cholesterol (BChol suggested that the latter probe has utility for prolonged live-cell imaging of sterol transport. Results We found that BChol is very photostable under two-photon (2P-excitation allowing the acquisition of several hundred frames without significant photobleaching. Therefore, long-term tracking and diffusion measurements are possible. Two-photon temporal image correlation spectroscopy (2P-TICS provided evidence for spatially heterogeneous diffusion constants of BChol varying over two orders of magnitude from the cell interior towards the plasma membrane, where D ~ 1.3 μm2/s. Number and brightness (N&B analysis together with stochastic simulations suggest that transient partitioning of BChol into convoluted membranes slows local sterol diffusion. We observed sterol endocytosis as well as fusion and fission of sterol-containing endocytic vesicles. The mobility of endocytic vesicles, as studied by particle tracking, is well described by a model for anomalous subdiffusion on short time scales with an anomalous exponent α ~ 0.63 and an anomalous diffusion constant of Dα = 1.95 x 10-3 μm2/sα. On a longer time scale (t > ~5 s, a transition to superdiffusion consistent with slow directed transport with an average velocity of v ~ 6 x 10-3 μm/s was observed. We present an analytical model that bridges the two regimes and fit this model to vesicle

A simple model of carcinogenic mutations with time delay and diffusion.

Science.gov (United States)

Piotrowska, Monika Joanna; Foryś, Urszula; Bodnar, Marek; Poleszczuk, Jan

2013-06-01

In the paper we consider a system of delay differential equations (DDEs) of Lotka-Volterra type with diffusion reflecting mutations from normal to malignant cells. The model essentially follows the idea of Ahangar and Lin (2003) where mutations in three different environmental conditions, namely favorable, competitive and unfavorable, were considered. We focus on the unfavorable conditions that can result from a given treatment, e.g. chemotherapy. Included delay stands for the interactions between benign and other cells. We compare the dynamics of ODEs system, the system with delay and the system with delay and diffusion. We mainly focus on the dynamics when a positive steady state exists. The system which is globally stable in the case without the delay and diffusion is destabilized by increasing delay, and therefore the underlying kinetic dynamics becomes oscillatory due to a Hopf bifurcation for appropriate values of the delay. This suggests the occurrence of spatially non-homogeneous periodic solutions for the system with the delay and diffusion.

In vivo P-31 MR diffusion spectroscopy

International Nuclear Information System (INIS)

Moonen, C.T.W.; Vanzijl, P.C.M.; LeBihan, D.

1988-01-01

This paper discusses the Stejskal-Tanner diffusion spin-echo sequence modified for the in vivo diffusion spectroscopy. The apparent diffusion constant D α was measured as a function of the diffusion time. Contrary to the results in phantom samples, a strong dependency of the D α for phosphocreatine (PCr) in the rat muscle tissue on diffusion time was observed, clearly indicating restricted diffusion effects and allowing an approximation of the size of the restricted volume (8-13 μm). This size fits well with the known dimensions of a normal muscle cell

Diffusion properties of active particles with directional reversal

International Nuclear Information System (INIS)

Großmann, R; Bär, M; Peruani, F

2016-01-01

The diffusion properties of self-propelled particles which move at constant speed and, in addition, reverse their direction of motion repeatedly are investigated. The internal dynamics of particles triggering these reversal processes is modeled by a stochastic clock. The velocity correlation function as well as the mean squared displacement is investigated and, furthermore, a general expression for the diffusion coefficient for self-propelled particles with directional reversal is derived. Our analysis reveals the existence of an optimal, finite rotational noise amplitude which maximizes the diffusion coefficient. We comment on the relevance of these results with regard to biological systems and suggest further experiments in this context. (paper)

A fractional spline collocation-Galerkin method for the time-fractional diffusion equation

Directory of Open Access Journals (Sweden)

Pezza L.

2018-03-01

Full Text Available The aim of this paper is to numerically solve a diffusion differential problem having time derivative of fractional order. To this end we propose a collocation-Galerkin method that uses the fractional splines as approximating functions. The main advantage is in that the derivatives of integer and fractional order of the fractional splines can be expressed in a closed form that involves just the generalized finite difference operator. This allows us to construct an accurate and efficient numerical method. Several numerical tests showing the effectiveness of the proposed method are presented.

The Galerkin finite element method for a multi-term time-fractional diffusion equation

KAUST Repository

Jin, Bangti

2015-01-01

© 2014 The Authors. We consider the initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space semidiscrete scheme based on the standard Galerkin finite element method using continuous piecewise linear functions. Nearly optimal error estimates for both cases of initial data and inhomogeneous term are derived, which cover both smooth and nonsmooth data. Further we develop a fully discrete scheme based on a finite difference discretization of the time-fractional derivatives, and discuss its stability and error estimate. Extensive numerical experiments for one- and two-dimensional problems confirm the theoretical convergence rates.

The measurement problem on classical diffusion process: inverse method on stochastic processes

International Nuclear Information System (INIS)

Bigerelle, M.; Iost, A.

2004-01-01

In a high number of diffusive systems, measures are processed to calculate material parameters such as diffusion coefficients, or to verify the accuracy of mathematical models. However, the precision of the parameter determination or of the model relevance depends on the location of the measure itself. The aim of this paper is first to analyse, for a mono-dimensional system, the precision of the measure in relation with its location by an inverse problem algorithm and secondly to examine the physical meaning of the results. Statistical mechanic considerations show that, passing over a time-distance criterion, measurement becomes uncertain whatever the initial conditions. The criterion proves that this chaotic mode is related to the production of anti-entropy at a mesoscopique scale that is in violation to quantum theory about measurement

Initial-boundary value problems for multi-term time-fractional diffusion equations with x-dependent coefficients

OpenAIRE

Li, Zhiyuan; Huang, Xinchi; Yamamoto, Masahiro

2018-01-01

In this paper, we discuss an initial-boundary value problem (IBVP) for the multi-term time-fractional diffusion equation with x-dependent coefficients. By means of the Mittag-Leffler functions and the eigenfunction expansion, we reduce the IBVP to an equivalent integral equation to show the unique existence and the analyticity of the solution for the equation. Especially, in the case where all the coefficients of the time-fractional derivatives are non-negative, by the Laplace and inversion L...

Determination of the diffusion coefficient of hydrogen ion in hydrogels.

Science.gov (United States)

Schuszter, Gábor; Gehér-Herczegh, Tünde; Szűcs, Árpád; Tóth, Ágota; Horváth, Dezső

2017-05-17

The role of diffusion in chemical pattern formation has been widely studied due to the great diversity of patterns emerging in reaction-diffusion systems, particularly in H + -autocatalytic reactions where hydrogels are applied to avoid convection. A custom-made conductometric cell is designed to measure the effective diffusion coefficient of a pair of strong electrolytes containing sodium ions or hydrogen ions with a common anion. This together with the individual diffusion coefficient for sodium ions, obtained from PFGSE-NMR spectroscopy, allows the determination of the diffusion coefficient of hydrogen ions in hydrogels. Numerical calculations are also performed to study the behavior of a diffusion-migration model describing ionic diffusion in our system. The method we present for one particular case may be extended for various hydrogels and diffusing ions (such as hydroxide) which are relevant e.g. for the development of pH-regulated self-healing mechanisms and hydrogels used for drug delivery.

A numerical solution for a class of time fractional diffusion equations with delay

Directory of Open Access Journals (Sweden)

Pimenov Vladimir G.

2017-09-01

Full Text Available This paper describes a numerical scheme for a class of fractional diffusion equations with fixed time delay. The study focuses on the uniqueness, convergence and stability of the resulting numerical solution by means of the discrete energy method. The derivation of a linearized difference scheme with convergence order O(τ2−α+ h4 in L∞-norm is the main purpose of this study. Numerical experiments are carried out to support the obtained theoretical results.

A systematic determination of diffusion coefficients of trace elements in open and restricted diffusive layers used by the diffusive gradients in a thin film technique

DEFF Research Database (Denmark)

Shiva, Amir Houshang; Teasdale, Peter R.; Bennett, William W.

2015-01-01

A systematic comparison of the diffusion coefficients of cations (Al, Cd, Co, Cu, Mn, Ni, Pb, Zn) and oxyanions (Al, As, Mo, Sb, V, W) in open (ODL) and restricted (RDL) diffusive layers used by the DGT technique was undertaken. Diffusion coefficients were measured using both the diffusion cell...... concentrations required with the Dcell measurements. This is the first time that D values have been reported for several oxyanions using RDL. Except for Al at pH 8.30 with ODL, all DDGT measurements were retarded relative to diffusion coefficients in water (DW) for both diffusive hydrogels. Diffusion in RDL...

Preclinical, fluorescence and diffuse optical tomography: non-contact instrumentation, modeling and time-resolved 3D reconstruction

International Nuclear Information System (INIS)

Nouizi, F.

2011-09-01

Time-Resolved Diffuse Optical Tomography (TR-DOT) is a new non-invasive imaging technique increasingly used in the clinical and preclinical fields. It yields optical absorption and scattering maps of the explored organs, and related physiological parameters. Time-Resolved Fluorescence Diffuse Optical Tomography (TR-FDOT) is based on the detection of fluorescence photons. It provides spatio-temporal maps of fluorescent probe concentrations and life times, and allows access to metabolic and molecular imaging which is important for diagnosis and therapeutic monitoring, particularly in oncology. The main goal of this thesis was to reconstruct 3D TR-DOT/TR-FDOT images of small animals using time-resolved optical technology. Data were acquired using optical fibers fixed around the animal without contact with its surface. The work was achieved in four steps: 1)- Setting up an imaging device to record the 3D coordinates of an animal's surface; 2)- Modeling the no-contact approach to solve the forward problem; 3)- Processing of the measured signals taking into account the impulse response of the device; 4)- Implementation of a new image reconstruction method based on a selection of carefully chosen points. As a result, good-quality 3D optical images were obtained owing to reduced cross-talk between absorption and scattering. Moreover, the computation time was cut down, compared to full-time methods using whole temporal profiles. (author)

Finite difference solution of the time dependent neutron group diffusion equations

International Nuclear Information System (INIS)

Hendricks, J.S.; Henry, A.F.

1975-08-01

In this thesis two unrelated topics of reactor physics are examined: the prompt jump approximation and alternating direction checkerboard methods. In the prompt jump approximation it is assumed that the prompt and delayed neutrons in a nuclear reactor may be described mathematically as being instantaneously in equilibrium with each other. This approximation is applied to the spatially dependent neutron diffusion theory reactor kinetics model. Alternating direction checkerboard methods are a family of finite difference alternating direction methods which may be used to solve the multigroup, multidimension, time-dependent neutron diffusion equations. The reactor mesh grid is not swept line by line or point by point as in implicit or explicit alternating direction methods; instead, the reactor mesh grid may be thought of as a checkerboard in which all the ''red squares'' and '' black squares'' are treated successively. Two members of this family of methods, the ADC and NSADC methods, are at least as good as other alternating direction methods. It has been found that the accuracy of implicit and explicit alternating direction methods can be greatly improved by the application of an exponential transformation. This transformation is incompatible with checkerboard methods. Therefore, a new formulation of the exponential transformation has been developed which is compatible with checkerboard methods and at least as good as the former transformation for other alternating direction methods

Experimental test of depth dependence of solutions for time-resolved diffusion equation

Energy Technology Data Exchange (ETDEWEB)

Laidevant, A.; Da Silva, A.; Moy, J.P.; Berger, M.; Dinten, J.M

2004-07-01

The determination of optical properties of a semi-infinite medium such as biological tissue has been widely investigated by many authors. Reflectance formulas can be derived from the diffusion equation for different boundary conditions at the medium-air interface. This quantity can be measured at the medium surface. For realistic objects, such as a mouse, tissue optical properties can realistically only be determined at the object surface. However, near the surface diffusion approximation is weak and boundary models have to be considered. In order to investigate the validity of the time resolved reflectance approach at the object boundary, we have estimated optical properties of a liquid semi-infinite medium by this method for different boundary conditions and different fiber's position beneath the surface. The time-correlated single photon counting (TCSPC) technique is used to measure the reflectance curve. Our liquid phantoms are made of water, Intra-lipid and Ink. Laser light is delivered by a pulsed laser diode. Measurements are then fitted to theoretical solutions expressed as a function of source and detector's depth and distance. By taking as reference the optical properties obtained from the infinite model for fibers deeply immersed, influence of the different boundary conditions and bias induced are established for different fibers' depth and a variety of solutions. This influence is analysed by comparing evolution of the reflectance models, as well as estimations of absorption and scattering coefficients. According to this study we propose a strategy for determining optical properties of a solid phantom where measurements can only be realized at the surface. (authors)

Assessment and diffusion of medical innovations in France: an overview.

Science.gov (United States)

Dubromel, Amélie; Geffroy, Loïc; Aulagner, Gilles; Dussart, Claude

2018-01-01

Background: In France, a significant part of health expenditure is publicly funding. This put a heavy burden on society. In an economic context requiring tight control of public spending, it seems relevant to control the diffusion of medical innovations. That is why health technology assessment is subject to an increasing interest at national level for management and approval decisions. This article provides an overview of the assessment and diffusion of medical innovation in France. Method: The data are extracted from French authorities or organisations websites and documents and from French legislative texts. In addition, regarding discussion, a search in MEDLINE database was carried out. Results: An overview of the assessment and diffusion of medical innovation in France is given by presenting the different types of medical innovations according to French health system definition (I); introducing French authorities participating to health technology assessment and describe assessment procedures of medical innovations (II); and giving details about market access process of innovative health product in France (III). Key opportunities and challenges of medical innovation assessment and diffusion in France are discussed at the end of this article. Conclusion: In France, medical innovation is considered as a crucial component for quality of care and performance of healthcare system. The aim of health technology assessment is to promote a secure and timely access to innovation for patients. Nevertheless, it appears necessary to improve regulatory mechanisms.

How attention influences perceptual decision making: Single-trial EEG correlates of drift-diffusion model parameters

Science.gov (United States)

Nunez, Michael D.; Vandekerckhove, Joachim; Srinivasan, Ramesh

2016-01-01

Perceptual decision making can be accounted for by drift-diffusion models, a class of decision-making models that assume a stochastic accumulation of evidence on each trial. Fitting response time and accuracy to a drift-diffusion model produces evidence accumulation rate and non-decision time parameter estimates that reflect cognitive processes. Our goal is to elucidate the effect of attention on visual decision making. In this study, we show that measures of attention obtained from simultaneous EEG recordings can explain per-trial evidence accumulation rates and perceptual preprocessing times during a visual decision making task. Models assuming linear relationships between diffusion model parameters and EEG measures as external inputs were fit in a single step in a hierarchical Bayesian framework. The EEG measures were features of the evoked potential (EP) to the onset of a masking noise and the onset of a task-relevant signal stimulus. Single-trial evoked EEG responses, P200s to the onsets of visual noise and N200s to the onsets of visual signal, explain single-trial evidence accumulation and preprocessing times. Within-trial evidence accumulation variance was not found to be influenced by attention to the signal or noise. Single-trial measures of attention lead to better out-of-sample predictions of accuracy and correct reaction time distributions for individual subjects. PMID:28435173

How attention influences perceptual decision making: Single-trial EEG correlates of drift-diffusion model parameters.

Science.gov (United States)

Nunez, Michael D; Vandekerckhove, Joachim; Srinivasan, Ramesh

2017-02-01

Perceptual decision making can be accounted for by drift-diffusion models, a class of decision-making models that assume a stochastic accumulation of evidence on each trial. Fitting response time and accuracy to a drift-diffusion model produces evidence accumulation rate and non-decision time parameter estimates that reflect cognitive processes. Our goal is to elucidate the effect of attention on visual decision making. In this study, we show that measures of attention obtained from simultaneous EEG recordings can explain per-trial evidence accumulation rates and perceptual preprocessing times during a visual decision making task. Models assuming linear relationships between diffusion model parameters and EEG measures as external inputs were fit in a single step in a hierarchical Bayesian framework. The EEG measures were features of the evoked potential (EP) to the onset of a masking noise and the onset of a task-relevant signal stimulus. Single-trial evoked EEG responses, P200s to the onsets of visual noise and N200s to the onsets of visual signal, explain single-trial evidence accumulation and preprocessing times. Within-trial evidence accumulation variance was not found to be influenced by attention to the signal or noise. Single-trial measures of attention lead to better out-of-sample predictions of accuracy and correct reaction time distributions for individual subjects.

Modelling accelerated degradation data using Wiener diffusion with a time scale transformation.

Science.gov (United States)

Whitmore, G A; Schenkelberg, F

1997-01-01

Engineering degradation tests allow industry to assess the potential life span of long-life products that do not fail readily under accelerated conditions in life tests. A general statistical model is presented here for performance degradation of an item of equipment. The degradation process in the model is taken to be a Wiener diffusion process with a time scale transformation. The model incorporates Arrhenius extrapolation for high stress testing. The lifetime of an item is defined as the time until performance deteriorates to a specified failure threshold. The model can be used to predict the lifetime of an item or the extent of degradation of an item at a specified future time. Inference methods for the model parameters, based on accelerated degradation test data, are presented. The model and inference methods are illustrated with a case application involving self-regulating heating cables. The paper also discusses a number of practical issues encountered in applications.

Analytical solutions to matrix diffusion problems

Energy Technology Data Exchange (ETDEWEB)

Kekäläinen, Pekka, E-mail: pekka.kekalainen@helsinki.fi [Laboratory of Radiochemistry, Department of Chemistry, P.O. Box 55, FIN-00014 University of Helsinki (Finland)

2014-10-06

We report an analytical method to solve in a few cases of practical interest the equations which have traditionally been proposed for the matrix diffusion problem. In matrix diffusion, elements dissolved in ground water can penetrate the porous rock surronuding the advective flow paths. In the context of radioactive waste repositories this phenomenon provides a mechanism by which the area of rock surface in contact with advecting elements is greatly enhanced, and can thus be an important delay mechanism. The cases solved are relevant for laboratory as well for in situ experiments. Solutions are given as integral representations well suited for easy numerical solution.

Global exponential stability for reaction-diffusion recurrent neural networks with multiple time varying delays

International Nuclear Information System (INIS)

Lou, X.; Cui, B.

