Search

In the study of femtoscopic correlations in high-energy physics, besides Bose–Einstein correlations, one has to take final-state interactions into account. Amongst them, Coulomb interactions play a prominent role in the case of charged particles. Recent measurements have shown that in heavy-ion collisions, Bose–Einstein correlations can be best described by Lévy-type sources instead of the more common Gaussian assumption. Furthermore, three-dimensional measurements have indicated that, depending on the choice of frame, a deviation from spherical symmetry observed under the assumption of Gaussian source functions persists in the case of Lévy-type sources. To clarify such three-dimensional Lévy-type correlation measurements, it is thus important to study the effect of Coulomb interactions in the case of non-spherical Lévy sources. We calculated the Coulomb correction factor numerically in the case of such a source function for assorted kinematic domains and parameter values using the Metropolis–Hastings algorithm and compared our results with previous methods to treat Coulomb interactions in the presence of Lévy sources.

In statistical mechanics, the ergodic hypothesis (i.e., the long-time average is the same as the ensemble average) accompanying anomalous diffusion has become a continuous topic of research, being closely related to irreversibility and increasing entropy. While measurement time is finite for a given process, the time average of an observable quantity might be a random variable, whose distribution width narrows with time, and one wonders how long it takes for the convergence rate to become a constant. This is also the premise of ergodic establishment, because the ensemble average is always equal to the constant. We focus on the time-dependent fluctuation width for the time average of both the velocity and kinetic energy of a force-free particle described by the generalized Langevin equation, where the stationary velocity autocorrelation function is considered. Subsequently, the shortest time scale can be estimated for a system transferring from a stationary state to an effective ergodic state. Moreover, a logarithmic spatial potential is used to modulate the processes associated with free ballistic diffusion and the control of diffusion, as well as the minimal realization of the whole power-law regime. The results presented suggest that non-ergodicity mimics the sparseness of the medium and reveals the unique role of logarithmic potential in modulating diffusion behavior.

An example of non-Markovian quantum dynamics is considered in the framework of a geometrical (topological) subordination approach. The specific property of the model is that it coincides exactly with the fractional diffusion equation, which describes the geometric Brownian motion on combs. Both classical diffusion and quantum dynamics are described using the dilatation operator xddx. Two examples of geometrical subordinators are considered. The first one is the Gaussian function, which is due to the comb geometry. For the quantum consideration with a specific choice of the initial conditions, it corresponds to the integral representation of the Mittag–Leffler function by means of the subordination integral. The second subordinator is the Dirac delta function, which results from the memory kernels that define the fractional time derivatives in the fractional diffusion equation.