2008-01-01

In this paper we consider the problem of exponential stability for recurrent neural networks with multiple time varying delays and reaction-diffusion terms. The activation functions are supposed to be bounded and globally Lipschitz continuous. By means of Lyapunov functional, sufficient conditions are derived, which guarantee global exponential stability of the delayed neural network. Finally, a numerical example is given to show the correctness of our analysis. (author)

A development of simulation and analytical program for through-diffusion experiments for a single layer of diffusion media

International Nuclear Information System (INIS)

Sato, Haruo

2001-01-01

A program (TDROCK1. FOR) for simulation and analysis of through-diffusion experiments for a single layer of diffusion media was developed. This program was made by Pro-Fortran language, which was suitable for scientific and technical calculations, and relatively easy explicit difference method was adopted for an analysis. In the analysis, solute concentration in the tracer cell as a function of time that we could not treat to date can be input and the decrease in the solute concentration as a function of time by diffusion from the tracer cell to the measurement cell, the solute concentration distribution in the porewater of diffusion media and the solute concentration in the measurement cell as a function of time can be calculated. In addition, solution volume in both cells and diameter and thickness of the diffusion media are also variable as an input condition. This simulation program could well explain measured result by simulating solute concentration in the measurement cell as a function of time for case which apparent and effective diffusion coefficients were already known. Based on this, the availability and applicability of this program to actual analysis and simulation were confirmed. This report describes the theoretical treatment for the through-diffusion experiments for a single layer of diffusion media, analytical model, an example of source program and the manual. (author)

Gold Cluster Diffusion Kinetics on Stoichiometric and Reduced Surfaces of Rutile TiO ₂ (110)

Energy Technology Data Exchange (ETDEWEB)

Goldman, Nir; Browning, Nigel D.

2011-06-16

Gold clusters on rutile TiO₂ are known to serve as efficient oxidation catalysts for pollutants and environmental contaminants. However, the mechanism by which highly mobile small clusters migrate and aggregate into larger species relevant to gold’s catalytic activity remains unresolved. We report herein on ab initio simulations of the diffusion of atomic gold clusters up to the trimer on rutile TiO₂(110) surfaces. We show that, on the stoichiometric surface, both the dimer and the trimer can exhibit relatively low surface mobility due to high energetic barriers for diffusion out of their energetic minima coupled with low barriers for the reverse motion. On the reduced surface, these clusters can diffuse relatively quickly between energetic minima within the oxygen vacancy site due to the large degree of vibrational entropy in their transition states. Our computed diffusion times provide a point of comparison for future experiments and will aid in development of models of gold cluster island sintering.

Correlated diffusion imaging

International Nuclear Information System (INIS)

Wong, Alexander; Glaister, Jeffrey; Cameron, Andrew; Haider, Masoom

2013-01-01

Prostate cancer is one of the leading causes of cancer death in the male population. Fortunately, the prognosis is excellent if detected at an early stage. Hence, the detection and localization of prostate cancer is crucial for diagnosis, as well as treatment via targeted focal therapy. New imaging techniques can potentially be invaluable tools for improving prostate cancer detection and localization. In this study, we introduce a new form of diffusion magnetic resonance imaging called correlated diffusion imaging, where the tissue being imaged is characterized by the joint correlation of diffusion signal attenuation across multiple gradient pulse strengths and timings. By taking into account signal attenuation at different water diffusion motion sensitivities, correlated diffusion imaging can provide improved delineation between cancerous tissue and healthy tissue when compared to existing diffusion imaging modalities. Quantitative evaluation using receiver operating characteristic (ROC) curve analysis, tissue class separability analysis, and visual assessment by an expert radiologist were performed to study correlated diffusion imaging for the task of prostate cancer diagnosis. These results are compared with that obtained using T2-weighted imaging and standard diffusion imaging (via the apparent diffusion coefficient (ADC)). Experimental results suggest that correlated diffusion imaging provide improved delineation between healthy and cancerous tissue and may have potential as a diagnostic tool for cancer detection and localization in the prostate gland. A new form of diffusion magnetic resonance imaging called correlated diffusion imaging (CDI) was developed for the purpose of aiding radiologists in cancer detection and localization in the prostate gland. Preliminary results show CDI shows considerable promise as a diagnostic aid for radiologists in the detection and localization of prostate cancer

Spatial characterization of T1 and T2 relaxation times and the water apparent diffusion coefficient in rabbit Achilles tendon subjected to tensile loading.

Science.gov (United States)

Wellen, J; Helmer, K G; Grigg, P; Sotak, C H

2005-03-01

Tendons exhibit viscoelastic mechanical behavior under tensile loading. The elasticity arises from the collagen chains that form fibrils, while the viscous response arises from the interaction of the water with the solid matrix. Therefore, an understanding of the behavior of water in response to the application of a load is crucial to the understanding of the origin of the viscous response. Three-dimensional MRI mapping of rabbit Achilles tendons was performed at 2.0 T to characterize the response of T(1) and T(2) relaxation times and the apparent diffusion coefficient (ADC) of water to tensile loading. The ADC was measured in directions both parallel (ADC( parallel)) and perpendicular (ADC( perpendicular)) to the long axis of the tendon. At a short diffusion time (5.8 ms) MR parameter maps showed the existence of two regions, here termed "core" and "rim", that exhibited statistically significant differences in T(1), T(2), and ADC( perpendicular) under the baseline loading condition. MR parameter maps were also generated at a second loading condition of approximately 1 MPa. At a diffusion time of 5.8 ms, there was a statistically significant increase in the rim region for both ADC( perpendicular) (57.5%) and ADC( parallel) (20.5%) upon tensile loading. The changes in core ADC(( perpendicular), ( parallel)), as well as the relaxation parameters in both core and rim regions, were not statistically significant. The effect of diffusion time on the ADC(( perpendicular), ( parallel)) values was investigated by creating maps at three additional diffusion times (50.0, 125.0, 250.0 ms) using a diffusion-weighted, stimulated-echo (DW-STE) pulse sequence. At longer diffusion times, ADC(( perpendicular), ( parallel)) values increased rather than approaching a constant value. This observation was attributed to T(1) spin-editing during the DW-STE pulse sequence, which resulted in the loss of short-T(1) components (with correspondingly lower ADCs) at longer diffusion times

Diffusion in Deterministic Interacting Lattice Systems

Science.gov (United States)

Medenjak, Marko; Klobas, Katja; Prosen, Tomaž

2017-09-01

We study reversible deterministic dynamics of classical charged particles on a lattice with hard-core interaction. It is rigorously shown that the system exhibits three types of transport phenomena, ranging from ballistic, through diffusive to insulating. By obtaining an exact expressions for the current time-autocorrelation function we are able to calculate the linear response transport coefficients, such as the diffusion constant and the Drude weight. Additionally, we calculate the long-time charge profile after an inhomogeneous quench and obtain diffusive profilewith the Green-Kubo diffusion constant. Exact analytical results are corroborated by Monte Carlo simulations.

Process of advective diffusive enrichment using differential gradients and the effects of variations in relaxation times

International Nuclear Information System (INIS)

Suarez Antola R.; Bernasconi, G.; Bertolotti, Angel

1995-01-01

A multicomponent solution is considered in advective diffusion chambers between two half-permeable barriers. A mathematical model is developed to calculate the concentration fields in the chamber. A new enrichment process is proposed and assessed using a digital simulation of space-time dynamics, based on the analytical solution of the model

Spectral Analysis and Computation of Effective Diffusivities in Space-time Periodic Incompressible Flows

Science.gov (United States)

2015-11-01

diffusive tracer fluxes, directed normal to the tracer gradient [64], are generally equivalent to antisymmetric components in the effective diffusivity...tensor D∗, while the symmetric part of D∗ represents irreversible diffusive effects [83, 87, 39] directed down the tracer gradient . The mixing of eddy...provides an operational calculus in Hilbert space which yields powerful integral representations involving the Stieltjes measures displayed in equation

Ag diffusion in cubic silicon carbide

International Nuclear Information System (INIS)

Shrader, David; Khalil, Sarah M.; Gerczak, Tyler; Allen, Todd R.; Heim, Andrew J.; Szlufarska, Izabela; Morgan, Dane

2011-01-01

The diffusion of Ag impurities in bulk 3C-SiC is studied using ab initio methods based on density functional theory. This work is motivated by the desire to reduce transport of radioactive Ag isotopes through the SiC boundary layer in the Tristructural-Isotropic (TRISO) fuel pellet, which is a significant concern for the Very High Temperature Reactor (VHTR) nuclear reactor concept. The structure and stability of charged Ag and Ag-vacancy clusters in SiC are calculated. Relevant intrinsic SiC defect energies are also determined. The most stable state for the Ag impurity in SiC is found to be a Ag atom substituting on the Si sub-lattice and bound to a C vacancy. Bulk diffusion coefficients are estimated for different impurity states and values are all found to have very high activation energy. The impurity state with the lowest activation energy for diffusion is found to be the Ag interstitial, with an activation energy of approximately 7.9 eV. The high activation energies for Ag diffusion in bulk 3C-SiC cause Ag transport to be very slow in the bulk and suggests that observed Ag transport in this material is due to an alternative mechanism (e.g., grain boundary diffusion).

Hopf Bifurcation Analysis of a Gene Regulatory Network Mediated by Small Noncoding RNA with Time Delays and Diffusion

Science.gov (United States)

Li, Chengxian; Liu, Haihong; Zhang, Tonghua; Yan, Fang

2017-12-01

In this paper, a gene regulatory network mediated by small noncoding RNA involving two time delays and diffusion under the Neumann boundary conditions is studied. Choosing the sum of delays as the bifurcation parameter, the stability of the positive equilibrium and the existence of spatially homogeneous and spatially inhomogeneous periodic solutions are investigated by analyzing the corresponding characteristic equation. It is shown that the sum of delays can induce Hopf bifurcation and the diffusion incorporated into the system can effect the amplitude of periodic solutions. Furthermore, the spatially homogeneous periodic solution always exists and the spatially inhomogeneous periodic solution will arise when the diffusion coefficients of protein and mRNA are suitably small. Particularly, the small RNA diffusion coefficient is more robust and its effect on model is much less than protein and mRNA. Finally, the explicit formulae for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by employing the normal form theory and center manifold theorem for partial functional differential equations. Finally, numerical simulations are carried out to illustrate our theoretical analysis.

Application of TRIZ Methodology in Diffusion Welding System Optimization

Science.gov (United States)

Ravinder Reddy, N.; Satyanarayana, V. V.; Prashanthi, M.; Suguna, N.

2017-12-01

Welding is tremendously used in metal joining processes in the manufacturing process. In recent years, diffusion welding method has significantly increased the quality of a weld. Nevertheless, diffusion welding has some extent short research and application progress. Therefore, diffusion welding has a lack of relevant information, concerned with the joining of thick and thin materials with or without interlayers, on welding design such as fixture, parameters selection and integrated design. This article intends to combine innovative methods in the application of diffusion welding design. This will help to decrease trial and error or failure risks in the welding process being guided by the theory of inventive problem solving (TRIZ) design method. This article hopes to provide welding design personnel with innovative design ideas under research and for practical application.

The out of equilibrium response function in sub-diffusive systems

International Nuclear Information System (INIS)

Gradenigo, G; Puglisi, A; Sarracino, A; Vulpiani, A; Villamaina, D

2012-01-01

We study the Einstein relation between spontaneous fluctuations and the response to an external perturbation for the comb model and the single file, which are examples of systems with sub-diffusive transport properties. The relevance of nonequilibrium conditions is investigated: when a stationary current (in the form of a drift or an energy flux) is present, the Einstein relation breaks down. In the case of the comb model, a general relation - appearing in the recent literature - between the response function and an unperturbed suitable correlation function allows us to explain the obtained results. This suggests that the relevant ingredient in breaking the Einstein formula, for stationary regimes, is not anomalous diffusion but the presence of currents driving the system out of equilibrium.

Modeling methanol transfer in the mesoporous catalyst for the methanol-to-olefins reaction by the time-fractional diffusion equation

Science.gov (United States)

Zhokh, Alexey A.; Strizhak, Peter E.

2018-04-01

The solutions of the time-fractional diffusion equation for the short and long times are obtained via an application of the asymptotic Green's functions. The derived solutions are applied to analysis of the methanol mass transfer through H-ZSM-5/alumina catalyst grain. It is demonstrated that the methanol transport in the catalysts pores may be described by the obtained solutions in a fairly good manner. The measured fractional exponent is equal to 1.20 ± 0.02 and reveals the super-diffusive regime of the methanol mass transfer. The presence of the anomalous transport may be caused by geometrical restrictions and the adsorption process on the internal surface of the catalyst grain's pores.

Relevance of quantum mechanics on some aspects of ion channel function

OpenAIRE

Roy, Sisir; Llinás, Rodolfo

2009-01-01

Mathematical modeling of ionic diffusion along K ion channels indicates that such diffusion is oscillatory, at the weak non-Markovian limit. This finding leads us to derive a Schrödinger–Langevin equation for this kind of system within the framework of stochastic quantization. The Planck’s constant is shown to be relevant to the Lagrangian action at the level of a single ion channel. This sheds new light on the issue of applicability of quantum formalism to ion channel dynamics and to the phy...

Stability and Hopf Bifurcation of a Reaction-Diffusion Neutral Neuron System with Time Delay

Science.gov (United States)

Dong, Tao; Xia, Linmao

2017-12-01

In this paper, a type of reaction-diffusion neutral neuron system with time delay under homogeneous Neumann boundary conditions is considered. By constructing a basis of phase space based on the eigenvectors of the corresponding Laplace operator, the characteristic equation of this system is obtained. Then, by selecting time delay and self-feedback strength as the bifurcating parameters respectively, the dynamic behaviors including local stability and Hopf bifurcation near the zero equilibrium point are investigated when the time delay and self-feedback strength vary. Furthermore, the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are obtained by using the normal form and the center manifold theorem for the corresponding partial differential equation. Finally, two simulation examples are given to verify the theory.

Measurement of Solute Diffusion Behavior in Fractured Waste Glass Media

International Nuclear Information System (INIS)

Saripalli, Kanaka P.; Lindberg, Michael J.; Meyer, Philip D.

2008-01-01

Determination of aqueous phase diffusion coefficients of solutes through fractured media is essential for understanding and modeling contaminants transport at many hazardous waste disposal sites. No methods for earlier measurements are available for the characterization of diffusion in fractured glass blocks. We report here the use of time-lag diffusion experimental method to assess the diffusion behavior of three different solutes (Cs, Sr and Pentafluoro Benzoic Acid or PFBA) in fractured, immobilized low activity waste (ILAW) glass forms. A fractured media time-lag diffusion experimental apparatus that allows the measurement of diffusion coefficients has been designed and built for this purpose. Use of time-lag diffusion method, a considerably easier experimental method than the other available methods, was not previously demonstrated for measuring diffusion in any fractured media. Hydraulic conductivity, porosity and diffusion coefficients of a solute were experimentally measured in fractured glass blocks using this method for the first time. Results agree with the range of properties reported for similar rock media earlier, indicating that the time-lag experimental method can effectively characterize the diffusion coefficients of fractured ILAW glass media

Distributed order reaction-diffusion systems associated with Caputo derivatives

Science.gov (United States)

Saxena, R. K.; Mathai, A. M.; Haubold, H. J.

2014-08-01

This paper deals with the investigation of the solution of an unified fractional reaction-diffusion equation of distributed order associated with the Caputo derivatives as the time-derivative and Riesz-Feller fractional derivative as the space-derivative. The solution is derived by the application of the joint Laplace and Fourier transforms in compact and closed form in terms of the H-function. The results derived are of general nature and include the results investigated earlier by other authors, notably by Mainardi et al. ["The fundamental solution of the space-time fractional diffusion equation," Fractional Calculus Appl. Anal. 4, 153-202 (2001); Mainardi et al. "Fox H-functions in fractional diffusion," J. Comput. Appl. Math. 178, 321-331 (2005)] for the fundamental solution of the space-time fractional equation, including Haubold et al. ["Solutions of reaction-diffusion equations in terms of the H-function," Bull. Astron. Soc. India 35, 681-689 (2007)] and Saxena et al. ["Fractional reaction-diffusion equations," Astrophys. Space Sci. 305, 289-296 (2006a)] for fractional reaction-diffusion equations. The advantage of using the Riesz-Feller derivative lies in the fact that the solution of the fractional reaction-diffusion equation, containing this derivative, includes the fundamental solution for space-time fractional diffusion, which itself is a generalization of fractional diffusion, space-time fraction diffusion, and time-fractional diffusion, see Schneider and Wyss ["Fractional diffusion and wave equations," J. Math. Phys. 30, 134-144 (1989)]. These specialized types of diffusion can be interpreted as spatial probability density functions evolving in time and are expressible in terms of the H-function in compact forms. The convergence conditions for the double series occurring in the solutions are investigated. It is interesting to observe that the double series comes out to be a special case of the Srivastava-Daoust hypergeometric function of two variables

Density-Dependent Conformable Space-time Fractional Diffusion-Reaction Equation and Its Exact Solutions

Science.gov (United States)

Hosseini, Kamyar; Mayeli, Peyman; Bekir, Ahmet; Guner, Ozkan

2018-01-01

In this article, a special type of fractional differential equations (FDEs) named the density-dependent conformable fractional diffusion-reaction (DDCFDR) equation is studied. Aforementioned equation has a significant role in the modelling of some phenomena arising in the applied science. The well-organized methods, including the \\exp (-φ (\\varepsilon )) -expansion and modified Kudryashov methods are exerted to generate the exact solutions of this equation such that some of the solutions are new and have been reported for the first time. Results illustrate that both methods have a great performance in handling the DDCFDR equation.

Particle diffusion in a spheromak

International Nuclear Information System (INIS)

Meyerhofer, D.D.; Levinton, F.M.; Yamada, M.

1988-01-01

The local carbon particle diffusion coefficient was measured in the Proto S-1/C spheromak using a test particle injection scheme. When the plasma was not in a force-free Taylor state, and when there were pressure gradients in the plasma, the particle diffusion was five times that predicted by Bohm and was consistent with collisional drift wave diffusion. The diffusion appears to be driven by correlations of the fluctuating electric field and density. During the decay phase of the discharge when the plasma was in the Taylor state, the diffusion coefficient of the carbon was classical. 23 refs., 4 figs

Modelling effects of tree population dynamics, tree throw and pit-mound formation/diffusion on microtopography over time in different forest settings

Science.gov (United States)

Martin, Y. E.; Johnson, E. A.; Gallaway, J.; Chaikina, O.

2011-12-01

Herein we conduct a followup investigation to an earlier research project in which we developed a numerical model of tree population dynamics, tree throw, and sediment transport associated with the formation of pit-mound features for Hawk Creek watershed, Canadian Rockies (Gallaway et al., 2009). We extend this earlier work by exploring the most appropriate transport relations to simulate the diffusion over time of newly-formed pit-pound features due to tree throw. We combine our earlier model with a landscape development model that can incorporate these diffusive transport relations. Using these combined models, changes in hillslope microtopography over time associated with the formation of pit-mound features and their decay will be investigated. The following ideas have motivated this particular study: (i) Rates of pit-mound degradation remain a source of almost complete speculation, as there is almost no long-term information on process rates. Therefore, we will attempt to tackle the issue of pit-mound degradation in a methodical way that can guide future field studies; (ii) The degree of visible pit-mound topography at any point in time on the landscape is a joint function of the rate of formation of new pit-mound features due to tree death/topple and their magnitude vs. the rate of decay of pit-mound features. An example of one interesting observation that arises is the following: it appears that pit-mound topography is often more pronounced in some eastern North American forests vs. field sites along the eastern slopes of the Canadian Rockies. Why is this the case? Our investigation begins by considering whether pit-mound decay might occur by linear or nonlinear diffusion. What differences might arise depending on which diffusive approach is adopted? What is the magnitude of transport rates associated with these possible forms of transport relations? We explore linear and nonlinear diffusion at varying rates and for different sizes of pit-mound pairs using a

Slow-fast stochastic diffusion dynamics and quasi-stationarity for diploid populations with varying size.

Science.gov (United States)

Coron, Camille

2016-01-01

We are interested in the long-time behavior of a diploid population with sexual reproduction and randomly varying population size, characterized by its genotype composition at one bi-allelic locus. The population is modeled by a 3-dimensional birth-and-death process with competition, weak cooperation and Mendelian reproduction. This stochastic process is indexed by a scaling parameter K that goes to infinity, following a large population assumption. When the individual birth and natural death rates are of order K, the sequence of stochastic processes indexed by K converges toward a new slow-fast dynamics with variable population size. We indeed prove the convergence toward 0 of a fast variable giving the deviation of the population from quasi Hardy-Weinberg equilibrium, while the sequence of slow variables giving the respective numbers of occurrences of each allele converges toward a 2-dimensional diffusion process that reaches (0,0) almost surely in finite time. The population size and the proportion of a given allele converge toward a Wright-Fisher diffusion with stochastically varying population size and diploid selection. We insist on differences between haploid and diploid populations due to population size stochastic variability. Using a non trivial change of variables, we study the absorption of this diffusion and its long time behavior conditioned on non-extinction. In particular we prove that this diffusion starting from any non-trivial state and conditioned on not hitting (0,0) admits a unique quasi-stationary distribution. We give numerical approximations of this quasi-stationary behavior in three biologically relevant cases: neutrality, overdominance, and separate niches.

Ion-Scale Structure in Mercury's Magnetopause Reconnection Diffusion Region

Science.gov (United States)

Gershman, Daniel J.; Dorelli, John C.; DiBraccio, Gina A.; Raines, Jim M.; Slavin, James A.; Poh, Gangkai; Zurbuchen, Thomas H.

2016-01-01

The strength and time dependence of the electric field in a magnetopause diffusion region relate to the rate of magnetic reconnection between the solar wind and a planetary magnetic field. Here we use approximately 150 milliseconds measurements of energetic electrons from the Mercury Surface, Space Environment, GEochemistry, and Ranging (MESSENGER) spacecraft observed over Mercury's dayside polar cap boundary (PCB) to infer such small-scale changes in magnetic topology and reconnection rates. We provide the first direct measurement of open magnetic topology in flux transfer events at Mercury, structures thought to account for a significant portion of the open magnetic flux transport throughout the magnetosphere. In addition, variations in PCB latitude likely correspond to intermittent bursts of approximately 0.3 to 3 millivolts per meter reconnection electric fields separated by approximately 5 to10 seconds, resulting in average and peak normalized dayside reconnection rates of approximately 0.02 and approximately 0.2, respectively. These data demonstrate that structure in the magnetopause diffusion region at Mercury occurs at the smallest ion scales relevant to reconnection physics.

An exploration into diffusion tensor imaging in the bovine ocular lens

Directory of Open Access Journals (Sweden)

Ehsan eVaghefi

2013-03-01

Full Text Available We describe our development of the diffusion tensor imaging modality for the bovine ocular lens. Diffusion gradients were added to a spin-echo pulse sequence and the relevant parameters of the sequence were refined to achieve good diffusion weighting in the lens tissue, which demonstrated heterogeneous regions of diffusive signal attenuation. Decay curves for b-value (loosely summarizes the strength of diffusion weighting and TE (determines the amount of MRI-obtained signal were used to estimate apparent diffusion coefficients (ADC and T2 in different lens regions. The ADCs varied by over an order of magnitude and revealed diffusive anisotropy in the lens. Up to 30 diffusion gradient directions, and 8 signal acquisition averages, were applied to lenses in culture in order to improve maps of diffusion tensor eigenvalues, equivalent to ADC, across the lens. From these maps, fractional anisotropy maps were calculated and compared to known spatial distributions of anisotropic molecular fluxes in the lens. This comparison suggested new hypotheses and experiments to quantitatively assess models of circulation in the avascular lens.

The limitation and modification of flux-limited diffusion theory

International Nuclear Information System (INIS)

Liu Chengan; Huang Wenkai

1986-01-01

The limitation of various typical flux-limited diffusion theory and advantages of asymptotic diffusion theory with time absorption constant are analyzed and compared. The conclusions are as following: Though the flux-limited problem in neutron diffusion theory are theoretically solved by derived flux-limited diffusion equation, it's going too far to limit flux due to the inappropriate assumption in deriving flux-limited diffusion equation. The asymptotic diffusion theory with time absorption constant has eliminated the above-mentioned limitation, and it is more accurate than flux-limited diffusion theory in describing neutron transport problem

Self-diffusion dynamics processes relevant to 2D homoepitaxy growth of Ni adatom on Ni(111) surface

Energy Technology Data Exchange (ETDEWEB)

Liu, Fusheng [College of Metallurgical Engineering, Hunan University of Technology, Zhuzhou 412007 (China); Chen, Yifeng, E-mail: yefengc63@sina.com [College of Metallurgical Engineering, Hunan University of Technology, Zhuzhou 412007 (China); Wang, Yufei, E-mail: yejin802@126.com [College of Metallurgical Engineering, Hunan University of Technology, Zhuzhou 412007 (China); Liu, Zhulin; Hu, Zhongliang [College of Metallurgical Engineering, Hunan University of Technology, Zhuzhou 412007 (China); Yang, Xiyuan [Department of Physics, Hunan University of Arts and Science, Changde 415000 (China); Luo, Wenhua [Department of Physics and Electronic Information Science, Hunan Institute of Science and Technology, Yueyang 414006 (China)

2014-07-01

Using molecular dynamics and modified analytic embedded atom methods, the atomic self-diffusion dynamics behaviors relevant to 2D crystal growth on Ni(111) surface have been studied between 150 and 600 K. On perfect Ni(111) surface, the activation energy and prefactor are 0.058±0.001 eV and 4.2×10{sup −4} cm{sup 2}/s between 150 and 350 K, and 0.082±0.003 eV and 7.8×10{sup −4} cm{sup 2}/s from 400 to 600 K. Ni adatom just hops along the directions of close-packed steps on stepped Ni(111) surface, the corresponding activation energies and prefactors are 0.188±0.002 eV and (3.8–4.4)×10{sup −3} cm{sup 2}/s along the direction of A-type step, 0.140±0.001 eV and (1.1–1.2)×10{sup −3} cm{sup 2}/s along the direction of B-type step, and both fitting lines of Arrhenius law intersect at T{sub c}=420–440 K. Our results show that the atomic growth dynamics under nonequilibrium conditions is gradually dominated by the prefactor with increasing temperature. In addition, the shape-change of the 2D nanometer-size island has been discussed on stepped Ni(111) surface in different temperature range.

Uniqueness for inverse problems of determining orders of multi-term time-fractional derivatives of diffusion equation

OpenAIRE

Li, Zhiyuan; Yamamoto, Masahiro

2014-01-01

This article proves the uniqueness for two kinds of inverse problems of identifying fractional orders in diffusion equations with multiple time-fractional derivatives by pointwise observation. By means of eigenfunction expansion and Laplace transform, we reduce the uniqueness for our inverse problems to the uniqueness of expansions of some special function and complete the proof.

Diffusion rates for elevated releases

International Nuclear Information System (INIS)

Ramsdell, J.V.

1983-11-01

A search of the literature related to diffusion from elevated sources has determined that an adequate data base exists for use in developing parameterizations for estimating diffusion rates for material released from free standing stacks at nuclear power plants. A review of published data analyses indicates that a new parameterization of horizontal diffusion rates specifically for elevated releases is not likely to significantly change the magnitudes of horizontal diffusion coefficients on the average. However, the uncertainties associated with horizontal diffusion coefficient estimates under any given set of atmospheric conditions could be reduced by a new parameterization. Similarly, a new parameterization of vertical diffusion rates would be unlikely to significantly alter the magnitudes of diffusion coefficients for unstable atmospheric conditons. However, for neutral and stable atmospheric conditions, a new parameterization of vertical diffusion rates might increase vertical diffusion coefficients significantly. The increase would move ground-level time-integrated concentration maxima closer to the plant and would increase the maxima. 55 references, 2 figures, 4 tables

A study of the diffusion mechanisms in amorphous metallic alloys: diffusion and diffusion under high pressure in an amorphous NiZr alloy

International Nuclear Information System (INIS)

Grandjean, A.

1996-01-01

The aim of this work is a better understanding of the diffusion mechanism in amorphous metallic alloys. Then interdiffusion and hafnium diffusion in amorphous NiZr alloy have been studied. Samples used are made by sputtering co-deposition under vacuum and are well relaxed before the diffusion measurements. The time evolution of resistivity during annealing due to the decay of a composition modulated film has been measured and from this change in resistivity interdiffusion coefficients have been determined. Dependence of Hf diffusion on temperature and pressure has been studied using (SIMS). In this two cases, the diffusion process obeys an Arrhenius law and gives an activation energy of 1.33 eV for interdiffusion, and 0.76 eV for Hf diffusion. An effect of pressure on Hf diffusion has been found leading to an activation volume of 8.5 angstrom 3 . Thanks to these results, two approaches of the diffusion mechanisms in these systems have been proposed. The first comes from a comparison with the diffusion mechanisms in crystalline metals, that is to say by point defects. The second is an hypothesis of collective motions in these non crystalline alloys. (author)

A time-domain fluorescence diffusion optical tomography system for breast tumor diagnosis

Science.gov (United States)

Zhang, Wei; Gao, Feng; Wu, LinHui; Ma, Wenjuan; Yang, Fang; Zhou, Zhongxing; Zhang, Limin; Zhao, Huijuan

2011-02-01

A prototype time-domain fluorescence diffusion optical tomography (FDOT) system using near-infrared light is presented. The system employs two pulsed light sources, 32 source fibers and 32 detection channels, working separately for acquiring the temporal distribution of the photon flux on the tissue surface. The light sources are provided by low power picosecond pulsed diode lasers at wavelengths of 780 nm and 830 nm, and a 1×32-fiber-optic-switch sequentially directs light sources to the object surface through 32 source fibers. The light signals re-emitted from the object are collected by 32 detection fibers connected to four 8×1 fiber-optic-switch and then routed to four time-resolved measuring channels, each of which consists of a collimator, a filter wheel, a photomultiplier tube (PMT) photon-counting head and a time-correlated single photon counting (TCSPC) channel. The performance and efficacy of the designed multi-channel PMT-TCSPC system are assessed by reconstructing the fluorescent yield and lifetime images of a solid phantom.

Applicable or relevant and appropriate requirements (ARARs) for remedial actions at the Paducah Gaseous Diffusion Plant: A compendium of environmental laws and guidance

International Nuclear Information System (INIS)

Etnier, E.L.; Eaton, L.A.

1992-03-01

Section 121 of the Comprehensive Environmental Response, Compensation, and Liability Act (CERCLA) of 1980 specifies that remedial actions for cleanup of hazardous substances found at sites placed on the National Priorities List (NPL) by the US Environmental Protection Agency (EPA) must comply with applicable or relevant and appropriate requirements (ARARs) or standards under federal and state environmental laws. To date, the US Department of Energy (DOE) Paducah Gaseous Diffusion Plant (PGDP) has not been on the NPL. Although DOE and EPA have entered into an Administrative Consent Order (ACO), the prime regulatory authority for cleanup at PGDP will be the Resource Conservation and Recovery Act (RCRA). This report supplies a preliminary list of available federal and state ARARs that might be considered for remedial response at PGDP in the event that the plant becomes included on the NPL or the ACO is modified to include CERCLA cleanup. A description of the terms ''applicable'' and ''relevant and appropriate'' is provided, as well as definitions of chemical-, location-, and action-specific ARARS. ARARs promulgated by the federal government and by the state of Kentucky are listed in tables. In addition, the major provisions of RCRA, the Safe Drinking Water Act, the Clean Water Act, the Clean Air Act, and other acts, as they apply to hazardous and radioactive waste cleanup, are discussed

Diffusion of gases in solids: rare gas diffusion in solids; tritium diffusion in fission and fusion reactor metals. Final report

International Nuclear Information System (INIS)

Abraham, P.M.; Chandra, D.; Mintz, J.M.; Elleman, T.S.; Verghese, K.

1976-01-01

Major results of tritium and rare gas diffusion research conducted under the contract are summarized. The materials studied were austenitic stainless steels, Zircaloy, and niobium. In all three of the metal systems investigated, tritium release rates were found to be inhibited by surface oxide films. The effective diffusion coefficients that control tritium release from surface films on Zircaloy and niobium were determined to be eight to ten orders of magnitude lower than the bulk diffusion coefficients. A rapid component of diffusion due to grain boundaries was identified in stainless steels. The grain boundary diffusion coefficient was determined to be about six orders of magnitude greater than the bulk diffusion coefficient for tritium in stainless steel. In Zircaloy clad fuel pins, the permeation rate of tritium through the cladding is rate-limited by the extremely slow diffusion rate in the surface films. Tritium diffusion rates through surface oxide films on niobium appear to be controlled by cracks in the surface films at temperatures up to 600 0 C. Beyond 600 0 C, the cracks appear to heal, thereby increasing the activation energy for diffusion through the oxide film. The steady-state diffusion of tritium in a fusion reactor blanket has been evaluated in order to calculate the equilibrium tritium transport rate, approximate time to equilibrium, and tritium inventory in various regions of the reactor blanket as a function of selected blanket parameters. Values for these quantities have been tabulated

Intercomparison of diffusion coefficient derived from the through-diffusion experiment using different numerical methods

International Nuclear Information System (INIS)

Chih-Lung Chen; Institute of Nuclear Energy Research, Taoyuan, Taiwan; Tsing-Hai Wang; Shi-Ping Teng; Ching-Hor Lee

2014-01-01

Diffusion is a dominant mechanism regulating the transport of released nuclides. The through-diffusion method is typically applied to determine the diffusion coefficients (D). Depending on the design of the experiment, the concentrations in the source term [i.e., inlet reservoir (IR)] or the end term [i.e., outlet reservoir (OR)] can be fixed or vary. The combinations involve four distinct models (i.e., the CC-CC model, CC-VC model, VC-CC model, and the VC-VC model). Studies discussing the VC-CC model are scant. An analytical method considering the decay effect is required to accurately interpret the radioactive nuclide diffusion experiment results. Therefore, we developed a CC-CC model and a CC-VC model with a decay effect and the simplified formulas of these two models to determine the diffusion coefficient (i.e., the CC-CC method and CC-VC method). We also proposed two simplified methods using the VC-VC model to determine the diffusion coefficient straightforwardly based upon the concentration variation in IR and OR. More importantly, the best advantage of proposed method over others is that one can derive three diffusion coefficients based on one run of experiment. In addition, applying our CC-VC method to those data reported from Radiochemica Acta 96:111-117, 2008; and J Contam Hydrol 35:55-65, 1998, derived comparable diffusion coefficient lying in the identical order of magnitude. Furthermore, we proposed a formula to determine the conceptual critical time (Tc), which is particularly beneficial for the selection of using CC-VC or VC-VC method. Based on our proposed method, it becomes possible to calculate diffusion coefficient from a through-diffusion experiment in a shorter period of time. (author)

Solutions for a non-Markovian diffusion equation

International Nuclear Information System (INIS)

Lenzi, E.K.; Evangelista, L.R.; Lenzi, M.K.; Ribeiro, H.V.; Oliveira, E.C. de

2010-01-01

Solutions for a non-Markovian diffusion equation are investigated. For this equation, we consider a spatial and time dependent diffusion coefficient and the presence of an absorbent term. The solutions exhibit an anomalous behavior which may be related to the solutions of fractional diffusion equations and anomalous diffusion.

Prostate cancer detection from model-free T1-weighted time series and diffusion imaging

Science.gov (United States)

Haq, Nandinee F.; Kozlowski, Piotr; Jones, Edward C.; Chang, Silvia D.; Goldenberg, S. Larry; Moradi, Mehdi

2015-03-01

The combination of Dynamic Contrast Enhanced (DCE) images with diffusion MRI has shown great potential in prostate cancer detection. The parameterization of DCE images to generate cancer markers is traditionally performed based on pharmacokinetic modeling. However, pharmacokinetic models make simplistic assumptions about the tissue perfusion process, require the knowledge of contrast agent concentration in a major artery, and the modeling process is sensitive to noise and fitting instabilities. We address this issue by extracting features directly from the DCE T1-weighted time course without modeling. In this work, we employed a set of data-driven features generated by mapping the DCE T1 time course to its principal component space, along with diffusion MRI features to detect prostate cancer. The optimal set of DCE features is extracted with sparse regularized regression through a Least Absolute Shrinkage and Selection Operator (LASSO) model. We show that when our proposed features are used within the multiparametric MRI protocol to replace the pharmacokinetic parameters, the area under ROC curve is 0.91 for peripheral zone classification and 0.87 for whole gland classification. We were able to correctly classify 32 out of 35 peripheral tumor areas identified in the data when the proposed features were used with support vector machine classification. The proposed feature set was used to generate cancer likelihood maps for the prostate gland.