[ES] Durante las últimas décadas el uso del aprendizaje automático (machine learning) y de la inteligencia artificial ha mostrado un crecimiento exponencial en muchas áreas de la ciencia. El hecho de que los ordenadores hayan aumentado sus restaciones a la vez que han reducido su precio, junto con la disponibilidad de entornos de desarrollo de código abierto han permitido el acceso a la inteligencia artificial a un gran rango de investigadores, democratizando de esta forma el acceso a métodos de inteligencia artificial a la comunidad investigadora. Es nuestra creencia que la multidisciplinaridad es clave para nuevos logros, con equipos compuestos de investigadores con diferentes preparaciones y de diferentes campos de especialización. Con este ánimo, hemos orientado esta tesis en el uso de machine learning inteligencia artificial, aprendizaje profundo o deep learning, entendiendo todas las anteriores como parte de un concepto global que concretamos en el término inteligencia artificial, a intentar arrojar luz a algunos problemas de los campos de las matemáticas y la física. Desarrollamos una arquitectura deep learning y la medimos con éxito en la caracterización de procesos de difusión anómala. Mientras que previamente se habían utilizado métodos estadísticos clásicos con este objetivo, los métodos de deep learning han demostrado mejorar las prestaciones de dichos métodos clásicos. Nuestra architectura demostró que puede inferir con precisión el exponente de difusión anómala y clasificar trayectorias entre un conjunto dado de modelos subyacentes de difusión . Mientras que las redes neuronales recurrentes irrumpieron recientemente, los modelos basados en redes convolucionales han sido ámpliamente testados en el campo del procesamiento de imagen durante más de 15 años. Existen muchos modelos y arquitecturas, pre-entrenados y listos para ser usados por la comunidad. No es necesario realizar investigación ya que dichos modelos han probado su valía durante años y están bien documentados en la literatura. Nuestro objetivo era ser capaces de usar esos modelos bien conocidos y fiables, con trayectorias de difusión anómala. Solo necesitábamos convertir una serie temporal en una imagen, cosa que hicimos aplicando gramian angular fields a las trayectorias, poniendo el foco en las trayectorias cortas. Hasta donde sabemos, ésta es la primera vez que dichas técnicas son usadas en este campo. Mostramos cómo esta aproximación mejora las prestaciones de cualquier otra propuesta en la clasificación del modelo subyacente de difusión anómala para trayectorias cortas. Más allá de la física están las matemáticas. Utilizamos nuestra arquitectura basada en redes recurrentes neuronales para inferir los parámetros que definen las trayectorias de Wu Baleanu. Mostramos que nuestra propuesta puede inferir con azonable precisión los parámetros mu y nu. Siendo la primera vez, de nuevo hasta donde llega nuestro conocimiento, que tales técnicas se aplican en este escenario. Extendemos este trabajo a las ecuaciones fraccionales discretas con retardo, obteniendo resultados similares en términos de precisión. Adicionalmente, mostramos que la misma arquitectura se puede usar para discriminar entre trayectorias con y sin retardo con gran confianza. Finalmente, también investigamos modelos fraccionales discretos. Hemos analizado esquemas de paso temporal con la cuadratura de Lubich en lugar del clásico esquema de orden 1 de Euler. En el primer estudio de este nuevo paradigma hemos comparado los diagramas de bifurcación de los mapas logístico y del seno, obtenidos de la discretización de Euler de orden 1, 2 y 1/2., [CAT] Durant les darreres dècades l'ús de l'aprenentatge automàtic (machine learning) i de la intel.ligència artificial ha mostrat un creixement exponencial en moltes àrees de la ciència. El fet que els ordinadors hagen augmentat les seues prestacions a la vegada que han reduït el seu preu, junt amb la disponibilitat d'entorns de desenvolupament de codi obert han permès l'accés a la intel.ligència artificial a un gran rang d'investigadors, democratitzant així l'accés a mètodes d'intel.ligència artificial a la comunitat investigadora. És la nostra creença que la multidisciplinaritat és clau per a nous èxits, amb equips compostos d'investigadors amb diferents preparacions i diferents camps d'especialització. Amb aquest ànim, hem orientat aquesta tesi en l'ús d'intel.ligència artificial machine learning, aprenentatge profund o deep learning, entenent totes les anteriors com a part d'un concepte global que concretem en el terme intel.ligència, a intentar donar llum a alguns problemes dels camps de les matemàtiques i la física. Desenvolupem una arquitectura deep learning i la mesurem amb èxit en la caracterització de processos de difusió anòmala. Mentre que prèviament s'havien utilitzat mètodes estadístics clàssics amb aquest objectiu, els mètodes de deep learning han demostrat millorar les prestacions d'aquests mètodes clàssics. La nostra architectura va demostrar que pot inferir amb precisió l'exponent de difusió anòmala i classificar trajectòries entre un conjunt donat de models subjacents de difusió. Mentre que les xarxes neuronals recurrents van irrompre recentment, els models basats en xarxes convolucionals han estat àmpliament testats al camp del processament d'imatge durant més de 15 anys. Hi ha molts models i arquitectures, pre-entrenats i llestos per ser usats per la comunitat. No cal fer recerca ja que aquests models han provat la seva vàlua durant anys i estan ben documentats a la literatura. El nostre objectiu era ser capaços de fer servir aquests models ben coneguts i fiables, amb trajectòries de difusió anòmala. Només necessitàvem convertir una sèrie temporal en una imatge, cosa que vam fer aplicant gramian angular fields a les trajectòries, posant el focus a les trajectòries curtes. Fins on sabem, aquesta és la primera vegada que aquestes tècniques són usades en aquest camp. Mostrem com aquesta aproximació millora les prestacions de qualsevol altra proposta a la classificació del model subjacent de difusió anòmala per a trajectòries curtes. Més enllà de la física hi ha les matemàtiques. Utilitzem la nostra arquitectura basada en xarxes recurrents neuronals per inferir els paràmetres que defineixen les trajectòries de Wu Baleanu. Mostrem que la nostra proposta pot inferir amb raonable precisió els paràmetres mu i nu. Sent la primera vegada, novament fins on arriba el nostre coneixement, que aquestes tècniques s'apliquen en aquest escenari. Estenem aquest treball a les equacions fraccionals discretes amb retard, obtenint resultats similars en termes de precisió. Addicionalment, mostrem que la mateixa arquitectura es pot fer servir per discriminar entre trajectòries amb i sense retard amb gran confiança. Finalment, també investiguem models fraccionals discrets. Hem analitzat esquemes de pas temporal amb la quadratura de Lubich en lloc del clàssic esquema d'ordre 1 d'Euler. Al primer estudi d'aquest nou paradigma hem comparat els diagrames de bifurcació dels mapes logístic i del sinus, obtinguts de la discretització d'Euler d'ordre 1, 2 i 1/2., [EN] During the last decades the use of machine learning and artificial intelligence have showed an exponential growth in many areas of science. The fact that computer's hardware has increased its performance while lowering the price and the availability of open source frameworks have enabled the access to artificial intelligence to a broad range of researchers, hence democratizing the access to artificial intelligence methods to the research community. It is our belief that multi-disciplinarity is the key to new achievements, with teams composed of researchers with different backgrounds and fields of specialization. With this aim, we focused this thesis in using machine learning, artificial intelligence, deep learing, all of them being understood as part of a whole concept we concrete in artificial intelligence, to try to shed light to some problems from the fields of mathematics and physics. A deep learning architecture was developed and successfully benchmarked with the characterization of anomalous diffusion processes. Whereas traditional statistical methods had previously been used with this aim, deep learing methods, mainly based on recurrent neural networks have proved to outperform these clasical methods. Our architecture showed it can precisely infer the anomalous diffusion exponent and accurately classify trajectories among a given set of underlaying diffusion models. While recurrent neural networks irrupted in the recent years, convolutional network based models had been extensively tested in the field of image processing for more than 15 years. There exist many models and architectures, pre-trained and set to be used by the community. No further investigation needs to be done since the architecture have proved their value for years and are very well documented in the literature. Our goal was being able to used this well-known and reliable models with anomalous diffusion trajectories. We only needed to be able to convert a time series into an image, which we successfully did by applying gramian angular fields to the trajectories, focusing on short ones. To our knowledge this is the first time these techniques were used in this field. We show how this approach outperforms any other proposal in the underlaying diffusion model classification for short trajectories. Besides physics it is maths. We used our recurrent neural networks architecture to infer the parameters that define the Wu Baleanu trajectories. We show that our proposal can precisely infer both the mu and nu parameters with a reasonable confidence. Being the first time, to the best of our knowledge, that such techniques were applied to this scenario. We extend this work to the discrete delayed fractional equations, obtaining similar results in terms of precision. Additionally, we showed that the same architecture can be used to discriminate delayed from non-delayed trajectories with a high confidence. Finally, we also searched fractional discrete models. We have considered Lubich's quadrature time-stepping schemes instead of the classical Euler scheme of order 1. As the first study with this new paradigm, we compare the bifurcation diagrams for the logistic and sine maps obtained from Euler discretizations of orders 1, 2, and 1/2., J.A.C. acknowledges support from ALBATROSS project (National Plan for Scientific and Technical Research and Innovation 2017-2020, No. PID2019-104978RB-I00). M.A.G.M. acknowledges funding from the Spanish Ministry of Education and Vocational Training (MEFP) through the Beatriz Galindo program 2018 (BEAGAL18/00203) and Spanish Ministry MINECO (FIDEUA PID2019- 106901GBI00/10.13039/501100011033). We thank M.A. Garc ́ıa-March for helpful comments and discussions on the topic. NF is sup- ported by the National University of Singapore through the Singapore International Graduate Student Award (SINGA) program. OGO and LS acknowledge funding from MINECO project, grant TIN2017-88476-C2-1-R. JAC acknowledges funding from grant PID2021-124618NB-C21 funded by MCIN/AEI/ 10.13039/501100011033 and by “ERDF A way of making Europe”, by the “European Union”. We also thank funding for the open access charges from CRUE-Universitat Politècnica de València.

The fractional Laplacian, ( − △ ) s , s ∈ ( 0 , 1 ) , appears in a wide range of physical systems, including Levy flights, some stochastic interfaces, and theoretical physics in connection to the problem of stability of the matter. In this paper, a matrix transfer technique (MTT) is employed combining with spectral/element method to solve fractional diffusion equations involving the fractional Laplacian. The convergence of the MTT method is analyzed by the abstract operator theory. Our method can be applied to solve various fractional equation involving fractional Laplacian on some complex domains. Numerical results indicate exponential convergence in the spatial discretization which is in good agreement with the theoretical analysis.