Modeling the diffusion of scientific publications

NARCIS (Netherlands)

D. Fok (Dennis); Ph.H.B.F. Franses (Philip Hans)

2005-01-01

textabstractThis paper illustrates that salient features of a panel of time series of annual citations can be captured by a Bass type diffusion model. We put forward an extended version of this diffusion model, where we consider the relation between key characteristics of the diffusion process and

Multi-site study of diffusion metric variability: effects of site, vendor, field strength, and echo time on regions-of-interest and histogram-bin analyses.

Science.gov (United States)

Helmer, K G; Chou, M-C; Preciado, R I; Gimi, B; Rollins, N K; Song, A; Turner, J; Mori, S

2016-02-27

It is now common for magnetic-resonance-imaging (MRI) based multi-site trials to include diffusion-weighted imaging (DWI) as part of the protocol. It is also common for these sites to possess MR scanners of different manufacturers, different software and hardware, and different software licenses. These differences mean that scanners may not be able to acquire data with the same number of gradient amplitude values and number of available gradient directions. Variability can also occur in achievable b-values and minimum echo times. The challenge of a multi-site study then, is to create a common protocol by understanding and then minimizing the effects of scanner variability and identifying reliable and accurate diffusion metrics. This study describes the effect of site, scanner vendor, field strength, and TE on two diffusion metrics: the first moment of the diffusion tensor field (mean diffusivity, MD), and the fractional anisotropy (FA) using two common analyses (region-of-interest and mean-bin value of whole brain histograms). The goal of the study was to identify sources of variability in diffusion-sensitized imaging and their influence on commonly reported metrics. The results demonstrate that the site, vendor, field strength, and echo time all contribute to variability in FA and MD, though to different extent. We conclude that characterization of the variability of DTI metrics due to site, vendor, field strength, and echo time is a worthwhile step in the construction of multi-center trials.

A New Approach and Solution Technique to Solve Time Fractional Nonlinear Reaction-Diffusion Equations

Directory of Open Access Journals (Sweden)

Inci Cilingir Sungu

2015-01-01

Full Text Available A new application of the hybrid generalized differential transform and finite difference method is proposed by solving time fractional nonlinear reaction-diffusion equations. This method is a combination of the multi-time-stepping temporal generalized differential transform and the spatial finite difference methods. The procedure first converts the time-evolutionary equations into Poisson equations which are then solved using the central difference method. The temporal differential transform method as used in the paper takes care of stability and the finite difference method on the resulting equation results in a system of diagonally dominant linear algebraic equations. The Gauss-Seidel iterative procedure then used to solve the linear system thus has assured convergence. To have optimized convergence rate, numerical experiments were done by using a combination of factors involving multi-time-stepping, spatial step size, and degree of the polynomial fit in time. It is shown that the hybrid technique is reliable, accurate, and easy to apply.

Atmospheric diffusion of large clouds

Energy Technology Data Exchange (ETDEWEB)

Crawford, T. V. [Univ. of California, Lawrence Radiation Lab., Livermore, California (United States)

1967-07-01

Clouds of pollutants travel within a coordinate system that is fixed to the earth's surface, and they diffuse and grow within a coordinate system fixed to the cloud's center. This paper discusses an approach to predicting the cloud's properties, within the latter coordinate system, on space scales of a few hundred meters to a few hundred kilometers and for time periods of a few days. A numerical cloud diffusion model is presented which starts with a cloud placed arbitrarily within the troposphere. Similarity theories of atmospheric turbulence are used to predict the horizontal diffusivity as a function of initial cloud size, turbulent atmospheric dissipation, and time. Vertical diffusivity is input as a function of time and height. Therefore, diurnal variations of turbulent diffusion in the boundary layer and effects of temperature inversions, etc. can be modeled. Nondiffusive cloud depletion mechanisms, such as dry deposition, washout, and radioactive decay, are also a part of this numerical model. An effluent cloud, produced by a reactor run at the Nuclear Rocket Development Station, Nevada, is discussed in this paper. Measurements on this cloud, for a period of two days, are compared to calculations with the above numerical cloud diffusion model. In general, there is agreement. within a factor of two, for airborne concentrations, cloud horizontal area, surface air concentrations, and dry deposition as airborne concentration decreased by seven orders of magnitude during the two-day period. (author)

Diffusion in the presence of a local attracting factor: Theory and interdisciplinary applications

Science.gov (United States)

Veermäe, Hardi; Patriarca, Marco

2017-06-01

In many complex diffusion processes the drift of random walkers is not caused by an external force, as in the case of Brownian motion, but by local variations of fitness perceived by the random walkers. In this paper, a simple but general framework is presented that describes such a type of random motion and may be of relevance in different problems, such as opinion dynamics, cultural spreading, and animal movement. To this aim, we study the problem of a random walker in d dimensions moving in the presence of a local heterogeneous attracting factor expressed in terms of an assigned position-dependent "attractiveness function." At variance with standard Brownian motion, the attractiveness function introduced here regulates both the advection and diffusion of the random walker, thus providing testable predictions for a specific form of fluctuation-relations. We discuss the relation between the drift-diffusion equation based on the attractiveness function and that describing standard Brownian motion, and we provide some explicit examples illustrating its relevance in different fields, such as animal movement, chemotactic diffusion, and social dynamics.

Diffusion tensor MR microscopy of tissues with low diffusional anisotropy.

Science.gov (United States)

Bajd, Franci; Mattea, Carlos; Stapf, Siegfried; Sersa, Igor

2016-06-01

Diffusion tensor imaging exploits preferential diffusional motion of water molecules residing within tissue compartments for assessment of tissue structural anisotropy. However, instrumentation and post-processing errors play an important role in determination of diffusion tensor elements. In the study, several experimental factors affecting accuracy of diffusion tensor determination were analyzed. Effects of signal-to-noise ratio and configuration of the applied diffusion-sensitizing gradients on fractional anisotropy bias were analyzed by means of numerical simulations. In addition, diffusion tensor magnetic resonance microscopy experiments were performed on a tap water phantom and bovine articular cartilage-on-bone samples to verify the simulation results. In both, the simulations and the experiments, the multivariate linear regression of the diffusion-tensor analysis yielded overestimated fractional anisotropy with low SNRs and with low numbers of applied diffusion-sensitizing gradients. An increase of the apparent fractional anisotropy due to unfavorable experimental conditions can be overcome by applying a larger number of diffusion sensitizing gradients with small values of the condition number of the transformation matrix. This is in particular relevant in magnetic resonance microscopy, where imaging gradients are high and the signal-to-noise ratio is low.

Computation of shear-induced collective-diffusivity in emulsions

Science.gov (United States)

Malipeddi, Abhilash Reddy; Sarkar, Kausik

2017-11-01

The shear-induced collective-diffusivity of drops in an emulsion is calculated through simulation. A front-tracking finite difference method is used to integrate the Navier-Stokes equations. When a cloud of drops is subjected to shear flow, after a certain time, the width of the cloud increases with the 1/3 power of time. This scaling of drop-cloud-width with time is characteristic of (sub-)diffusion that arises from irreversible two-drop interactions. The collective diffusivity is calculated from this relationship. A feature of the procedure adopted here is the modest computational requirement, wherein, a few drops ( 70) in shear for short time ( 70 strain) is found to be sufficient to get a good estimate. As far as we know, collective-diffusivity has not been calculated for drops through simulation till now. The computed values match with experimental measurements reported in the literature. The diffusivity in emulsions is calculated for a range of Capillary (Ca) and Reynolds (Re) numbers. It is found to be a unimodal function of Ca , similar to self-diffusivity. A sub-linear increase of the diffusivity with Re is seen for Re < 5 . This work has been limited to a viscosity matched case.

Diffusion-weighted MR imaging in leukodystrophies

Energy Technology Data Exchange (ETDEWEB)

Patay, Zoltan [King Faisal Specialist Hospital and Research Centre, Department of Radiology, Riyadh (Saudi Arabia)

2005-11-01

Leukodystrophies are genetically determined metabolic diseases, in which the underlying biochemical abnormality interferes with the normal build-up and/or maintenance of myelin, which leads to hypo- (or arrested) myelination, or dysmyelination with resultant demyelination. Although conventional magnetic resonance imaging has significantly contributed to recent progress in the diagnostic work-up of these diseases, diffusion-weighted imaging has the potential to further improve our understanding of underlying pathological processes and their dynamics through the assessment of normal and abnormal diffusion properties of cerebral white matter. Evaluation of conventional diffusion-weighted and ADC map images allows the detection of major diffusion abnormalities and the identification of various edema types, of which the so-called myelin edema is particularly relevant to leukodystrophies. Depending on the nature of histopathological changes, stage and progression gradient of diseases, various diffusion-weighted imaging patterns may be seen in leukodystrophies. Absent or low-grade myelin edema is found in mucopolysaccharidoses, GM gangliosidoses, Zellweger disease, adrenomyeloneuropathy, L-2-hydroxyglutaric aciduria, non-ketotic hyperglycinemia, classical phenylketonuria, Van der Knaap disease and the vanishing white matter, medium grade myelin edema in metachromatic leukodystrophy, X-linked adrenoleukodystrophy and HMG coenzyme lyase deficiency and high grade edema in Krabbe disease, Canavan disease, hyperhomocystinemias, maple syrup urine disease and leukodystrophy with brainstem and spinal cord involvement and high lactate. (orig.)

Diffusion-weighted MR imaging in leukodystrophies

International Nuclear Information System (INIS)

Patay, Zoltan

2005-01-01

Leukodystrophies are genetically determined metabolic diseases, in which the underlying biochemical abnormality interferes with the normal build-up and/or maintenance of myelin, which leads to hypo- (or arrested) myelination, or dysmyelination with resultant demyelination. Although conventional magnetic resonance imaging has significantly contributed to recent progress in the diagnostic work-up of these diseases, diffusion-weighted imaging has the potential to further improve our understanding of underlying pathological processes and their dynamics through the assessment of normal and abnormal diffusion properties of cerebral white matter. Evaluation of conventional diffusion-weighted and ADC map images allows the detection of major diffusion abnormalities and the identification of various edema types, of which the so-called myelin edema is particularly relevant to leukodystrophies. Depending on the nature of histopathological changes, stage and progression gradient of diseases, various diffusion-weighted imaging patterns may be seen in leukodystrophies. Absent or low-grade myelin edema is found in mucopolysaccharidoses, GM gangliosidoses, Zellweger disease, adrenomyeloneuropathy, L-2-hydroxyglutaric aciduria, non-ketotic hyperglycinemia, classical phenylketonuria, Van der Knaap disease and the vanishing white matter, medium grade myelin edema in metachromatic leukodystrophy, X-linked adrenoleukodystrophy and HMG coenzyme lyase deficiency and high grade edema in Krabbe disease, Canavan disease, hyperhomocystinemias, maple syrup urine disease and leukodystrophy with brainstem and spinal cord involvement and high lactate. (orig.)

The mean first passage time in an energy-diffusion controlled regime with power-law distributions

International Nuclear Information System (INIS)

Zhou, Yanjun; Du, Jiulin

2013-01-01

Based on the mean first passage time (MFPT) theory, we derive an expression of the MFPT in an energy-diffusion controlled regime with a power-law distribution. We discuss the finite barrier effect (i.e. the thermal energy k B T is not small with respect to the potential barrier E b ) and compare it with Kramers’ infinite barrier result both in a power-law distribution and in a Maxwell–Boltzmann distribution. It is shown that the MFPT with a power-law distribution extends Kramers’ low-damping result to a relatively low barrier. We pay attention to the energy-diffusion controlled regime, which is of great interest in the context of Josephson junctions, and study how the power-law parameter κ affects the current distribution function in experiments with Josephson junctions. (paper)

Use of x-ray absorption imaging to evaluate the effects of heterogeneity on matrix diffusion

International Nuclear Information System (INIS)

Altman, S.J.; Tidwell, V.C.; McKenna, S.A.; Meigs, L.C.

1998-01-01

An understanding of matrix diffusion is important in assessing potential nuclear waste repositories in geologic media, as it is a potentially significant process in retarding the transport of contaminant species. Recent work done in evaluating the Waste Isolation Pilot Plant (WIPP) in southeastern New Mexico has brought up two issues that complicate the incorporation of diffusion in Performance Assessment calculations. First, interpretations of single-well tracer test data suggest that the tracer was diffusing at multiple rates. Second, the estimated relevant rate(s) of diffusion are dependent on the time and length scales of the problem. To match the observed tracer test data, a model with a distribution of diffusion coefficients was required. This has led to the proposal of applying a model with multiple rates of diffusion, the multirate model, to Performance Assessment calculations for the WIPP. A series of laboratory- scale experiments have been designed for the purpose of evaluating heterogeneity and scaling properties of diffusion rates and to test the multirate model. X-ray absorption imaging was used to visualize and quantify the effects of matrix heterogeneity on the diffusion characteristics for four different centimeter-scale samples of dolomite. The samples were obtained from the Culebra dolomite at the WIPP site. Significant variations in diffusion rates were observed over relatively small length and time (months) scales for the preliminary laboratory experiments. A strong correlation between diffusion rate and porosity was also observed in each of the samples. Two sets of experiments are planned for 1998. The first set of experiments is similar to those described above. For these experiments, fourteen samples exhibiting a broader range of physical characteristics are being tested. The second set of experiments will visualize the combined effect of advection in a fracture and diffusion into adjacent matrix materials. Tracer solution will flow through

Benchmark calculations of excess electrons in water cluster cavities: balancing the addition of atom-centered diffuse functions versus floating diffuse functions.

Science.gov (United States)

Zhang, Changzhe; Bu, Yuxiang

2016-09-14

Diffuse functions have been proved to be especially crucial for the accurate characterization of excess electrons which are usually bound weakly in intermolecular zones far away from the nuclei. To examine the effects of diffuse functions on the nature of the cavity-shaped excess electrons in water cluster surroundings, both the HOMO and LUMO distributions, vertical detachment energies (VDEs) and visible absorption spectra of two selected (H2O)24(-) isomers are investigated in the present work. Two main types of diffuse functions are considered in calculations including the Pople-style atom-centered diffuse functions and the ghost-atom-based floating diffuse functions. It is found that augmentation of atom-centered diffuse functions contributes to a better description of the HOMO (corresponding to the VDE convergence), in agreement with previous studies, but also leads to unreasonable diffuse characters of the LUMO with significant red-shifts in the visible spectra, which is against the conventional point of view that the more the diffuse functions, the better the results. The issue of designing extra floating functions for excess electrons has also been systematically discussed, which indicates that the floating diffuse functions are necessary not only for reducing the computational cost but also for improving both the HOMO and LUMO accuracy. Thus, the basis sets with a combination of partial atom-centered diffuse functions and floating diffuse functions are recommended for a reliable description of the weakly bound electrons. This work presents an efficient way for characterizing the electronic properties of weakly bound electrons accurately by balancing the addition of atom-centered diffuse functions and floating diffuse functions and also by balancing the computational cost and accuracy of the calculated results, and thus is very useful in the relevant calculations of various solvated electron systems and weakly bound anionic systems.

Confinement and diffusion in tokamaks

International Nuclear Information System (INIS)

McWilliams, R.

1988-01-01

The effect of electric field fluctuations on confinement and diffusion in tokamak is discussed. Based on the experimentally determined cross-field turbolent diffusion coefficient, D∼3.7*cT e /eB(δn i /n i ) rms which is also derived by a simple theory, the cross-field diffusion time, tp=a 2 /D, is calculated and compared to experimental results from 51 tokamak for standard Ohmic operation

Apparent diffusive motion of centrin foci in living cells: implications for diffusion-based motion in centriole duplication

Science.gov (United States)

Rafelski, Susanne M.; Keller, Lani C.; Alberts, Jonathan B.; Marshall, Wallace F.

2011-04-01

The degree to which diffusion contributes to positioning cellular structures is an open question. Here we investigate the question of whether diffusive motion of centrin granules would allow them to interact with the mother centriole. The role of centrin granules in centriole duplication remains unclear, but some proposed functions of these granules, for example, in providing pre-assembled centriole subunits, or by acting as unstable 'pre-centrioles' that need to be captured by the mother centriole (La Terra et al 2005 J. Cell Biol. 168 713-22), require the centrin foci to reach the mother. To test whether diffusive motion could permit such interactions in the necessary time scale, we measured the motion of centrin-containing foci in living human U2OS cells. We found that these centrin foci display apparently diffusive undirected motion. Using the apparent diffusion constant obtained from these measurements, we calculated the time scale required for diffusion to capture by the mother centrioles and found that it would greatly exceed the time available in the cell cycle. We conclude that mechanisms invoking centrin foci capture by the mother, whether as a pre-centriole or as a source of components to support later assembly, would require a form of directed motility of centrin foci that has not yet been observed.

Gaseous diffusion flames: simple structures and their interaction

Energy Technology Data Exchange (ETDEWEB)

Cavaliere, A. [Universita degli Studi Federico II, Naples (Italy). Dip. di Ingegneria Chimica; Ragucci, R. [Istituto di Ricerche sulla Combustione C,N.R., Naples (Italy)

2001-07-01

This is a synoptic overview of a selection of works dealing with single diffusive structures, with their mutual interaction in simple flows and their statistical modeling in complex flows. The focus is on reacting conditions pertaining to gaseous diffusion flames, but isothermal structures are also described when they are of some conceptual interest. This paper considers only few representative works for each subject, which are functional in explaining the key characteristics of the diffusive structures. The extension, given to single subjects, is not weighed according to the number of related publications but on the relevance to the basic understanding of the general framework concerning diffusion flames. One-dimensional structures are first discussed. They are ordered according to the number of balance equation terms needed for their description. Two-dimensional (2D) structures are then introduced following an order based on their convolution level. Some pioneering work on three-dimensional structures is further quoted. The temporal evolution of simple structures in quiescent or simple flowing 2D systems is considered. The latter case is exploited to present classification of diffusion-controlled mixing regimes. Modeling characterization approach of turbulent diffusion flames is also described in order to yield a self-sufficient didactic presentation. The approach based on the flame surface density model is specifically discussed because of its potential use in the determination of qualitative and quantitative features of simple diffusion flames. (author)

Real-time in vivo tissue characterization with diffuse reflectance spectroscopy during transthoracic lung biopsy: a clinical feasibility study

NARCIS (Netherlands)

Spliethoff, Jarich; Prevoo, Warner; Meier, Mark A.J.; de Jong, Jeroen; Evers, Daniel; Evers, Daniel J.; Sterenborg, Hendricus J.C.M.; Lucassen, Gerald; Lucassen, Gerald W.; Hendriks, Benno H.W.; Ruers, Theo J.M.