M. B. and J. D. acknowledge support by the state of BadenWurttemberg through bwHPCand the German Research Foundation (DFG) through grant no INST 39/963-1 FUGG (bw ForCluster NEMO) and by the Deutsche Forschungsgemeinschaft (DFG) via grant WO 2410/2-1 within the framework of the Research Unit FOR 5099 ``Reducing complexity of nonequilibrium'' (project No. 431945604). P. I. H. and A. M.-J acknowledge the financial support provided by the Spanish Ministry and Agencia Estatal de Investigacio ' n (AEI) through Grants PID2020-113681GB-I00 and FIS2017-84256-P, the Junta de Andaluci ' a and European Regional Development Fund Consejeri ' a de Conocimiento, Investigacion y Universidad, Junta de Andaluci ' a (Projects PY20-00241, A-FQM-90-UGR20, A-FQM175-UGR18 and SOMM17/6105/UGR), and the program Visiting Scholars of the University of Granada (Project PPVS2018-08). Finally, we thank Nils Goth for inspiring discussions and useful comments, and the computational resources and assistance provided by PROTEUS, the supercomputing center of Institute Carlos I for Theoretical and Computational Physics at the University of Granada, Spain., We employ Reactive Dynamical Density Functional Theory (R-DDFT) and Reactive Brownian Dynamics (R-BD) simulations to investigate the dynamics of a suspension of active soft Gaussian colloids with binary interaction switching, i.e., a one-component colloidal system in which every particle stochastically switches at predefined rates between two interaction states with different mobility. Using R-DDFT we extend a theory previously developed to access the dynamics of inhomogeneous liquids [Archer et al., Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2007, 75, 040501] to study the influence of the switching activity on the self and distinct part of the Van Hove function in bulk solution, and determine the corresponding mean squared displacement of the switching particles. Our results demonstrate that, even though the average diffusion coefficient is not affected by the switching activity, it significantly modifies the non-equilibrium dynamics and diffusion coefficients of the individual particles, leading to a crossover from short to long times, with a regime for intermediate times showing anomalous diffusion. In addition, the self-part of the van Hove function has a Gaussian form at short and long times, but becomes non-Gaussian at intermediates ones, having a crossover between short and large displacements. The corresponding self-intermediate scattering function shows the two-step relaxation patters typically observed in soft materials with heterogeneous dynamics such as glasses and gels. We also introduce a phenomenological Continuous Time Random Walk (CTRW) theory to understand the heterogeneous diffusion of this system. R-DDFT results are in excellent agreement with R-BD simulations and the analytical predictions of CTRW theory, thus confirming that R-DDFT constitutes a powerful method to investigate not only the structure and phase behavior, but also the dynamical properties of non-equilibrium active switching colloidal suspensions., BadenWurttemberg through bwHPC, German Research Foundation (DFG) INST 39/963-1 FUGG WO 2410/2-1 FOR 5099 431945604, Spanish Ministry and Agencia Estatal de Investigacion (AEI) PID2020-113681GB-I00 FIS2017-84256-P, Junta de Andalucia, European Regional Development Fund Consejeria de Conocimiento, Investigacion y Universidad, Junta de Andalucia PY20-00241 A-FQM-90-UGR20 A-FQM175-UGR18 SOMM17/6105/UGR, University of Granada PPVS2018-08

We study a one-dimensional sluggish random walk with space-dependent transition probabilities between nearest-neighbour lattice sites. Motivated by trap models of slow dynamics, we consider a model in which the trap depth increases logarithmically with distance from the origin. This leads to a random walk which has symmetric transition probabilities that decrease with distance $|k|$ from the origin as $1/|k|$ for large $|k|$. We show that the typical position after time $t$ scales as $t^{1/3}$ with a nontrivial scaling function for the position distribution which has a trough (a cusp singularity) at the origin. Therefore an effective central bias away from the origin emerges even though the transition probabilities are symmetric. We also compute the survival probability of the walker in the presence of a sink at the origin and show that it decays as $t^{-1/3}$ at late times. Furthermore we compute the distribution of the maximum position, $M(t)$, to the right of the origin up to time $t$, and show that it has a nontrivial scaling function. Finally we provide a generalisation of this model where the transition probabilities decay as $1/|k|^\alpha$ with $\alpha >0$., Comment: 17 pages, revised version accepted for J. Stat. Mech

Data Availability: The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request. Copyright © The Author(s) 2023. A recurrent neural network is developed for segmenting between anomalous and normal diffusion in single-particle trajectories. Accurate segmentation infers a distinct change point that is used to approximate an Einstein linear regime in the mean-squared displacement curve via the transition density function, a unique physical descriptor for short-lived and delayed transiency. Through several artificial and simulated scenarios, we demonstrate the compelling accuracy of our model for dissecting linear and nonlinear behaviour. The inherent practicality of our model lies in its ability to substantiate the self-diffusion coefficient through offline trajectory segmentation, which is opposed to the common ‘best-guess’ linear fitting standard. Additionally, we show that the transition density function has fundamental implications and correspondence to underlying mechanisms that influence transition. In particular, we show that the known proportionality between salt concentration and diffusion of water also influences delayed anomalous behaviour. Engineering and Physical Sciences Research Council (EPSRC; Grant number EP/T033940/1); Royal Society (Grant number IES\R3\193152).

A comb structure consists of a one-dimensional backbone with lateral branches. These structures have widespread application in medicine and biology. Such a structure promotes an anomalous diffusion process along the backbone (x-direction), along with classical diffusion along the branches (y-direction). In this work, we propose a distributed-order time- and space-fractional diffusion-wave equation to model a comb structure in the more general setting. The distributed-order time- and space-fractional diffusion-wave equation is firstly formulated to study the anomalous diffusion in the comb model subject to an irregular convex domain with the motivation that the time-fractional derivative considers the memory characteristic and the space one with the variable diffusion coefficient possesses the nonlocal characteristic. The finite element method is applied to obtain the numerical solution. The stability and convergence of the numerical discretization scheme are derived and analyzed. Two numerical examples of relevance to the comb model are given to verify the correctness of the numerical method. Moreover, the influence of the involved parameters on the three-dimensional and axial projection drawing particle distribution subject to an elliptical domain are analyzed, and the physical meanings are interpreted in detail.

[ES] El análisis deportivo es un campo el cual ha ido creciendo mucho estos últimos años. De la mano del Big Data se han empezado a hacer muchos más estudio y con más posibilidades. En el mundo del fútbol la Ciencia de Datos junto con el machine learning ha cambiado por completo muchos de los análisis que existían y se han creado otros nuevos. En este proyecto hemos seguido la metodología CRISP-DM [1] utilizando principalmente python como lenguaje de programación. Se ha hecho uso de diversas librerías como pueden ser pandas, matplotlyb,fbm,sklearn, entre otras. El proyecto se divide en dos análisis, el principal y más innovador, en el cual hacemos uso de la difusión anómala para obtener información de las distintas trayectorias del balón durante un partido. El análisis secundario se basa en observar los distintos estilos de juego de las selecciones mediante grafos y teoría de redes, en este caso, redes de pases. En cuanto a la parte de difusión anómala se han utilizado modelos de redes neuronales convolucionales que han sido elegidos tras realizar varias pruebas y descartar los peores modelos., [EN] Sports analysis is a field which has been growing a lot in recent years. With the help of Big Data, many more studies have begun to be carried out and with more possibilities. In the world of football, Data Science together with machine learning has completely changed many of the existing analyses and new ones have been created. In this project we have followed the methodology CRISP-DM [1] using mainly python as programming language. We have made use of several libraries such as pandas, matplotlyb,fbm,sklearn, among others. The project is divided into two analyses, the main and most innovative, in which we make use of anomalous diffusion to obtain information on the different trajectories of the ball during a match. The secondary analysis is based on observing the different styles of play of the teams using graphs and network theory, in this case, passing networks. As for the anomalous diffusion part, convolutional neural network models have been used, which have been chosen after carrying out several tests and discarding the worst ones., [CA] L’anàlisi esportiu és un camp el qual ha anat creixent molt estos últims anys. De la mà del Big Data s’han començat a fer molts més estudis i amb més possibilitats. En el món del futbol la Ciència de Dades junt amb el machine learning ha canviat per complet molts dels anàlisis que existien i s’han creat uns altres de nous. En este projecte hem seguit la metodologia CRISP-DM [1] utilitzant principalment python com a llenguatge de programació. S’ha fet ús de diverses llibreries com poden ser pandas, matplotlyb,fbm,sklearn, entre altres. El projecte es dividix en dos anàlisis, el principal i més innovador, en el qual fem ús de la difusió anòmala per a obtindre informació de les distintes trajectòries del baló durant un partit. L’anàlisi secundària es basa a observar els distints estils de joc de les seleccions per mitjà de grafos i teoria de xarxes, en este cas, xarxes de passes. En quant a la part de difusió anòmala s’han utilitzat models de xarxes neuronals convolucionals que han sigut triats després de realitzar diverses proves i descartar els pitjors models.

Molecular transport through a composite multilayer membrane is a central process in transdermal drug delivery (TDD). Classical Fickean approach treats skin as a pseudo-homogenous membrane, while in reality skin is highly heterogeneous system as shown in basic physiological research. Particle transport across such systems shows anomalous diffusive behavior that is described by fractional models. These models don't consider experimentally observed dependence of particle transport nature on time scale. The possible way of inclusion of that observation in model of transdermal transport is presented in this paper. The generalized fractional models of the spectral functions of the concentration profile and the cumulative amount of the drug absorbed through the bloodstream are derived. The derived model predicts resonances in concentration profile and larger cumulative amount of the drug in both the short-time limit and the long-time limit, which can have significant physiological implications. © 2023 The Authors

International audience; This paper is concerned with a new type of inverse obstacle problem governed by a variable-order time-fraction diffusion equation in a bounded domain. The unknown obstacle is a region where the space dependent variable-order of fractional time derivative of the governing equation deviates from a known homogeneous background one. The observation data is given by the Neumann data of the solution of the governing equation for a specially designed Dirichlet data. Under a suitable jump condition on the deviation, it is shown that the most recent version of the time domain enclosure method enables one to extract information about the geometry of the obstacle and a qualitative nature of the jump, from the observation data.

In this paper, we consider the initial-boundary value problem of determining the stationary right-hand side function in the anomalous diffusion equation with a Caputo fractional derivative with res...

Fractional advection-diffusion equation, as a generalization of classical advection-diffusion equation, has been always mentioned to simulate anomalous diffusion in porous media. This work introduces a meshless generalized finite difference method (GFDM) to solve a class of three-dimensional variable-order time fractional advection-diffusion equation (TFADE) in finite domains. Three examples with known analytic solutions in different domains are given to demonstrate that the method is accurate and stable. To reduce computational and storage cost, we discretize the time derivative terms of TFADE by a fast finite difference method (FFDM) based on sum-of-exponentials (SOE) approximation. Meanwhile, discretizing space derivative terms, GFDM generates a linear equation set including function values of neighboring nodes with various weight coefficients. Then the partial derivatives of TFADE are indicated as the linear system above. Also, this paper investigates the irregular mesh in the finite spatial domain, which is more closely meets the description of practice problems. Numerical results indicate that models with irregular mesh can also be simulated by GFDM which maintains high accuracy. Furthermore, the method is stable and accurate in solving three-dimensional irregular domain problems, where the relative errors can be less than 0.01%. This paper shows that FFDM based on SOE approximation can improve computational efficiency, and GFDM can flexibly and efficiently solve three-dimensional variable-order and variable-coefficient TFADE.

Hydration and crosslinking in hydrophilic ionic polymers give rise to microstructural features that affect the diffusion of water and proton conductivity. In this work, we show that the local heterogeneities arising from domains that are more cross-linked and regions that are less cross-linked result in differential swelling behavior during diffusion of water and differential stresses during oscillatory deformation. Distinct signatures in the water uptake kinetics and the dynamic mechanical behavior are shown to be due to these heterogeneities, which are prominent at high and intermediate water contents and are unnoticeable or absent at low water contents. Using polyvinyl alcohol (PVA) cross-linked with sulfosuccinic acid (SSA) as a sample system, we show that differential swelling can lead to anomalous diffusion. In addition, the deformation of these polymers, carried out through large amplitude oscillatory shear experiments, results in strain hardening behavior due to the increased viscous dissipation arising from the differential movements of the polymer network due to the local heterogeneities. The proton conductivity of these materials is affected not only by these heterogeneities but also by the water distribution among the two types of hydrophilic groups (–SO3H and –OH) present in the system. Overall, we demonstrate the important role of crosslink heterogeneities and competitive hydration on the transport and deformation behavior of cross-linked hydrophilic ionic polymer systems. Hydration and crosslinking in hydrophilic ionic polymers give rise to microstructural features which affect diffusion of water and proton conductivity in them. Crosslinking in these systems gives rise to the presence of crosslink heterogeneities resulting in more-crosslinked domains and less-crosslinked regions. Because of the difference in elasticity between the two regions the polymer matrix swells differentially resulting in anomalous water sorption kinetics. The diffused water is distributed among hydroxyl and sulfonic groups and the crosslinking alters this distribution resulting in an increase in conductivity.