2016-01-01

Purpose: This study presents the first in vivo real-time tissue characterization during image-guided percutaneous lung biopsies using diffuse reflectance spectroscopy (DRS) sensing at the tip of a biopsy needle with integrated optical fibers. Experimental Design: Tissues from 21 consented patients

Identifiability analysis of rotational diffusion tensor and electronic transition moments measured in time-resolved fluorescence depolarization experiment

International Nuclear Information System (INIS)

Szubiakowski, Jacek P.

2014-01-01

The subject of this paper is studies of the deterministic identifiability of molecular parameters, such as rotational diffusion tensor components and orientation of electronic transition moments, resulting from the time-resolved fluorescence anisotropy experiment. In the most general case considered, a pair of perpendicularly polarized emissions enables the unique determination of all the rotational diffusion tensor's principal components. The influence of the tensor's symmetry and the associated degeneration of its eigenvalues on the identifiability of the electronic transitions moments is systematically investigated. The analysis reveals that independently of the rotational diffusion tensor's symmetry, the transition moments involved in photoselection and emission processes cannot be uniquely identified without a priori information about their mutual orientation or their orientation with respect to the principal axes of the tensor. Moreover, it is shown that increasing the symmetry of the rotational diffusion tensor deteriorates the degree of the transition moments identifiability. To obtain these results analytically, a novel approach to solve bilinear system of equations for Markov parameters is applied. The effect of the additional information, obtained from fluorescence measurements for different molecular mobilities, to improve the identifiability at various levels of analysis is shown. The effectiveness and reliability of the target analysis method for experimental determination of the molecular parameters is also discussed

Fractional Diffusion Equations and Anomalous Diffusion

Science.gov (United States)

Evangelista, Luiz Roberto; Kaminski Lenzi, Ervin

2018-01-01

Preface; 1. Mathematical preliminaries; 2. A survey of the fractional calculus; 3. From normal to anomalous diffusion; 4. Fractional diffusion equations: elementary applications; 5. Fractional diffusion equations: surface effects; 6. Fractional nonlinear diffusion equation; 7. Anomalous diffusion: anisotropic case; 8. Fractional Schrödinger equations; 9. Anomalous diffusion and impedance spectroscopy; 10. The Poisson–Nernst–Planck anomalous (PNPA) models; References; Index.

Tiny Molybdenites Tell Diffusion Tales

Science.gov (United States)

Stein, H. J.; Hannah, J. L.

2014-12-01

Diffusion invokes micron-scale exchange during crystal growth and dissolution in magma chambers on short time-scales. Fundamental to interpreting such data are assumptions on magma-fluid dynamics at all scales. Nevertheless, elemental diffusion profiles are used to estimate time scales for magma storage, eruption, and recharge. An underutilized timepiece to evaluate diffusion and 3D mobility of magmatic fluids is high-precision Re-Os dating of molybdenite. With spatially unique molybdenite samples from a young ore system (e.g., 1 Ma) and a double Os spike, analytical errors of 1-3 ka unambiguously separate events in time. Re-Os ages show that hydrous shallow magma chambers locally recharge and expel Cu-Mo-Au-silica as superimposed stockwork vein networks at time scales less than a few thousand years [1]. Re-Os ages provide diffusion rates controlled by a dynamic crystal mush, accumulation and expulsion of metalliferous fluid, and magma reorganization after explosive crystallization events. Importantly, this approach has broad application far from ore deposits. Here, we use Re-Os dating of molybdenite to assess time scales for generating and diffusing metals through the deep crust. To maximize opportunity for chemical diffusion, we use a continental-scale Sveconorwegian mylonite zone for the study area. A geologically constrained suite of molybdenite samples was acquired from quarry exposures. Molybdenite, previously unreported, is extremely scarce. Tiny but telling molybdenites include samples from like occurrences to assure geologic accuracy in Re-Os ages. Ages range from mid-Mesoproterozoic to mid-Neoproterozoic, and correspond to early metamorphic dehydration of a regionally widespread biotite-rich gneiss, localized melting of gneiss to form cm-m-scale K-feldspar ± quartz pods, development of vapor-rich, vuggy mm stringers that serve as volatile collection surfaces in felsic leucosomes, and low-angle (relative to foliation) cross-cutting cm-scale quartz veins

Diffusion coefficients of decay products of radon and thoron

International Nuclear Information System (INIS)

Raghunath, B.; Kotrappa, P.

1979-01-01

The diffusion coefficients of the decay products of radon and thoron have relevance in the evaluation of inhalation hazards in uranium and thorium processing industries. A recently developed diffusion sampler, based on Mercer's theory of diffusional deposition between the concentric circular plates, has been used for determining the diffusion coefficients of the unattached decay products of radon and thoron (RaA, RaB, RaC and ThB). Experiments were conducted at different ventilation rates (6 and 60 changes/hr) at different relative humidities (10 and 90%) and both in air and argon atmospheres. Diffusion coefficients were found to increase with increasing ventilation rates and were found to decrease at higher relative humidities, the effect being more marked at lower ventilation rates. Both of these effects were less pronounced in argon than in air. Results are discussed in light of the known properties of these decay products. (author)

Information filtering via preferential diffusion

Science.gov (United States)

Lü, Linyuan; Liu, Weiping

2011-06-01

Recommender systems have shown great potential in addressing the information overload problem, namely helping users in finding interesting and relevant objects within a huge information space. Some physical dynamics, including the heat conduction process and mass or energy diffusion on networks, have recently found applications in personalized recommendation. Most of the previous studies focus overwhelmingly on recommendation accuracy as the only important factor, while overlooking the significance of diversity and novelty that indeed provide the vitality of the system. In this paper, we propose a recommendation algorithm based on the preferential diffusion process on a user-object bipartite network. Numerical analyses on two benchmark data sets, MovieLens and Netflix, indicate that our method outperforms the state-of-the-art methods. Specifically, it can not only provide more accurate recommendations, but also generate more diverse and novel recommendations by accurately recommending unpopular objects.

Ageing in dense colloids as diffusion in the logarithm of time

International Nuclear Information System (INIS)

Boettcher, Stefan; Sibani, Paolo

2011-01-01

The far-from-equilibrium dynamics of glassy systems share important phenomenological traits. A transition is generally observed from a time-homogeneous dynamical regime to an ageing regime where physical changes occur intermittently and, on average, at a decreasing rate. It has been suggested that a global change of the independent time variable to its logarithm may render the ageing dynamics homogeneous: for colloids, this entails diffusion but on a logarithmic timescale. Our novel analysis of experimental colloid data confirms that the mean square displacement grows linearly in time at low densities and shows that it grows linearly in the logarithm of time at high densities. Correspondingly, pairs of particles initially in close contact survive as pairs with a probability which decays exponentially in either time or its logarithm. The form of the probability density function of the displacements shows that long-ranged spatial correlations are very long-lived in dense colloids. A phenomenological stochastic model is then introduced which relies on the growth and collapse of strongly correlated clusters ('dynamic heterogeneity'), and which reproduces the full spectrum of observed colloidal behaviors depending on the form assumed for the probability that a cluster collapses during a Monte Carlo update. In the limit where large clusters dominate, the collapse rate is ∝1/t, implying a homogeneous, log-Poissonian process that qualitatively reproduces the experimental results for dense colloids. Finally, an analytical toy-model is discussed to elucidate the strong dependence of the simulation results on the integrability (or lack thereof) of the cluster collapse probability function.

Diffusion Tensor Imaging for the Differentiation of Microangiopathy, Infarction and Perfusion-Diffusion Mismatch Lesions

International Nuclear Information System (INIS)

Ha, Dong Ho; Choi, Sun Seob; Kang, Myong Jin; Lee, Jin Hwa; Yoon, Seong Kuk; Nam, Kyung Jin

2009-01-01

This study was designed to evaluate the usefulness of diffusion tensor imaging (DTI) and the DTI indices for differentiating between microangiopathy lesions, acute infarction lesions and perfusion-diffusion mismatch areas. DTI was performed in 35 patients with the use of a 1.5 Tesla MRI system. The MRI parameters were as follows: a spin echo EPI sequence with a bvalue = 1000 s/mm 2 , 25 diffusion directions, a repetition time of 8400 msec, an echo time of 75 msec, a matrix size of 128 x 128, a FOV of 22 cm and a 4 mm slice thickness. From the diffusion tensor images, the apparent diffusion coefficient (ADC), fractional anisotropy (FA), volume ratio (VR), relative anisotropy (RA), anisotropy index (AI), exponential ADC (eADC) and magnitude diffusion coefficient (MDC) were measured for the contra-lateral normal area (28 cases), the microangiopathy lesions (10 cases), the infarction lesions (17 cases) and the perfusion-diffusion mismatch area (8 cases). As compared to the normal area, the microangiopathy lesions showed increased ADC and MDC values and decreased FA, VR, RA, AI and eADC values. The infarction lesions showed increased VR, RA and eADC values, a normal FA, a decreased AI and decreased ADC and MDC values. The mismatch area showed a similar pattern as that for the microangiopathy lesions; however, the differences were not prominent, with an increase of the ADC and MDC values and a decrease of FA, VR, RA, AI and eADC values. The DTI indices could have a role in making the differential diagnosis of microangiopathy, acute infarction and perfusion-diffusion mismatch lesions

Modelling of Innovation Diffusion

Directory of Open Access Journals (Sweden)

Arkadiusz Kijek

2010-01-01

Full Text Available Since the publication of the Bass model in 1969, research on the modelling of the diffusion of innovation resulted in a vast body of scientific literature consisting of articles, books, and studies of real-world applications of this model. The main objective of the diffusion model is to describe a pattern of spread of innovation among potential adopters in terms of a mathematical function of time. This paper assesses the state-of-the-art in mathematical models of innovation diffusion and procedures for estimating their parameters. Moreover, theoretical issues related to the models presented are supplemented with empirical research. The purpose of the research is to explore the extent to which the diffusion of broadband Internet users in 29 OECD countries can be adequately described by three diffusion models, i.e. the Bass model, logistic model and dynamic model. The results of this research are ambiguous and do not indicate which model best describes the diffusion pattern of broadband Internet users but in terms of the results presented, in most cases the dynamic model is inappropriate for describing the diffusion pattern. Issues related to the further development of innovation diffusion models are discussed and some recommendations are given. (original abstract

Drug diffusion across skin with diffusivity spatially modulated

Science.gov (United States)

Montoya Arroyave, Isabel

2014-05-01

A diffusion and delivery model of a drug across the skin with diffusivity spatially modulated is formulated and solved analytically using computer algebra. The model is developed using one-dimensional diffusion equation with a diffusivity which is a function of position in the skin; with an initial condition which is describing that the drug is initially contained inside a therapeutic patch; with a boundary condition according to which the change in concentration in the patch is minimal, such that assumption of zero flux at the patch-skin interface is valid; and with other boundary condition according to which the microcirculation in the capillaries just below the dermis carries the drug molecules away from the site at a very fast rate, maintaining the inner concentration at 0. The model is solved analytically by the method of the Laplace transform, with Bromwich integral and residue theorem. The concentration profile of the drug in the skin is expressed as an infinite series of Bessel functions. The corresponding total amount of delivered drug is expressed as an infinite series of decreasing exponentials. Also, the corresponding effective time for the therapeutic patch is determined. All computations were performed using computer algebra software, specifically Maple. The analytical results obtained are important for understanding and improving currentapplications of therapeutic patches. For future research it is interesting to consider more general models of spatial modulation of the diffusivity and the possible application of other computer algebra software such as Mathematica and Maxima.

Degenerate nonlinear diffusion equations

CERN Document Server

Favini, Angelo

2012-01-01

The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asympt...

Competitive autocatalytic reactions in chaotic flows with diffusion: Prediction using finite-time Lyapunov exponents

International Nuclear Information System (INIS)

Schlick, Conor P.; Umbanhowar, Paul B.; Ottino, Julio M.; Lueptow, Richard M.

2014-01-01

We investigate chaotic advection and diffusion in autocatalytic reactions for time-periodic sine flow computationally using a mapping method with operator splitting. We specifically consider three different autocatalytic reaction schemes: a single autocatalytic reaction, competitive autocatalytic reactions, which can provide insight into problems of chiral symmetry breaking and homochirality, and competitive autocatalytic reactions with recycling. In competitive autocatalytic reactions, species B and C both undergo an autocatalytic reaction with species A such that A+B→2B and A+C→2C. Small amounts of initially spatially localized B and C and a large amount of spatially homogeneous A are advected by the velocity field, diffuse, and react until A is completely consumed and only B and C remain. We find that local finite-time Lyapunov exponents (FTLEs) can accurately predict the final average concentrations of B and C after the reaction completes. The species that starts in the region with the larger FTLE has, with high probability, the larger average concentration at the end of the reaction. If B and C start in regions with similar FTLEs, their average concentrations at the end of the reaction will also be similar. When a recycling reaction is added, the system evolves towards a single species state, with the FTLE often being useful in predicting which species fills the entire domain and which is depleted. The FTLE approach is also demonstrated for competitive autocatalytic reactions in journal bearing flow, an experimentally realizable flow that generates chaotic dynamics

Inertial effects in diffusion-limited reactions

International Nuclear Information System (INIS)

Dorsaz, N; Foffi, G; De Michele, C; Piazza, F

2010-01-01

Diffusion-limited reactions are commonly found in biochemical processes such as enzyme catalysis, colloid and protein aggregation and binding between different macromolecules in cells. Usually, such reactions are modeled within the Smoluchowski framework by considering purely diffusive boundary problems. However, inertial effects are not always negligible in real biological or physical media on typical observation time frames. This is all the more so for non-bulk phenomena involving physical boundaries, that introduce additional time and space constraints. In this paper, we present and test a novel numerical scheme, based on event-driven Brownian dynamics, that allows us to explore a wide range of velocity relaxation times, from the purely diffusive case to the underdamped regime. We show that our algorithm perfectly reproduces the solution of the Fokker-Planck problem with absorbing boundary conditions in all the regimes considered and is thus a good tool for studying diffusion-guided reactions in complex biological environments.

Development, relevance, and applications of 'atom-at-a-time' techniques

International Nuclear Information System (INIS)

Hoffman, D.C.

2012-01-01

A brief history of the development and some of the first uses of 'atom-at-a-time' techniques to investigate the chemical and nuclear properties of the actinide and transactinide elements are presented. The currently known transactinides (all elements with Z > 103) were discovered using physical (nuclear) techniques rather than chemical separation techniques because of their short half-lives and low production rates and the difficulty in accurately predicting chemical properties of the heaviest elements because of relativistic effects. Some of the constraints on systems suitable for such studies and whether these tracer-scale results can be extended to the macro-scale are discussed. The relevance and importance of the methods and their potential for application to some current problems such as nuclear forensics and proliferation and environmental concerns are considered. The value of graduate research utilizing such techniques in helping to attract and educate the next generation of nuclear scientists is highlighted. (author)

Disposable glucose test strip for whole blood with integrated sensing/diffusion-limiting layer

Energy Technology Data Exchange (ETDEWEB)

Chen Zhencheng [Department of Biomedical Engineering, School of Info-Physics and Geomatics Engineering, Central South University, Changsha 410083 (China); Fang Cheng, E-mail: fangpingchuan@163.co [Department of Biomedical Engineering, School of Info-Physics and Geomatics Engineering, Central South University, Changsha 410083 (China); Wang Hongyan; He Jishan [Department of Biomedical Engineering, School of Info-Physics and Geomatics Engineering, Central South University, Changsha 410083 (China)

2009-12-30

A disposable glucose test strip with an integrated sensing/diffusion-limiting layer was developed. A formulation containing filler, glucose oxidase and electronic mediator was screen-printed over two carbon electrodes to form an integrated sensing/diffusion-limiting layer. On rehydration, the integrated layer does not break up, but swells to form a gelled and three-dimensional meshy reaction zone on the surface of the underlying conductive elements in which reactants and mediator move freely, but interfering species such as red blood cells containing oxygenated hemoglobin are excluded. On the same time, the integrated layer maintains a rate of permeation of the analyte through it with a variation of less than 10% at temperatures ranging from 15 deg. C to 42 deg. C. This biosensor is substantially insensitive to interferents and essentially independent to relevant temperature, which provides a more reliable reading of actual blood glucose value in human whole blood.

Predictability of motor outcome according to the time of diffusion tensor imaging in patients with cerebral infarct

Energy Technology Data Exchange (ETDEWEB)

Kwon, Yong Hyun [Yeungnam College of Science and Technology, Department of Physical Therapy, Taegu (Korea, Republic of); Jeoung, Yong Jae [Yeungnam University, Department of Physical Medicine and Rehabilitation, College of Medicine, Taegu (Korea, Republic of); Lee, Jun [Yeungnam University, Department of Neurology, College of Medicine, Taegu (Korea, Republic of); Son, Su Min; Jang, Sung Ho [Yeungnam University 317-1, Department of Physical Medicine and Rehabilitation, College of Medicine, Taegu (Korea, Republic of); Kim, Saeyoon [Yeungnam University, Department of Pediatrics, College of Medicine, Taegu (Korea, Republic of); Kim, Chulseung [Medical Devices Clinical Trial Center of Yeungnam University Hospital, Taegu (Korea, Republic of)

2012-07-15

Predictability of diffusion tensor imaging tractography (DTT) for motor outcome can differ according to the time of DTT. We attempted to compare the predictability for motor outcome according to the time of diffusion tensor imaging (DTI) by analyzing the corticospinal tract (CST) integrity on DTT in patients with corona radiata (CR) infarct. Seventy-one consecutive hemiparetic patients with CR infarct were recruited. Motor function of the affected extremities was measured twice: at onset and at 6 months from onset. According to the time of DTI, patients were classified into two groups: the early scanning group (ES group) within 14 days since stroke onset; and the late scanning group (LS group) 15-28 days. Motor outcome was compared with the CST integrity on DTT. Motor prognosis was predicted from scan time of DTI and the CST integrity on DTT in the logistic regression model. According to separate regression analysis, the CST integrity of the late group was found to predict MI score (OR = 14.000, 95% CI = 3.194-61.362, p < 0.05), whereas the CST integrity of the early group was not found to predict MI score. In terms of both positive and negative predictabilities, we found that predictability of DTT for motor outcome was better in patients who were scanned later (15-28 days after onset) than in patients who were scanned earlier (1-14 days after onset). (orig.)

Predictability of motor outcome according to the time of diffusion tensor imaging in patients with cerebral infarct

International Nuclear Information System (INIS)

Kwon, Yong Hyun; Jeoung, Yong Jae; Lee, Jun; Son, Su Min; Jang, Sung Ho; Kim, Saeyoon; Kim, Chulseung

2012-01-01

Predictability of diffusion tensor imaging tractography (DTT) for motor outcome can differ according to the time of DTT. We attempted to compare the predictability for motor outcome according to the time of diffusion tensor imaging (DTI) by analyzing the corticospinal tract (CST) integrity on DTT in patients with corona radiata (CR) infarct. Seventy-one consecutive hemiparetic patients with CR infarct were recruited. Motor function of the affected extremities was measured twice: at onset and at 6 months from onset. According to the time of DTI, patients were classified into two groups: the early scanning group (ES group) within 14 days since stroke onset; and the late scanning group (LS group) 15-28 days. Motor outcome was compared with the CST integrity on DTT. Motor prognosis was predicted from scan time of DTI and the CST integrity on DTT in the logistic regression model. According to separate regression analysis, the CST integrity of the late group was found to predict MI score (OR = 14.000, 95% CI = 3.194-61.362, p < 0.05), whereas the CST integrity of the early group was not found to predict MI score. In terms of both positive and negative predictabilities, we found that predictability of DTT for motor outcome was better in patients who were scanned later (15-28 days after onset) than in patients who were scanned earlier (1-14 days after onset). (orig.)

Diffusion and sorption properties of radionuclides in compacted bentonite

Energy Technology Data Exchange (ETDEWEB)

Yu Ji-Wei; Neretnieks, I. [Royal Inst. of Tech., Stockholm (Sweden). Dept. of Chemical Engineering and Technology

1997-07-01

In this report, recent studies on sorption and diffusion of radionuclides in compacted bentonite have been reviewed. The sorption distribution coefficient and diffusion coefficient data obtained from experiments in the literature have been compiled. Based on these experimental data and the report SKB-TR--91-16 (Brandberg and Skagius, 1991), this report proposes a set of sorption distribution coefficient and diffusion coefficient values for modelling purpose for safety analysis of nuclear waste repositories. The variability and uncertainty of the diffusivity data span somewhat more than an order or magnitude up and down. Most of the nuclides have an effective diffusivity in around 10{sup -10} m{sup 2}/s. Ion exclusion effects are observed for C, Cl and for Tc in oxidizing waters. Effective diffusivities are nearly tow orders of magnitude lower for these elements and of the order of 10{sup -12} m{sup 2}/s. Surface diffusion effects are found for Cs, Ni, Pa, Pb, Ra, Sn, Sr and Zr. Effective diffusivities for these elements are of the order of 10{sup -8} m{sup 2}/s. The surface diffusion effect should decrease in saline waters which is seen for Cs and Sr where there are data available. It is also deemed that Ra will have this effect because of its similarity with Sr. The other nuclides should also show this decrease but no data is available. Sorption and diffusion mechanisms in compacted bentonite are discussed in the report. In highly compacted bentonite, sorption and hence its distribution coefficient is not well defined, and a pore diffusion coefficient or a surface diffusion coefficient is not well defined either. Therefore, an apparent diffusion coefficient and a total concentration gradient should be more relevant in describing the diffusion process in compacted bentonite. 99 refs.

A study of the diffusion mechanisms in amorphous metallic alloys: diffusion and diffusion under high pressure in an amorphous NiZr alloy; Contribution a l`etude des mecanismes de transport dans les materiaux metalliques amorphes: diffusion et diffusion sous pression dans NiZr amorphe

Energy Technology Data Exchange (ETDEWEB)

Grandjean, A.

1996-03-01

The aim of this work is a better understanding of the diffusion mechanism in amorphous metallic alloys. Then interdiffusion and hafnium diffusion in amorphous NiZr alloy have been studied. Samples used are made by sputtering co-deposition under vacuum and are well relaxed before the diffusion measurements. The time evolution of resistivity during annealing due to the decay of a composition modulated film has been measured and from this change in resistivity interdiffusion coefficients have been determined. Dependence of Hf diffusion on temperature and pressure has been studied using (SIMS). In this two cases, the diffusion process obeys an Arrhenius law and gives an activation energy of 1.33 eV for interdiffusion, and 0.76 eV for Hf diffusion. An effect of pressure on Hf diffusion has been found leading to an activation volume of 8.5 angstrom{sup 3}. Thanks to these results, two approaches of the diffusion mechanisms in these systems have been proposed. The first comes from a comparison with the diffusion mechanisms in crystalline metals, that is to say by point defects. The second is an hypothesis of collective motions in these non crystalline alloys. (author).

Error analysis of semidiscrete finite element methods for inhomogeneous time-fractional diffusion

KAUST Repository

Jin, B.; Lazarov, R.; Pasciak, J.; Zhou, Z.

2014-01-01

© 2014 Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. We consider the initial-boundary value problem for an inhomogeneous time-fractional diffusion equation with a homogeneous Dirichlet boundary condition, a vanishing initial data and a nonsmooth right-hand side in a bounded convex polyhedral domain. We analyse two semidiscrete schemes based on the standard Galerkin and lumped mass finite element methods. Almost optimal error estimates are obtained for right-hand side data f (x, t) ε L∞ (0, T; Hq(ω)), ≤1≥ 1, for both semidiscrete schemes. For the lumped mass method, the optimal L2(ω)-norm error estimate requires symmetric meshes. Finally, twodimensional numerical experiments are presented to verify our theoretical results.

Error analysis of semidiscrete finite element methods for inhomogeneous time-fractional diffusion

KAUST Repository

Jin, B.

2014-05-30

© 2014 Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. We consider the initial-boundary value problem for an inhomogeneous time-fractional diffusion equation with a homogeneous Dirichlet boundary condition, a vanishing initial data and a nonsmooth right-hand side in a bounded convex polyhedral domain. We analyse two semidiscrete schemes based on the standard Galerkin and lumped mass finite element methods. Almost optimal error estimates are obtained for right-hand side data f (x, t) ε L∞ (0, T; Hq(ω)), ≤1≥ 1, for both semidiscrete schemes. For the lumped mass method, the optimal L2(ω)-norm error estimate requires symmetric meshes. Finally, twodimensional numerical experiments are presented to verify our theoretical results.

Strong Stationary Duality for Diffusion Processes

OpenAIRE

Fill, James Allen; Lyzinski, Vince

2014-01-01

We develop the theory of strong stationary duality for diffusion processes on compact intervals. We analytically derive the generator and boundary behavior of the dual process and recover a central tenet of the classical Markov chain theory in the diffusion setting by linking the separation distance in the primal diffusion to the absorption time in the dual diffusion. We also exhibit our strong stationary dual as the natural limiting process of the strong stationary dual sequence of a well ch...

Apparent diffusive motion of centrin foci in living cells: implications for diffusion-based motion in centriole duplication

International Nuclear Information System (INIS)

Rafelski, Susanne M; Keller, Lani C; Marshall, Wallace F; Alberts, Jonathan B

2011-01-01

The degree to which diffusion contributes to positioning cellular structures is an open question. Here we investigate the question of whether diffusive motion of centrin granules would allow them to interact with the mother centriole. The role of centrin granules in centriole duplication remains unclear, but some proposed functions of these granules, for example, in providing pre-assembled centriole subunits, or by acting as unstable 'pre-centrioles' that need to be captured by the mother centriole (La Terra et al 2005 J. Cell Biol. 168 713–22), require the centrin foci to reach the mother. To test whether diffusive motion could permit such interactions in the necessary time scale, we measured the motion of centrin-containing foci in living human U2OS cells. We found that these centrin foci display apparently diffusive undirected motion. Using the apparent diffusion constant obtained from these measurements, we calculated the time scale required for diffusion to capture by the mother centrioles and found that it would greatly exceed the time available in the cell cycle. We conclude that mechanisms invoking centrin foci capture by the mother, whether as a pre-centriole or as a source of components to support later assembly, would require a form of directed motility of centrin foci that has not yet been observed

Diffuse mode and diffuse-to-filamentary transition in a high pressure nanosecond scale corona discharge under high voltage

International Nuclear Information System (INIS)

Tardiveau, P; Moreau, N; Bentaleb, S; Postel, C; Pasquiers, S

2009-01-01

The dynamics of a point-to-plane corona discharge induced in high pressure air under nanosecond scale high overvoltage is investigated. The electrical and optical properties of the discharge can be described in space and time with fast and precise current measurements coupled to gated and intensified imaging. Under atmospheric pressure, the discharge exhibits a diffuse pattern like a multielectron avalanche propagating through a direct field ionization mechanism. The diffuse regime can exist since the voltage rise time is much shorter than the characteristic time of the field screening effects, and as long as the local field is higher than the critical ionization field in air. As one of these conditions is not fulfilled, the discharge turns into a multi-channel regime and the diffuse-to-filamentary transition strongly depends on the overvoltage, the point-to-plane gap length and the pressure. When pressure is increased above atmospheric pressure, the diffuse stage and its transition to streamers seem to satisfy similarity rules as the key parameter is the reduced critical ionization field only. However, above 3 bar, neither diffuse avalanche nor streamer filaments are observed but a kind of streamer-leader regime, due to the fact that mechanisms such as photoionization and heat diffusion are not similar to pressure.

Development and application of two independent real-time PCR assays to detect clinically relevant Mucorales species.

Science.gov (United States)

Springer, Jan; Goldenberger, Daniel; Schmidt, Friderike; Weisser, Maja; Wehrle-Wieland, Elisabeth; Einsele, Hermann; Frei, Reno; Löffler, Jürgen

2016-03-01

PCR-based detection of Mucorales species could improve diagnosis of suspected invasive fungal infection, leading to a better patient outcome. This study describes two independent probe-based real-time PCR tests for detection of clinically relevant Mucorales, targeting specific fragments of the 18S and the 28S rRNA genes. Both assays have a short turnaround time, allow fast, specific and very sensitive detection of clinically relevant Mucorales and have the potential to be used as quantitative tests. They were validated on various clinical samples (fresh and formalin-fixed paraffin-embedded specimens, mainly biopsies, n = 17). The assays should be used as add-on tools to complement standard techniques; a combined approach of both real-time PCR assays has 100 % sensitivity. Genus identification by subsequent sequencing is possible for amplicons of the 18S PCR assay. In conclusion, combination of the two independent Mucorales assays described in this study, 18S and 28S, detected all clinical samples associated with proven Mucorales infection (n = 10). Reliable and specific identification of Mucorales is a prerequisite for successful antifungal therapy as these fungi show intrinsic resistance to voriconazole and caspofungin.

Diffuse Cosmic Infrared Background Radiation

Science.gov (United States)

Dwek, Eli

2002-01-01

The diffuse cosmic infrared background (CIB) consists of the cumulative radiant energy released in the processes of structure formation that have occurred since the decoupling of matter and radiation following the Big Bang. In this lecture I will review the observational data that provided the first detections and limits on the CIB, and the theoretical studies explaining the origin of this background. Finally, I will also discuss the relevance of this background to the universe as seen in high energy gamma-rays.

Feynman-Kac equations for reaction and diffusion processes

Science.gov (United States)

Hou, Ru; Deng, Weihua

2018-04-01

This paper provides a theoretical framework for deriving the forward and backward Feynman-Kac equations for the distribution of functionals of the path of a particle undergoing both diffusion and reaction processes. Once given the diffusion type and reaction rate, a specific forward or backward Feynman-Kac equation can be obtained. The results in this paper include those for normal/anomalous diffusions and reactions with linear/nonlinear rates. Using the derived equations, we apply our findings to compute some physical (experimentally measurable) statistics, including the occupation time in half-space, the first passage time, and the occupation time in half-interval with an absorbing or reflecting boundary, for the physical system with anomalous diffusion and spontaneous evanescence.

Time-driven activity-based costing in an outpatient clinic environment: development, relevance and managerial impact.

Science.gov (United States)

Demeere, Nathalie; Stouthuysen, Kristof; Roodhooft, Filip

2009-10-01

Healthcare managers are continuously urged to provide better patient services at a lower cost. To cope with these cost pressures, healthcare management needs to improve its understanding of the relevant cost drivers. Through a case study, we show how to perform a time-driven activity-based costing of five outpatient clinic's departments and provide evidence of the benefits of such an analysis.

Phase-space diffusion in turbulent plasmas: The random acceleration problem revisited

DEFF Research Database (Denmark)

Pécseli, H.L.; Trulsen, J.

1991-01-01

Phase-space diffusion of test particles in turbulent plasmas is studied by an approach based on a conditional statistical analysis of fluctuating electrostatic fields. Analytical relations between relevant conditional averages and higher-order correlations, , and triple...

Time-independent hybrid enrichment for finite element solution of transient conduction–radiation in diffusive grey media

Energy Technology Data Exchange (ETDEWEB)

Mohamed, M. Shadi, E-mail: m.s.mohamed@durham.ac.uk [School of Engineering and Computing Sciences, University of Durham, South Road, Durham DH1 3LE (United Kingdom); Seaid, Mohammed; Trevelyan, Jon [School of Engineering and Computing Sciences, University of Durham, South Road, Durham DH1 3LE (United Kingdom); Laghrouche, Omar [Institute for Infrastructure and Environment, Heriot-Watt University, Edinburgh EH14 4AS (United Kingdom)

2013-10-15

We investigate the effectiveness of the partition-of-unity finite element method for transient conduction–radiation problems in diffusive grey media. The governing equations consist of a semi-linear transient heat equation for the temperature field and a stationary diffusion approximation to the radiation in grey media. The coupled equations are integrated in time using a semi-implicit method in the finite element framework. We show that for the considered problems, a combination of hyperbolic and exponential enrichment functions based on an approximation of the boundary layer leads to improved accuracy compared to the conventional finite element method. It is illustrated that this approach can be more efficient than using h adaptivity to increase the accuracy of the finite element method near the boundary walls. The performance of the proposed partition-of-unity method is analyzed on several test examples for transient conduction–radiation problems in two space dimensions.

Measuring Restriction Sizes Using Diffusion Weighted Magnetic Resonance Imaging: A Review

Directory of Open Access Journals (Sweden)

Melanie Martin

2013-01-01

Full Text Available This article reviews a new concept in magnetic resonance as applied to cellular and biological systems. Diffusion weighted magnetic resonance imaging can be used to infer information about restriction sizes of samples being measured. The measurements rely on the apparent diffusion coefficient changing with diffusion times as measurements move from restricted to free diffusion regimes. Pulsed gradient spin echo (PGSE measurements are limited in the ability to shorten diffusion times and thus are limited in restriction sizes which can be probed. Oscillating gradient spin echo (OGSE measurements could provide shorter diffusion times so smaller restriction sizes could be probed.

Double diffusivity model under stochastic forcing

Science.gov (United States)

Chattopadhyay, Amit K.; Aifantis, Elias C.

2017-05-01

The "double diffusivity" model was proposed in the late 1970s, and reworked in the early 1980s, as a continuum counterpart to existing discrete models of diffusion corresponding to high diffusivity paths, such as grain boundaries and dislocation lines. It was later rejuvenated in the 1990s to interpret experimental results on diffusion in polycrystalline and nanocrystalline specimens where grain boundaries and triple grain boundary junctions act as high diffusivity paths. Technically, the model pans out as a system of coupled Fick-type diffusion equations to represent "regular" and "high" diffusivity paths with "source terms" accounting for the mass exchange between the two paths. The model remit was extended by analogy to describe flow in porous media with double porosity, as well as to model heat conduction in media with two nonequilibrium local temperature baths, e.g., ion and electron baths. Uncoupling of the two partial differential equations leads to a higher-ordered diffusion equation, solutions of which could be obtained in terms of classical diffusion equation solutions. Similar equations could also be derived within an "internal length" gradient (ILG) mechanics formulation applied to diffusion problems, i.e., by introducing nonlocal effects, together with inertia and viscosity, in a mechanics based formulation of diffusion theory. While being remarkably successful in studies related to various aspects of transport in inhomogeneous media with deterministic microstructures and nanostructures, its implications in the presence of stochasticity have not yet been considered. This issue becomes particularly important in the case of diffusion in nanopolycrystals whose deterministic ILG-based theoretical calculations predict a relaxation time that is only about one-tenth of the actual experimentally verified time scale. This article provides the "missing link" in this estimation by adding a vital element in the ILG structure, that of stochasticity, that takes into

Two-state random walk model of lattice diffusion - 1. Self-correlation function

International Nuclear Information System (INIS)

Balakrishnan, V.; Venkataraman, G.