The application of fractional calculus in the field of kinetic theory begins with questions raised by Bernoulli, Clausius, and Maxwell about the motion of molecules in gases and liquids. Causality, locality, and determinism underly the early work, which led to the development of statistical mechanics by Boltzmann, Gibbs, Enskog, and Chapman. However, memory and nonlocality influence the future course of molecular interactions (e.g., persistence of velocity and inelastic collisions); hence, modifications to the thermodynamic equations of state, the non-equilibrium transport equations, and the dynamics of phase transitions are needed to explain experimental measurements. In these situations, the inclusion of space- and time-fractional derivatives within the context of the continuous time random walk (CTRW) model of diffusion encodes particle jumps and trapping. Thus, we anticipate using fractional calculus to extend the classical equations of diffusion. The solutions obtained illuminate the structure and dynamics of the materials (gases and liquids) at the molecular, mesoscopic, and macroscopic time/length scales. The development of these models requires building connections between kinetic theory, physical chemistry, and applied mathematics. In this paper, we focus on the kinetic theory of gases and liquids, with particular emphasis on descriptions of phase transitions, inter-phase mixing, and the transport of mass, momentum, and energy. As an example, we combine the pressure–temperature phase diagrams of simple molecules with the corresponding anomalous diffusion phase diagram of fractional calculus. The overlap suggests links between sub- and super-diffusion and molecular motion in the liquid and the vapor phases.

Numerical modeling is an important tool when studying various natural processes and phenomena. Fractional diffusion can be used for modeling many processes in biology, for example in silico experiments in molecular biology and medicine design, protein diffusion within cells, complex media geometry, etc. The problem is usually reduced to a system of linear algebraic equations and in many cases this system has a dense coefficient matrix. Numerically solving such problems with the traditional LU factorization is a computationally expensive endeavour - $O(n^3)$. In this paper we explore the use of a hierarchical compression method based on Hierarchical Semi-Separable compression and ULV-like factorization from the STRUctured Matrices PACKage (STRUMPACK) software library for a flow around airfoils problem discretized with Boundary Element Method and fractional diffusion problem discretized with the Finite Element Method. The HSS based method promises better overall computational complexity of $O(r^2n)$ for problems with suitable structure - low rank off-diagonal blocks. Here $r$ is the maximum rank of the off-diagonal blocks. We present analysis of the performance and accuracy of the HSS based method and compare it with the state of the art direct LU factorization solvers. This paper is based on the PhD thesis Composite Numerical Methods and Scalable Tile Algorithms of the author defended on 17.05.2022 in the Institute of Information and Communication Technologies at the Bulgarian Academy of Sciences.

Peripheral membrane proteins bind transiently to membrane surfaces as part of many signaling pathways. The bound proteins perform two-dimensional (2-D) diffusion on the membrane surface during the recruitment function. To better understand the interplay between the 2-D diffusion of these protein domains and their membrane binding modes, we performed multimicrosecond all-atom molecular dynamics simulations of two regulatory domains, a C2 domain and a pleckstrin homology (PH) domain, in their experimentally determined bound configuration to a lipid bilayer. The protein bound configurations are preserved throughout the simulation trajectories. Both protein domains exhibit anomalous diffusion with distinct features in their dynamics that reflect their different modes of binding. An analysis of their diffusive behavior reveals common features with the diffusion of lipid molecules in lipid bilayers, suggesting that the 2-D motion of protein domains bound to the membrane surface is modulated by the viscoelastic nature of the lipid bilayer.

Anomalous diffusion behavior can be observed in many single-particle (contained in crowded environments) tracking experimental data. Numerous models can be used to describe such data. In this paper, we focus on two common processes: fractional Brownian motion (fBm) and scaled Brownian motion (sBm). We proposed novel methods for sBm anomalous diffusion parameter estimation based on the autocovariance function (ACVF). Such a function, for centered Gaussian processes, allows its unique identification. The first estimation method is based solely on theoretical calculations, and the other one additionally utilizes neural networks (NN) to achieve a more robust and well-performing estimator. Both fBm and sBm methods were compared between the theoretical estimators and the ones utilizing artificial NN. For the NN-based approaches, we used such architectures as multilayer perceptron (MLP) and long short-term memory (LSTM). Furthermore, the analysis of the additive noise influence on the estimators’ quality was conducted for NN models with and without the regularization method.

This paper presents an unified mathematical and computational framework for mechanics-coupled “anomalous” transport phenomena in porous media. The anomalous diffusion is mainly due to variable fluid flow rates caused by spatially and temporally varying permeability. This type of behaviour is described by a fractional pore pressure diffusion equation. The diffusion transient phenomena is significantly affected by the order of the fractional operators. In order to solve 3D consolidation problems of large scale structures, the fractional pore pressure diffusion equation is implemented in a finite element framework adopting the discretised formulation of fractional derivatives given by Grunwald–Letnikov (GL). Here the fractional pore pressure diffusion equation is implemented in the commercial software Abaqus through an open-source UMATHT subroutine. The similarity between pore pressure, heat and hydrogen transport is also discussed in order to show that it is possible to use the coupled thermal-stress analysis to solve fractional consolidation problems.

The theory of magnetic-source electromagnetic anomalous diffusion is developed in this article. As the geological medium is spatially rough, the late-time tail phenomenon can be explained as a multiscale electromagnetic anomalous diffusion, which is a union of fractional subdiffusion and regular diffusion. The roughness parameter $\beta $ and weighting parameter $W$ are introduced into the generalized electrical conductivity to indicate the roughness level and ratio. The characteristics and superiority of the improved generalized electrical conductivity are analyzed in the time domain. A 3-D modeling method is proposed based on the fractional finite-difference time-domain method. The introduced Caputo fractional derivative in the time domain is calculated by the Alikhanov superconvergent approximation method, so that the stability of the solution is improved. Several half-space models are designed to verify the 3-D modeling efficiency. It turns out that the improved generalized electrical conductivity can model the electromagnetic late-time tail efficiently, which is characterized by responses that coincide with the classical attenuation law at earlier times and the departure at later times. Moreover, this approach is also applied to anomalous models with 3-D bodies; the results indicate that the proposed method can recognize 3-D anomalous bodies efficiently. The improved method can model the complex electromagnetic propagation in the rough geologic medium more accurately, providing a theoretical basis for multiscale and refined detection.