1981-01-01

Diffusion with interruptions (arising from localized oscillations, or traps, or mixing between jump diffusion and fluid-like diffusion, etc.) is a very general phenomenon. Its manifestations range from superionic conductance to the behaviour of hydrogen in metals. Based on a continuous-time random walk approach, we present a comprehensive two-state random walk model for the diffusion of a particle on a lattice, incorporating arbitrary holding-time distributions for both localized residence at the sites and inter-site flights, and also the correct first-waiting-time distributions. A synthesis is thus achieved of the two extremes of jump diffusion (zero flight time) and fluid-like diffusion (zero residence time). Various earlier models emerge as special cases of our theory. Among the noteworthy results obtained are: closed-form solutions (in d dimensions, and with arbitrary directional bias) for temporarily uncorrelated jump diffusion and for the fluid diffusion counterpart; a compact, general formula for the mean square displacement; the effects of a continuous spectrum of time scales in the holding-time distributions, etc. The dynamic mobility and the structure factor for 'oscillatory diffusion' are taken up in part 2. (author)

DNS: Diffuse scattering neutron time-of-flight spectrometer

Directory of Open Access Journals (Sweden)

Yixi Su

2015-08-01

Full Text Available DNS is a versatile diffuse scattering instrument with polarisation analysis operated by the Jülich Centre for Neutron Science (JCNS, Forschungszentrum Jülich GmbH, outstation at the Heinz Maier-Leibnitz Zentrum (MLZ. Compact design, a large double-focusing PG monochromator and a highly efficient supermirror-based polarizer provide a polarized neutron flux of about 107 n cm-2 s-1. DNS is used for the studies of highly frustrated spin systems, strongly correlated electrons, emergent functional materials and soft condensed matter.

The American Foreign Exchange Option in Time-Dependent One-Dimensional Diffusion Model for Exchange Rate

International Nuclear Information System (INIS)

Rehman, Nasir; Shashiashvili, Malkhaz

2009-01-01

The classical Garman-Kohlhagen model for the currency exchange assumes that the domestic and foreign currency risk-free interest rates are constant and the exchange rate follows a log-normal diffusion process.In this paper we consider the general case, when exchange rate evolves according to arbitrary one-dimensional diffusion process with local volatility that is the function of time and the current exchange rate and where the domestic and foreign currency risk-free interest rates may be arbitrary continuous functions of time. First non-trivial problem we encounter in time-dependent case is the continuity in time argument of the value function of the American put option and the regularity properties of the optimal exercise boundary. We establish these properties based on systematic use of the monotonicity in volatility for the value functions of the American as well as European options with convex payoffs together with the Dynamic Programming Principle and we obtain certain type of comparison result for the value functions and corresponding exercise boundaries for the American puts with different strikes, maturities and volatilities.Starting from the latter fact that the optimal exercise boundary curve is left continuous with right-hand limits we give a mathematically rigorous and transparent derivation of the significant early exercise premium representation for the value function of the American foreign exchange put option as the sum of the European put option value function and the early exercise premium.The proof essentially relies on the particular property of the stochastic integral with respect to arbitrary continuous semimartingale over the predictable subsets of its zeros. We derive from the latter the nonlinear integral equation for the optimal exercise boundary which can be studied by numerical methods

Apparent diffusion coefficient measurement in glioma: Influence of region-of-interest determination methods on apparent diffusion coefficient values, interobserver variability, time efficiency, and diagnostic ability.

Science.gov (United States)

Han, Xu; Suo, Shiteng; Sun, Yawen; Zu, Jinyan; Qu, Jianxun; Zhou, Yan; Chen, Zengai; Xu, Jianrong

2017-03-01

To compare four methods of region-of-interest (ROI) placement for apparent diffusion coefficient (ADC) measurements in distinguishing low-grade gliomas (LGGs) from high-grade gliomas (HGGs). Two independent readers measured ADC parameters using four ROI methods (single-slice [single-round, five-round and freehand] and whole-volume) on 43 patients (20 LGGs, 23 HGGs) who had undergone 3.0 Tesla diffusion-weighted imaging and time required for each method of ADC measurements was recorded. Intraclass correlation coefficients (ICCs) were used to assess interobserver variability of ADC measurements. Mean and minimum ADC values and time required were compared using paired Student's t-tests. All ADC parameters (mean/minimum ADC values of three single-slice methods, mean/minimum/standard deviation/skewness/kurtosis/the10 th and 25 th percentiles/median/maximum of whole-volume method) were correlated with tumor grade (low versus high) by unpaired Student's t-tests. Discriminative ability was determined by receiver operating characteristic curves. All ADC measurements except minimum, skewness, and kurtosis of whole-volume ROI differed significantly between LGGs and HGGs (all P determination methods. Whole-volume histogram analysis did not yield better results than single-slice methods and took longer. Mean ADC value derived from single-round ROI is the most optimal parameter for differentiating LGGs from HGGs. 3 J. Magn. Reson. Imaging 2017;45:722-730. © 2016 International Society for Magnetic Resonance in Medicine.

Planning the diffusion of a neck-injury prevention programme among community rugby union coaches.

Science.gov (United States)

Donaldson, Alex; Poulos, Roslyn G

2014-01-01

This paper describes the development of a theory-informed and evidence-informed, context-specific diffusion plan for the Mayday Safety Procedure (MSP) among community rugby coaches in regional New South Wales, Australia. Step 5 of Intervention Mapping was used to plan strategies to enhance MSP adoption and implementation. Coaches were identified as the primary MSP adopters and implementers within a system including administrators, players and referees. A local advisory group was established to ensure context relevance. Performance objectives (eg, attend MSP training for coaches) and determinants of adoption and implementation behaviour (eg, knowledge, beliefs, skills and environment) were identified, informed by Social Cognitive Theory. Adoption and implementation matrices were developed and change-objectives for coaches were identified (eg, skills to deliver MSP training to players). Finally, intervention methods and specific strategies (eg, coach education, social marketing and policy and by-law development) were identified based on advisory group member experience, evidence of effective coach safety behaviour-change interventions and Diffusion of Innovations theory. This is the first published example of a systematic approach to plan injury prevention programme diffusion in community sports. The key strengths of this approach were an effective researcher-practitioner partnership; actively engaging local sports administrators; targeting specific behaviour determinants, informed by theory and evidence; and taking context-related practical strengths and constraints into consideration. The major challenges were the time involved in using a systematic diffusion planning approach for the first time; and finding a planning language that was acceptable and meaningful to researchers and practitioners.

Helium diffusion in nickel at high temperatures

International Nuclear Information System (INIS)

Philipps, V.

1980-09-01

Helium has been implanted at certain temperatures between 800 and 1250 0 C into single and polycrystalline Ni-samples with implantation depths between 15 and 90 μm. Simultaneously the helium reemission from the sample is measured by a mass-spectrometer. It has been shown that the time dependence of the observed reemission rate is governed by volume diffusion of the helium. Measuring this time dependence as a function of temperature the helium diffusion constant has been determined. The He-diffusion is interpreted as a interstitial diffusion hindered by thermal vacancies. Depending on the implantation depth more or less of the implanted helium remains in the sample and forms large helium bubbles. (orig./GSCH)

User perspectives on relevance criteria

DEFF Research Database (Denmark)

Maglaughlin, Kelly L.; Sonnenwald, Diane H.

2002-01-01

, partially relevant, or not relevant to their information need; and explained their decisions in an interview. Analysis revealed 29 criteria, discussed positively and negatively, that were used by the participants when selecting passages that contributed or detracted from a document's relevance......This study investigates the use of criteria to assess relevant, partially relevant, and not-relevant documents. Study participants identified passages within 20 document representations that they used to make relevance judgments; judged each document representation as a whole to be relevant...... matter, thought catalyst), full text (e.g., audience, novelty, type, possible content, utility), journal/publisher (e.g., novelty, main focus, perceived quality), and personal (e.g., competition, time requirements). Results further indicate that multiple criteria are used when making relevant, partially...

Optical decoherence times and spectral diffusion in an Er-doped optical fiber measured by two-pulse echoes, stimulated photon echoes, and spectral hole burning

International Nuclear Information System (INIS)

Macfarlane, R.M.; Sun, Y.; Sellin, P.B.; Cone, R.L.

2007-01-01

Two-pulse and stimulated photon echoes and spectral hole burning were measured on the transition from the lowest component of the 4 I 15/2 manifold to the lowest component of 4 I 13/2 of Er 3+ in a silicate optical fiber at 1.6 K. The two-pulse echo decays gave decoherence times as long as 230 ns for magnetic fields above 2 T. A large field dependent contribution to the homogeneous line width of >2 MHz was found and interpreted in terms of coupling to magnetic tunneling modes (TLS) in the glass. The stimulated echoes measured at 2 T showed spectral diffusion of 0.8 MHz/decade of time between 0.4 and 500 μs. Spectral diffusion in this high field region is attributed to coupling to elastic TLS modes which have a distribution of flip rates in glasses. Time-resolved spectral hole burning at very low field showed stronger spectral diffusion of 5.7 MHz/decade of time, attributed to coupling to magnetic spin-elastic TLS modes

Effects of MR parameter changes on the quantification of diffusion anisotropy and apparent diffusion coefficient in diffusion tensor imaging: Evaluation using a diffusional anisotropic phantom

Energy Technology Data Exchange (ETDEWEB)

Kim, Sang Joon; Choi, Choong Gon; Kim, Jeong Kon [Dept. of Radiology, Asan Medical Center, University of Ulsan College of Medicine, Seoul (Korea, Republic of); Yun, Sung Cheol [Dept. of Biostatistics, University of Ulsan College of Medicine, Seoul (Korea, Republic of); Jeong, Ha Kyu [Dept. of Radiology, East-West Neomedical Center, Kyung Hee University College of Medicine, Seoul (Korea, Republic of); Kim, Eun Ju [Clinical Scientist, MR, Philips Healthcare, Seoul (Korea, Republic of)

2015-04-15

To validate the usefulness of a diffusional anisotropic capillary array phantom and to investigate the effects of diffusion tensor imaging (DTI) parameter changes on diffusion fractional anisotropy (FA) and apparent diffusion coefficient (ADC) using the phantom. Diffusion tensor imaging of a capillary array phantom was performed with imaging parameter changes, including voxel size, number of sensitivity encoding (SENSE) factor, echo time (TE), number of signal acquisitions, b-value, and number of diffusion gradient directions (NDGD), one-at-a-time in a stepwise-incremental fashion. We repeated the entire series of DTI scans thrice. The coefficients of variation (CoV) were evaluated for FA and ADC, and the correlation between each MR imaging parameter and the corresponding FA and ADC was evaluated using Spearman's correlation analysis. The capillary array phantom CoVs of FA and ADC were 7.1% and 2.4%, respectively. There were significant correlations between FA and SENSE factor, TE, b-value, and NDGD, as well as significant correlations between ADC and SENSE factor, TE, and b-value. A capillary array phantom enables repeated measurements of FA and ADC. Both FA and ADC can vary when certain parameters are changed during diffusion experiments. We suggest that the capillary array phantom can be used for quality control in longitudinal or multicenter clinical studies.

How Body Orientation Affects Concepts of Space, Time and Valence: Functional Relevance of Integrating Sensorimotor Experiences during Word Processing.

Directory of Open Access Journals (Sweden)

Martin Lachmair

Full Text Available The aim of the present study was to test the functional relevance of the spatial concepts UP or DOWN for words that use these concepts either literally (space or metaphorically (time, valence. A functional relevance would imply a symmetrical relationship between the spatial concepts and words related to these concepts, showing that processing words activate the related spatial concepts on one hand, but also that an activation of the concepts will ease the retrieval of a related word on the other. For the latter, the rotation angle of participant's body position was manipulated either to an upright or a head-down tilted body position to activate the related spatial concept. Afterwards participants produced in a within-subject design previously memorized words of the concepts space, time and valence according to the pace of a metronome. All words were related either to the spatial concept UP or DOWN. The results including Bayesian analyses show (1 a significant interaction between body position and words using the concepts UP and DOWN literally, (2 a marginal significant interaction between body position and temporal words and (3 no effect between body position and valence words. However, post-hoc analyses suggest no difference between experiments. Thus, the authors concluded that integrating sensorimotor experiences is indeed of functional relevance for all three concepts of space, time and valence. However, the strength of this functional relevance depends on how close words are linked to mental concepts representing vertical space.

Modeling Diffusion and Buoyancy-Driven Convection with Application to Geological CO2 Storage

KAUST Repository

Allen, Rebecca

2015-04-01

ABSTRACT Modeling Diffusion and Buoyancy-Driven Convection with Application to Geological CO2 Storage Rebecca Allen Geological CO2 storage is an engineering feat that has been undertaken around the world for more than two decades, thus accurate modeling of flow and transport behavior is of practical importance. Diffusive and convective transport are relevant processes for buoyancy-driven convection of CO2 into underlying fluid, a scenario that has received the attention of numerous modeling studies. While most studies focus on Darcy-scale modeling of this scenario, relatively little work exists at the pore-scale. In this work, properties evaluated at the pore-scale are used to investigate the transport behavior modeled at the Darcy-scale. We compute permeability and two different forms of tortuosity, namely hydraulic and diffusive. By generating various pore ge- ometries, we find hydraulic and diffusive tortuosity can be quantitatively different in the same pore geometry by up to a factor of ten. As such, we emphasize that these tortuosities should not be used interchangeably. We find pore geometries that are characterized by anisotropic permeability can also exhibit anisotropic diffusive tortuosity. This finding has important implications for buoyancy-driven convection modeling; when representing the geological formation with an anisotropic permeabil- ity, it is more realistic to also account for an anisotropic diffusivity. By implementing a non-dimensional model that includes both a vertically and horizontally orientated 5 Rayleigh number, we interpret our findings according to the combined effect of the anisotropy from permeability and diffusive tortuosity. In particular, we observe the Rayleigh ratio may either dampen or enhance the diffusing front, and our simulation data is used to express the time of convective onset as a function of the Rayleigh ratio. Also, we implement a lattice Boltzmann model for thermal convective flows, which we treat as an analog for

Nonergodicity, fluctuations, and criticality in heterogeneous diffusion processes.

Science.gov (United States)

Cherstvy, A G; Metzler, R

2014-07-01

We study the stochastic behavior of heterogeneous diffusion processes with the power-law dependence D(x) ∼ |x|(α) of the generalized diffusion coefficient encompassing sub- and superdiffusive anomalous diffusion. Based on statistical measures such as the amplitude scatter of the time-averaged mean-squared displacement of individual realizations, the ergodicity breaking and non-Gaussianity parameters, as well as the probability density function P(x,t), we analyze the weakly nonergodic character of the heterogeneous diffusion process and, particularly, the degree of irreproducibility of individual realizations. As we show, the fluctuations between individual realizations increase with growing modulus |α| of the scaling exponent. The fluctuations appear to diverge when the critical value α = 2 is approached, while for even larger α the fluctuations decrease, again. At criticality, the power-law behavior of the mean-squared displacement changes to an exponentially fast growth, and the fluctuations of the time-averaged mean-squared displacement do not converge for increasing number of realizations. From a systematic comparison we observe some striking similarities of the heterogeneous diffusion process with the familiar subdiffusive continuous time random walk process with power-law waiting time distribution and diverging characteristic waiting time.

Cerebral NMR spectroscopy to study intracellular space in vivo: methodological development for diffusion weighted spectroscopy at short time scale and for pH measurement using 31P detection

International Nuclear Information System (INIS)

Marchadour, Charlotte

2013-01-01

NMR spectroscopy is a unique modality to evaluate intracellular environment in vivo. Indeed observed molecules are specifically intracellular and generally have a biochemistry role and a specific cellular compartmentation. That could be a useful tool to understand cell functioning in their environment. My thesis work consisted in development of new sequence in both diffusion and phosphorus NMR spectroscopy.My first study was to develop a diffusion-weighted spectroscopy at ultra-short diffusion time to look at the anomalous diffusion in the rat brain. ADC evolution as a function of time shows that brain metabolites motion is mainly due to random diffusion and that active transport (if exist) are negligible. Data modeling evidences that diffusion at short diffusion time is sensitive to cytoplasm viscosity and short scale crowding. In collaboration with the pharmaceutical company, this technique was chosen to follow up transgenic mice (rTg4510), model of tau pathology. Preliminary results show significant differences of ADC at an early stage of neuro-degenerescence (3 and 6 months).Phosphorus spectroscopy allows observation of metabolites directly implicated in energetic processes. During this thesis, localization sequences were developed to measure intracellular pH in the primate striatum. These sequences are supposed to be used to evaluate the potential of pH as a bio-marker of neuro-degenerescence in a phenotypic model of the Huntington disease in the non-human primate. (author) [fr

Diffusion

International Nuclear Information System (INIS)

Kubaschewski, O.

1983-01-01

The diffusion rate values of titanium, its compounds and alloys are summarized and tabulated. The individual chemical diffusion coefficients and self-diffusion coefficients of certain isotopes are given. Experimental methods are listed which were used for the determination of diffusion coefficients. Some values have been taken over from other studies. Also given are graphs showing the temperature dependences of diffusion and changes in the diffusion coefficient with concentration changes

Continuous diffusion signal, EAP and ODF estimation via Compressive Sensing in diffusion MRI.

Science.gov (United States)

Merlet, Sylvain L; Deriche, Rachid

2013-07-01

In this paper, we exploit the ability of Compressed Sensing (CS) to recover the whole 3D Diffusion MRI (dMRI) signal from a limited number of samples while efficiently recovering important diffusion features such as the Ensemble Average Propagator (EAP) and the Orientation Distribution Function (ODF). Some attempts to use CS in estimating diffusion signals have been done recently. However, this was mainly an experimental insight of CS capabilities in dMRI and the CS theory has not been fully exploited. In this work, we also propose to study the impact of the sparsity, the incoherence and the RIP property on the reconstruction of diffusion signals. We show that an efficient use of the CS theory enables to drastically reduce the number of measurements commonly used in dMRI acquisitions. Only 20-30 measurements, optimally spread on several b-value shells, are shown to be necessary, which is less than previous attempts to recover the diffusion signal using CS. This opens an attractive perspective to measure the diffusion signals in white matter within a reduced acquisition time and shows that CS holds great promise and opens new and exciting perspectives in diffusion MRI (dMRI). Copyright © 2013 Elsevier B.V. All rights reserved.