Anomalous diffusion is a widespread physical phenomenon, and numerical methods of fractional diffusion models are of important scientific significance and engineering application value. For time fractional diffusion-wave equation with damping, a difference (ASC-N, alternating segment Crank-Nicolson) scheme with intrinsic parallelism is proposed. Based on alternating technology, the ASC-N scheme is constructed with four kinds of Saul’yev asymmetric schemes and Crank-Nicolson (C-N) scheme. The unconditional stability and convergence are rigorously analyzed. The theoretical analysis and numerical experiments show that the ASC-N scheme is effective for solving time fractional diffusion-wave equation.

By collecting from literature data experimental evidence of anomalous diffusion of passive tracers inside cytoplasm, and in particular of subdiffusion of mRNA molecules inside live Escherichia coli cells, we obtain the probability density function of molecules’ displacement and we derive the corresponding Fokker–Planck equation. Molecules’ distribution emerges to be related to the Krätzel function and its Fokker–Planck equation to be a fractional diffusion equation in the Erdélyi–Kober sense. The irreducibility of the derived Fokker–Planck equation to those of other literature models is also discussed., BERC 2018–2021 BERC 2022–2025

Gas drainage in deep coal seam is a critical issue ensuring the safety of mining and an important measure to obtain gas as a kind of clean available energy. In order to get a better understanding of gas flow and diffusion for gas drainage in deep coal seams, a dual-zone gas flow model, including the drainage damage zone (DDZ) and the non-damaged zone (NDZ), are characterized by different permeability models and anomalous diffusion models to analyze the influence of damage induced by drilling boreholes on gas flow. The permeability model and anomalous diffusion model are verified with experiment and field data. A series of finite-element numerical simulations based on developed models are carried out, indicating that, compared with normal diffusion model, the anomalous diffusion is more accurate and appropriate to field test data. The coal fracture permeability increases rapidly with the distance decreasing from the borehole, and the area of DDZ is increasing significantly with the extraction time. Moreover, with the increasing of fractional derivative order, the diffusion model transforms the anomalous diffusion to the normal gradually, and the decay of gas pressure is aggravated. The higher value of non-uniform coefficient results in the larger increment of fracture permeability. The permeability–damage coefficient increase makes the increment of fracture permeability bigger.

The unexpectable variations of the diagnosed disease symptoms are quite often observed during medical diagnosis. In stochastics, such behavior is called “grey swan” or “black swan” as synonyms of sudden, unpredictable change. Evolution of the disease’s symptoms is usually described by means of Markov processes, where dependency on process history is neglected. The common expectation is that such processes are Gaussian. It is demonstrated here that medical observation can be described as a Markov process and is non-Gaussian. Presented non-Gaussian processes have “fat tail” probability density distribution (pdf). “Fat tail” permits a slight change of probability density distribution and triggers an unexpectable big variation of the diagnosed parameter. Such “fat tail” solution is delivered by the anomalous diffusion model applied here to describe disease evolution and to explain the possible presence of “swans” mentioned above. The proposed model has been obtained as solution of the Fractal Fokker–Planck equation (FFPE). The paper shows a comparison of the results of the theoretical model of anomalous diffusion with experimental results of clinical studies using bioimpedance measurements in cardiology. This allows us to consider the practical usefulness of the proposed solutions.

We consider the two-dimensional (2D) noisy Kuramoto model of synchronization with short-range coupling and a Gaussian distribution of intrinsic frequencies, and investigate its ordering dynamics following a quench. We consider both underdamped (inertial) and over-damped dynamics, and show that the long-term properties of this intrinsically out-of-equilibrium system do not depend on the inertia of individual oscillators. The model does not exhibit any phase transition as its correlation length remains finite, scaling as the inverse of the standard deviation of the distribution of intrinsic frequencies. The quench dynamics proceeds via domain growth, with a characteristic length that initially follows the growth law of the 2D XY model, although is not given by the mean separation between defects. Topological defects are generically free, breaking the Berezinskii-Kosterlitz-Thouless scenario of the 2D XY model. Vortices perform a random walk reminiscent of the self-avoiding random walk, advected by the dynamic network of boundaries between synchronised domains; featuring long-time super-diffusion, with the anomalous exponent $\alpha=3/2$., Comment: 13 pages, 13 figures

We investigate the solutions of a two-dimensional Schrödinger equation in the presence of geometric constraints, represented by a backbone structure with branches, by taking a position-dependent effective mass for each direction into account. We use Green’s function approach to obtain the solutions, which are given in terms of stretched exponential functions. The results can be linked to the properties of the system and show anomalous spreading for the wave packet. We also analyze the interplay between the backbone structure with branches constraining the different directions and the effective mass. In particular, we show how a fractional Schrödinger equation emerges from this scenario.

The fractional differential equation has been used to describe many phenomenons in almost all applied sciences, such as fluid flow in porous materials, anomalous diffusion transport, acoustic wave propagation in viscoelastic materials, and others. In some cases, it is complicated to find the analytical solution of a fractional differential equation, so there are some special techniques to approximate the solution. In this paper, a new collocation method for a class of semilinear fractional differential equations has been constructed. The convergence properties of the proposed methods and the computational complexity are treated. Some numerical experiments are presented to validate the theoretical results. The proposed numerical method provides an alternative way to study some physical phenomena by fractional differential equations.

Quantifying ecological memory could be done at several levels from the rate of physiological changes in an ecosystem all the way down to responses at the genetic level. One way of unlocking the information encoded in a collective environmental memory is to examine the recorded time-series data generated by different components of an ecosystem. In this paper, we probe into the case of the Great Barrier Reef (GBR) which is threatened by elevated sea surface temperatures (SST) and ocean acidification attributed to rising atmospheric CO2 levels. Specifically, we investigate the interrelated dynamics between the degradation of the GBR, SST, and rising atmospheric CO2 levels, by considering three datasets: (a) the mean percentage hard coral cover of the GBR from the archives of the Australian Institute of Marine Science; (b) SST close to the GBR from the National Oceanic and Atmospheric Administration; and (c) the Keeling curve for atmospheric CO2 levels measured by the Mauna Loa Observatory. We show that fluctuating observables in these datasets have the same memory behavior described by a non-Markovian stochastic process. All three datasets show a good match between empirical and analytical mean square deviation. An explicit analytical form for the corresponding probability density function is obtained which obeys a modified diffusion equation with a time dependent diffusion coefficient. This study provides a new perspective on the similarities of and interaction between the GBR’s declining hard coral cover, SST, and rising atmospheric CO2 levels by putting all three systems into one unified framework indexed by a memory parameter $$\mu $$ and a characteristic frequency $$\nu $$ . The short-time dynamics of CO2 levels and SST fall in the superdiffusive regime, while the GBR exhibits hyperballistic fluctuation in percent coral cover with the highest values for $$\mu $$ and $$\nu $$ .