Particle Simulation of Fractional Diffusion Equations

KAUST Repository

Allouch, Samer

2017-07-12

This work explores different particle-based approaches to the simulation of one-dimensional fractional subdiffusion equations in unbounded domains. We rely on smooth particle approximations, and consider four methods for estimating the fractional diffusion term. The first method is based on direct differentiation of the particle representation, it follows the Riesz definition of the fractional derivative and results in a non-conservative scheme. The other three methods follow the particle strength exchange (PSE) methodology and are by construction conservative, in the sense that the total particle strength is time invariant. The first PSE algorithm is based on using direct differentiation to estimate the fractional diffusion flux, and exploiting the resulting estimates in an integral representation of the divergence operator. Meanwhile, the second one relies on the regularized Riesz representation of the fractional diffusion term to derive a suitable interaction formula acting directly on the particle representation of the diffusing field. A third PSE construction is considered that exploits the Green\\'s function of the fractional diffusion equation. The performance of all four approaches is assessed for the case of a one-dimensional diffusion equation with constant diffusivity. This enables us to take advantage of known analytical solutions, and consequently conduct a detailed analysis of the performance of the methods. This includes a quantitative study of the various sources of error, namely filtering, quadrature, domain truncation, and time integration, as well as a space and time self-convergence analysis. These analyses are conducted for different values of the order of the fractional derivatives, and computational experiences are used to gain insight that can be used for generalization of the present constructions.

Particle Simulation of Fractional Diffusion Equations

KAUST Repository

Allouch, Samer; Lucchesi, Marco; Maî tre, O. P. Le; Mustapha, K. A.; Knio, Omar

2017-01-01

This work explores different particle-based approaches to the simulation of one-dimensional fractional subdiffusion equations in unbounded domains. We rely on smooth particle approximations, and consider four methods for estimating the fractional diffusion term. The first method is based on direct differentiation of the particle representation, it follows the Riesz definition of the fractional derivative and results in a non-conservative scheme. The other three methods follow the particle strength exchange (PSE) methodology and are by construction conservative, in the sense that the total particle strength is time invariant. The first PSE algorithm is based on using direct differentiation to estimate the fractional diffusion flux, and exploiting the resulting estimates in an integral representation of the divergence operator. Meanwhile, the second one relies on the regularized Riesz representation of the fractional diffusion term to derive a suitable interaction formula acting directly on the particle representation of the diffusing field. A third PSE construction is considered that exploits the Green's function of the fractional diffusion equation. The performance of all four approaches is assessed for the case of a one-dimensional diffusion equation with constant diffusivity. This enables us to take advantage of known analytical solutions, and consequently conduct a detailed analysis of the performance of the methods. This includes a quantitative study of the various sources of error, namely filtering, quadrature, domain truncation, and time integration, as well as a space and time self-convergence analysis. These analyses are conducted for different values of the order of the fractional derivatives, and computational experiences are used to gain insight that can be used for generalization of the present constructions.

Molecular dynamics simulation of metallic impurity diffusion in liquid lead-bismuth eutectic (LBE)

Science.gov (United States)

Gao, Yun; Takahashi, Minoru; Cavallotti, Carlo; Raos, Guido

2018-04-01

Corrosion of stainless steels by lead-bismuth eutectic (LBE) is an important problem which depends, amongst other things, on the diffusion of the steel components inside this liquid alloy. Here we present the results of classical molecular dynamics simulations of the diffusion of Fe and Ni within LBE. The simulations complement experimental studies of impurity diffusion by our group and provide an atomic-level understanding of the relevant diffusion phenomena. They are based on the embedded atom method (EAM) to represent many-body interactions among atoms. The EAM potentials employed in our simulations have been validated against ab initio density functional calculations. We show that the experimental and simulation results for the temperature-dependent viscosity of LBE and the impurity diffusion coefficients can be reconciled by assuming that the Ni and Fe diffuse mainly as nanoscopic clusters below 1300 K. The average Fe and Ni cluster sizes decrease with increasing the temperature and there is essentially single-atom diffusion at higher temperatures.

Multicomponent diffusion in basaltic melts at 1350 °C

Science.gov (United States)

Guo, Chenghuan; Zhang, Youxue

2018-05-01

Nine successful diffusion couple experiments were conducted in an 8-component SiO2-TiO2-Al2O3-FeO-MgO-CaO-Na2O-K2O system at ∼1350 °C and at 1 GPa, to study multicomponent diffusion in basaltic melts. At least 3 traverses were measured to obtain diffusion profiles for each experiment. Multicomponent diffusion matrix at 1350 °C was obtained by simultaneously fitting diffusion profiles of diffusion couple experiments. Furthermore, in order to better constrain the diffusion matrix and reconcile mineral dissolution data, mineral dissolution experiments in the literature and diffusion couple experiments from this study, were fit together. All features of diffusion profiles in both diffusion couple and mineral dissolution experiments were well reproduced by the diffusion matrix. Diffusion mechanism is inferred from eigenvectors of the diffusion matrix, and it shows that the diffusive exchange between network-formers SiO2 and Al2O3 is the slowest, the exchange of SiO2 with other oxide components is the second slowest with an eigenvalue that is only ∼10% larger, then the exchange between divalent oxide components and all the other oxide components is the third slowest with an eigenvalue that is twice the smallest eigenvalue, then the exchange of FeO + K2O with all the other oxide components is the fourth slowest with an eigenvalue that is 5 times the smallest eigenvalue, then the exchange of MgO with FeO + CaO is the third fastest with an eigenvalue that is 6.3 times the smallest eigenvalue, then the exchange of CaO + K2O with all the other oxide components is the second fastest with an eigenvalue that is 7.5 times the smallest eigenvalue, and the exchange of Na2O with all other oxide components is the fastest with an eigenvalue that is 31 times the smallest eigenvalue. The slowest and fastest eigenvectors are consistent with those for simpler systems in most literature. The obtained diffusion matrix was successfully applied to predict diffusion profiles during

NMR diffusion simulation based on conditional random walk.

Science.gov (United States)

Gudbjartsson, H; Patz, S

1995-01-01

The authors introduce here a new, very fast, simulation method for free diffusion in a linear magnetic field gradient, which is an extension of the conventional Monte Carlo (MC) method or the convolution method described by Wong et al. (in 12th SMRM, New York, 1993, p.10). In earlier NMR-diffusion simulation methods, such as the finite difference method (FD), the Monte Carlo method, and the deterministic convolution method, the outcome of the calculations depends on the simulation time step. In the authors' method, however, the results are independent of the time step, although, in the convolution method the step size has to be adequate for spins to diffuse to adjacent grid points. By always selecting the largest possible time step the computation time can therefore be reduced. Finally the authors point out that in simple geometric configurations their simulation algorithm can be used to reduce computation time in the simulation of restricted diffusion.

Multi-site Study of Diffusion Metric Variability: Characterizing the Effects of Site, Vendor, Field Strength, and Echo Time using the Histogram Distance

Science.gov (United States)

Helmer, K. G.; Chou, M-C.; Preciado, R. I.; Gimi, B.; Rollins, N. K.; Song, A.; Turner, J.; Mori, S.

2016-01-01

MRI-based multi-site trials now routinely include some form of diffusion-weighted imaging (DWI) in their protocol. These studies can include data originating from scanners built by different vendors, each with their own set of unique protocol restrictions, including restrictions on the number of available gradient directions, whether an externally-generated list of gradient directions can be used, and restrictions on the echo time (TE). One challenge of multi-site studies is to create a common imaging protocol that will result in a reliable and accurate set of diffusion metrics. The present study describes the effect of site, scanner vendor, field strength, and TE on two common metrics: the first moment of the diffusion tensor field (mean diffusivity, MD), and the fractional anisotropy (FA). We have shown in earlier work that ROI metrics and the mean of MD and FA histograms are not sufficiently sensitive for use in site characterization. Here we use the distance between whole brain histograms of FA and MD to investigate within- and between-site effects. We concluded that the variability of DTI metrics due to site, vendor, field strength, and echo time could influence the results in multi-center trials and that histogram distance is sensitive metrics for each of these variables. PMID:27350723

Multi-site Study of Diffusion Metric Variability: Characterizing the Effects of Site, Vendor, Field Strength, and Echo Time using the Histogram Distance.

Science.gov (United States)

Helmer, K G; Chou, M-C; Preciado, R I; Gimi, B; Rollins, N K; Song, A; Turner, J; Mori, S

2016-02-27

MRI-based multi-site trials now routinely include some form of diffusion-weighted imaging (DWI) in their protocol. These studies can include data originating from scanners built by different vendors, each with their own set of unique protocol restrictions, including restrictions on the number of available gradient directions, whether an externally-generated list of gradient directions can be used, and restrictions on the echo time (TE). One challenge of multi-site studies is to create a common imaging protocol that will result in a reliable and accurate set of diffusion metrics. The present study describes the effect of site, scanner vendor, field strength, and TE on two common metrics: the first moment of the diffusion tensor field (mean diffusivity, MD), and the fractional anisotropy (FA). We have shown in earlier work that ROI metrics and the mean of MD and FA histograms are not sufficiently sensitive for use in site characterization. Here we use the distance between whole brain histograms of FA and MD to investigate within- and between-site effects. We concluded that the variability of DTI metrics due to site, vendor, field strength, and echo time could influence the results in multi-center trials and that histogram distance is sensitive metrics for each of these variables.

Distributed Control Diffusion

DEFF Research Database (Denmark)

Schultz, Ulrik Pagh

2007-01-01

. Programming a modular, self-reconfigurable robot is however a complicated task: the robot is essentially a real-time, distributed embedded system, where control and communication paths often are tightly coupled to the current physical configuration of the robot. To facilitate the task of programming modular....... This approach allows the programmer to dynamically distribute behaviors throughout a robot and moreover provides a partial abstraction over the concrete physical shape of the robot. We have implemented a prototype of a distributed control diffusion system for the ATRON modular, self-reconfigurable robot......, self-reconfigurable robots, we present the concept of distributed control diffusion: distributed queries are used to identify modules that play a specific role in the robot, and behaviors that implement specific control strategies are diffused throughout the robot based on these role assignments...

Mode coupling theory analysis of electrolyte solutions: Time dependent diffusion, intermediate scattering function, and ion solvation dynamics.

Science.gov (United States)

Roy, Susmita; Yashonath, Subramanian; Bagchi, Biman

2015-03-28

A self-consistent mode coupling theory (MCT) with microscopic inputs of equilibrium pair correlation functions is developed to analyze electrolyte dynamics. We apply the theory to calculate concentration dependence of (i) time dependent ion diffusion, (ii) intermediate scattering function of the constituent ions, and (iii) ion solvation dynamics in electrolyte solution. Brownian dynamics with implicit water molecules and molecular dynamics method with explicit water are used to check the theoretical predictions. The time dependence of ionic self-diffusion coefficient and the corresponding intermediate scattering function evaluated from our MCT approach show quantitative agreement with early experimental and present Brownian dynamic simulation results. With increasing concentration, the dispersion of electrolyte friction is found to occur at increasingly higher frequency, due to the faster relaxation of the ion atmosphere. The wave number dependence of intermediate scattering function, F(k, t), exhibits markedly different relaxation dynamics at different length scales. At small wave numbers, we find the emergence of a step-like relaxation, indicating the presence of both fast and slow time scales in the system. Such behavior allows an intriguing analogy with temperature dependent relaxation dynamics of supercooled liquids. We find that solvation dynamics of a tagged ion exhibits a power law decay at long times-the decay can also be fitted to a stretched exponential form. The emergence of the power law in solvation dynamics has been tested by carrying out long Brownian dynamics simulations with varying ionic concentrations. The solvation time correlation and ion-ion intermediate scattering function indeed exhibit highly interesting, non-trivial dynamical behavior at intermediate to longer times that require further experimental and theoretical studies.

Locating the source of diffusion in complex networks by time-reversal backward spreading

Science.gov (United States)

Shen, Zhesi; Cao, Shinan; Wang, Wen-Xu; Di, Zengru; Stanley, H. Eugene

2016-03-01

Locating the source that triggers a dynamical process is a fundamental but challenging problem in complex networks, ranging from epidemic spreading in society and on the Internet to cancer metastasis in the human body. An accurate localization of the source is inherently limited by our ability to simultaneously access the information of all nodes in a large-scale complex network. This thus raises two critical questions: how do we locate the source from incomplete information and can we achieve full localization of sources at any possible location from a given set of observable nodes. Here we develop a time-reversal backward spreading algorithm to locate the source of a diffusion-like process efficiently and propose a general locatability condition. We test the algorithm by employing epidemic spreading and consensus dynamics as typical dynamical processes and apply it to the H1N1 pandemic in China. We find that the sources can be precisely located in arbitrary networks insofar as the locatability condition is assured. Our tools greatly improve our ability to locate the source of diffusion in complex networks based on limited accessibility of nodal information. Moreover, they have implications for controlling a variety of dynamical processes taking place on complex networks, such as inhibiting epidemics, slowing the spread of rumors, pollution control, and environmental protection.

Study of mechanism of hydrogen diffusion in separation devices. Progress report for 1980-1983

International Nuclear Information System (INIS)

Lee, M.H.

1983-01-01

For the purpose of studying the mechanisms of hydrogen diffusion in separation devices e.g. transition-metal membranes, we have developed a microscopic dynamic model appropriate for describing the nonequilibrium statistical mechanics of hydrogen-in-a-metal. Using this model we have carried out a detailed analysis to obtain the autocorrelation function of density fluctuations in the model. Our model is built on the physical idea that, at low temperatures, spin clusters are the basic units or aggregates of transport. Our work can explain the reversed isotope effect in diffusion. We have also obtained an expression for the relative diffusivity, verifiable by experiments with tritium in metals. Our notion of spin clusters is novel. There is some evidence of their existence. The interstitial spin clusters are comparable to atomic and nuclear spin clusters, the only other natural spin clusters. Our demonstration of a long-time tail in the autocorrelation function is also novel. Diffusion can be anomalous if long time tails exist, a current topic in nonlinear behavior of fluids and solids. Our progress has been made possible by our development in the mathematical method of solving the generalized Langevin equation. This method is applicable to any time-dependent quantum many-body model. The underlying basis of this method is our discovery of a new orthogonalization process in Hilbert space, first since Gram and Schmidt over 100 years ago. Our process is simpler if Hilbert space is realized as is for all physical problems. To demonstrate the power and utility of our method we considered a well established model of metals, thereby discovering the existence of a low-frequency electronic mobility. This kind of intrinsic conductivity should exist in ensembles of all light particles, hence also relevant to hydrogen and its isotopes in metals

Polymer diffusion in the interphase between surface and solution.

Science.gov (United States)

Weger, Lukas; Weidmann, Monika; Ali, Wael; Hildebrandt, Marcus; Gutmann, Jochen Stefan; Hoffmann-Jacobsen, Kerstin

2018-05-22

Total internal reflection fluorescence correlation spectroscopy (TIR-FCS) is applied to study the self-diffusion of polyethylene glycol solutions in the presence of weakly attractive interfaces. Glass coverslips modified with aminopropyl- and propyl-terminated silanes are used to study the influence of solid surfaces on polymer diffusion. A model of three phases of polymer diffusion allows to describe the experimental fluorescence autocorrelation functions. Besides the two-dimensional diffusion of adsorbed polymer on the substrate and three-dimensional free diffusion in bulk solution, a third diffusion time scale is observed with intermediate diffusion times. This retarded three-dimensional diffusion in solution is assigned to long range effects of solid surfaces on diffusional dynamics of polymers. The respective diffusion constants show Rouse scaling (D~N -1 ) indicating a screening of hydrodynamic interactions by the presence of the surface. Hence, the presented TIR-FCS method proves to be a valuable tool to investigate the effect of surfaces on polymer diffusion beyond the first adsorbed polymer layer on the 100 nm length scale.

Fractional Diffusion Limit for Collisional Kinetic Equations

KAUST Repository

Mellet, Antoine

2010-08-20

This paper is devoted to diffusion limits of linear Boltzmann equations. When the equilibrium distribution function is a Maxwellian distribution, it is well known that for an appropriate time scale, the small mean free path limit gives rise to a diffusion equation. In this paper, we consider situations in which the equilibrium distribution function is a heavy-tailed distribution with infinite variance. We then show that for an appropriate time scale, the small mean free path limit gives rise to a fractional diffusion equation. © 2010 Springer-Verlag.

Neodymium ion diffusion during sintering of Nd : YAG transparent ceramics

Energy Technology Data Exchange (ETDEWEB)

Hollingsworth, Joel P; Kuntz, Joshua D; Soules, Thomas F [Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, CA, 94550 (United States)

2009-03-07

Using an electron microprobe, we measured and characterized the Nd{sup 3+} ion diffusion across a boundary between Nd doped and undoped ceramic yttrium aluminium garnet (YAG) for different temperature ramps and hold times and temperatures. The results show significant Nd ion diffusion on the order of micrometres to tens of micrometres depending on the time and temperature of sintering. The data fit well a model including bulk diffusion, grain boundary diffusion and grain growth. Grain boundary diffusion dominates and grain growth limits grain boundary diffusion by reducing the total cross-sectional area of grain boundaries. (fast track communication)

Ageing dynamics of translational and rotational diffusion in a colloidal glass

International Nuclear Information System (INIS)

Jabbari-Farouji, Sara; Eiser, Erika; Wegdam, Gerard H; Bonn, Daniel

2004-01-01

We study the dynamics of translational and rotational diffusion during the ageing of a colloidal glass of Laponite using polarized and depolarized dynamic light scattering. The dynamics are qualitatively similar between the two degrees of freedom. The short-time diffusion is independent of the time elapsed since the sample preparation. The intermediate- and long-time diffusion, on the other hand, slows down by several orders of magnitude during the ageing. The slowing down of the rotational diffusion is found to be much faster than that of the translational diffusion. (letter to the editor)

Diffusion of 64Cu in copper-containing chalcogenide glasses

International Nuclear Information System (INIS)

Vlasov, Yu.G.; Bychkov, E.A.; Bolotov, A.M.; Tsegel'nik, V.S.; Gavrilov, Yu.A.

1996-01-01

Diffusion experiments with 64 Cu radioactive tracer for a number of copper-containing chalcogenide glasses CuI-As 2 Se 3 , Cu-SbI 3 -As 2 Se 3 , CuI-PbI 2 -As 2 Se 3 , CuI-PbI 2 -SbI 3 -As 2 Se 3 and Cu 2 Se-As 2 Se 3 are carried out for the first time. The results of diffusion and electrodiffusion measurements are in correspondence with information on electroconductivity and diffusion in a limited space (cage diffusion) from the Moessbauer spectroscopy on 124 I. It is shown for the first time that the Cheivin factor index for copper-conducting glasses in by 2-3 times higher as compared to silver-conducting glasses with approximate diffusion coefficients indices. 27 refs., 3 figs., 1 tab