In this work, we investigate the presence of sub-diffusive behavior in the Chirikov-Taylor Standard Map. We show that the stickiness phenomena, present in the mixed phase space of the map setup, can be characterized as a Continuous Time Random Walk model and connected to the theoretical background for anomalous diffusion. Additionally, we choose a variant of the Ulam method to numerically approximate the Perron-Frobenius operator for the map, allowing us to calculate the anomalous diffusion exponent via an eigenvalue problem, compared to the solution of the Fractional Diffusion Equation. The results here corroborate other findings in the literature of anomalous transport in Hamiltonian maps and can be suitable to describe transport properties of other dynamical systems., Submitted to EPJ-ST

In this contribution, we investigate an initial-boundary value problem for a fractional diffusion equation with Caputo fractional derivative of space-dependent variable order where the coefficients are dependent on spatial and time variables. We consider a bounded Lipschitz domain and a homogeneous Dirichlet boundary condition. Variable-order fractional differential operators originate in anomalous diffusion modelling. Using the strongly positive definiteness of the governing kernel, we establish the existence of a unique weak solution in $u\in \operatorname{L}^{\infty } ((0,T),\operatorname{H}^{1}_{0}( \Omega ) )$ u ∈ L ∞ ( ( 0 , T ) , H 0 1 ( Ω ) ) to the problem if the initial data belongs to $\operatorname{H}^{1}_{0}(\Omega )$ H 0 1 ( Ω ) . We show that the solution belongs to $\operatorname{C} ([0,T],{\operatorname{H}^{1}_{0}(\Omega )}^{*} )$ C ( [ 0 , T ] , H 0 1 ( Ω ) ∗ ) in the case of a Caputo fractional derivative of constant order. We generalise a fundamental identity for integro-differential operators of the form $\frac{\mathrm{d}}{\mathrm{d}t} (k\ast v)(t)$ d d t ( k ∗ v ) ( t ) to a convolution kernel that is also space-dependent and employ this result when searching for more regular solutions. We also discuss the situation that the domain consists of separated subdomains.

Compartmental model is the classic and widely used approach in pharmacokinetics. Recently, fractional calculus is introduced to describe the time course of drugs in human body which follow the anomalous diffusion mechanism. To consider the different fractional order transmission process, the two compartmental fractional model has been proposed and studied. And, it will be of great significance to find out a simple and efficient numerical method to solve the model and estimate model parameters. This work investigates two numerical methods of the two compartmental fractional model using finite difference schemes, which are based on the shifted Grunwald-Letnikov approximate formula and L1 formula, respectively. The hybrid Nelder-Mead simplex search and particle swarm optimization, denoted as NMSS-PSO, is provided to estimate the fractional model parameters. Comparison between the numerical solution and the solution by the numerical inverse Laplace transform method establishes the validity of the developed numerical algorithms. Then, the influence of the order of fractional derivative on the drug amount in human body is also discussed. Finally, the two compartmental fractional model is applied to fit the amiodarone pharmacokinetics data based on the NMSS-PSO algorithms. This work will be of importance for the development of fractional pharmacokinetics.

We establish the existence in the sense of sequences of solutions for certain integro-differential type equations in two dimensions involving the normal diffusion in one direction and the anomalous diffusion in the other direction in H 2 ( R 2 ) via the fixed point technique. The elliptic equation contains a second order differential operator without the Fredholm property. It is proved that, under the reasonable technical conditions, the convergence in L 1 ( R 2 ) of the integral kernels implies the existence and convergence in H 2 ( R 2 ) of the solutions.

This study is devoted to the construction and software implementation of a computational algorithm for modeling the process of anomalous diffusion. The mathematical model is formulated as an initial-boundary value problem for a semilinear partial differential equation of fractional order. An implicit finite-difference scheme is constructed based on the approximation of a higher order of accuracy for the Caputo derivative. An application program for computer modeling of the anomalous diffusion process is developed. Using a test problem, a numerical study of the accuracy of approximate solutions is carried out. The results of the computational experiments are presented on the example of modeling a fractional semilinear dynamic system of the reaction-diffusion type.

This paper is devoted to study an anomalous diffusion model of Kirchhoff type driven by a nonlocal integro-differential operator. The properties of solutions, such as vacuum isolating phenomena, global existence, extinction, exponentially decay, exponentially growth, and finite time blow-up were studied by potential well method and energy estimate method. The results of this paper extend and complete the recent studies on this model.

In a porous fractal medium, the transport dynamics is sometimes anomalous as well as the crossover between numerous transport regimes occurs. In this paper, we experimentally investigate the mass transfer of the diffusing agents of various classes in the composite porous particle with fractal geometry. It is shown that transport mechanisms differ at short and long times. At the beginning, pure advection is observed, whereas the longtime transport follows a convective mechanism. Moreover, the longtime transport experiences either Fickian or non-Fickian kinetics depending on the diffusing agent. The non-Fickian transport is justified for the diffusing agent with higher adsorption energy. Therefore, we speculate that non-Fickian transport arises due to the strong irreversible adsorption sticking of the diffusing molecules on the surface of the porous particle. For the distinguishing of the transport regimes, an approach admitting the transformations of the experimental data and the relevant analytic solutions in either semi-logarithmic or logarithmic coordinates is developed. The time-fractional advection–diffusion equation is used on a phenomenological basis to describe the experimental data exhibiting non-Fickian kinetics. The obtained anomalous diffusion exponent corresponds to the superdiffusive transport.

This work is devoted to examine the uniqueness and existence of kinetic solutions for a class of scalar conservation laws involving a nonlocal super-critical diffusion operator and a multiplicative noise. Our proof for uniqueness is based upon the analysis on double variables method and the existence is enabled by a parabolic approximation., arXiv admin note: substantial text overlap with arXiv:1001.5415, arXiv:1611.00984 by other authors

We consider a class of discrete-time random walks with directed unit steps on the integer line. The direction of the steps is reversed at the time instants of events in a discrete-time renewal process and is maintained at uneventful time instants. This model represents a discrete-time semi-Markovian generalization of the telegraph process. We derive exact formulae for the propagator using generating functions. We prove that for geometrically distributed waiting times in the diffusive limit, this walk converges to the classical telegraph process. We consider the large-time asymptotics of the expected position: For waiting time densities with finite mean the walker remains in the average localized close to the departure site whereas escapes for fat-tailed waiting-time densities (i.e. densities with infinite mean) by a sublinear power-law. We explore anomalous diffusion features by accounting for the `aging effect' as a hallmark of non-Markovianity where the discrete-time version of the `aging renewal process' comes into play. By deriving pertinent distributions of this process we obtain explicit formulae for the variance when the waiting-times are Sibuya-distributed. In this case and generally for fat-tailed waiting time PDFs a $t^2$-ballistic superdiffusive scaling emerges in the large time limit. In contrast if the waiting time PDF between the step reversals is light-tailed (`narrow' with finite mean and variance) the walk exhibits normal diffusion and for `broad' waiting time PDFs (with finite mean and infinite variance) superdiffusive large time scaling. We also consider time-changed versions where the walk is subordinated to a continuous-time point process such as the time-fractional Poisson process. This defines a new class of biased continuous-time random walks exhibiting several regimes of anomalous diffusion.

Salted chickpea (Cicer arietinum L.) is increasingly used in snack production and in home cooking by soaking in brines. Order to achieve better quality and higher nutrient content, it is important to model and understand the mass transfer processes during this operation. In this work, brine salting of chickpea was studied at 1, 5 and 20% salt concentrations, at temperatures of 25, 50, 75 and 100 °C. Water uptake, salt uptake and non-ash solids loss over time were modeled using the Peleg, Fickian diffusion and anomalous diffusion models. Salt content of brines significantly affects the changes occurring during chickpea soaking. At 1% salt content, the volume gain is larger than when soaking in water, while at 5 and 20% swelling decreases, with a lower solids’ loss. The fit of each model to experimental data was assessed using the Coefficient of Determination, the Root Mean Square Error, the Akaike Information Criterion, and the errors of the fitted parameters of each model. The results show that the Fick model is at least as good as the Peleg model in predicting the mass transfer of each considered component, but the influence of the equilibrium parameter is more clear on the Peleg model, resulting in better forecasts of the kinetic parameter. The anomalous diffusion model was not adequate to fit neither the water, the salt nor the solids loss, resulting in large errors in both the diffusion coefficient and the equilibrium parameter.

Fractional telegraph equation is introduced to promote a sub-diffusive transport model of the neutrons inside a nuclear reactor. Here, the time derivatives of the classical telegraph equation have been replaced by the Caputo fractional derivative. In this paper, the fractional solutions are obtained through a technique that relies heavily on Fourier and Laplace transformations and is given in terms of the M-Wright function. The neutron flux density is clarified for different values of the time-fractional order.

In the course of various biological processes, specific DNA-binding proteins must efficiently find a particular target sequence/protein or a damaged site on the DNA. DNA-binding proteins perform this task based on diffusion. Nevertheless, investigations over recent decades have found that the diffusion dynamics of DNA-binding proteins are generally complicated and, further, protein specific. In this review, we collect experimental and theoretical studies that quantify the diffusion dynamics of DNA-binding proteins and review them from the viewpoint of diffusion processes.

Using diffraction-limited ultrafast imaging techniques, we investigate the propagation of singlet and triplet excitons in single-crystal tetracene. Instead of an expected broadening, the distribution of singlet excitons narrows on a nanosecond time scale after photoexcitation. This narrowing results in an effective negative diffusion in which singlet excitons migrate toward the high-density region, eventually leading to a singlet exciton distribution that is smaller than the laser excitation spot. Modeling the excited-state dynamics demonstrates that the origin of the anomalous diffusion is rooted in nonlinear triplet–triplet annihilation (TTA). We anticipate that this is a general phenomenon that can be used to study exciton diffusion and nonlinear TTA rates in semiconductors relevant for organic optoelectronics.

Recent experiments on self-diffusion in associative networks have shown superdiffusive scaling hypothesized to originate from molecular diffusive mechanisms, which include walking and hopping of th...

Mixed fluids confined in porous solid hosts present challenges for the accurate characterization of individual-component behavior. NMR diffusometry with chemical resolution is used to identify unexpected loading- and composition-dependent anomalous diffusion in water/cyclohexane mixtures confined to solid nanoporous glass (NPG) hosts. Diffusion NMR results indicate that data obtained on pure-component liquids in confinement cannot be extrapolated to their nonideal liquid mixtures confined in the same solid host. Loading-dependent data must be obtained on each component in the confined mixture in order to determine which of the liquid components exhibits chemical affinity for the host and, conversely, which of the components exhibits anomalous diffusivity. Most notably, NMR diffusometry revealed that cyclohexane diffusivity varied by 2 orders of magnitude in a water-rich mixture depending on the total fluid loading in the NPG host, ranging from anomalously high diffusivities that significantly exceeded that for pure cyclohexane in NPG at low fluid loadings to kinetically trapped sequestration at high fluid loadings. NMR diffusometry indicates that nonideal solution behavior in fluids confined within nanoporous hosts may have practical implications for enhanced oil recovery methods. Specifically, kinetic trapping of hydrocarbons in water-flooding regimes can result from complex liquid-vapor equilibrium that is significantly perturbed from that which exists in bulk or microporous confinement.

The analytical expression for the Voigt profile, along with its simplified forms for the Gaussian and Lorentzian dominance, is presented. The applicability of the Voigt profile in the description of anomalous diffusion phenomena, ubiquitous in different fields of science including protein folding, is discussed. It is shown that the Voigt profile is a good descriptor of the processes occurring in protein folding and in the native state. The usefulness of the Voigt profile in deriving important information of the diffusive motions in proteins from a quasielastic incoherent neutron scattering experiments is illustrated.

We are witnessing a notable rise in the translational use of information technology and control systems engineering tools in clinical practice. This paper empowers the computer based drug dosing optimization of general anesthesia management by means of multiple variables for patient state stabilization. The patient simulator platform is designed through an interdisciplinary combination of medical, clinical practice and systems engineering expertise gathered in the last decades by our team. The result is an open source patient simulator in Matlab/Simulink from Mathworks(R). Simulator features include complex synergic and antagonistic interaction aspects between general anesthesia and hemodynamic stabilization variables. The anesthetic system includes the hypnosis, analgesia and neuromuscular blockade states, while the hemodynamic system includes the cardiac output and mean arterial pressure. Nociceptor stimulation is also described and acts as a disturbance together with predefined surgery profiles from a translation into signal form of most commonly encountered events in clinical practice. A broad population set of pharmacokinetic and pharmacodynamic (PKPD) variables are available for the user to describe both intra- and inter-patient variability. This simulator has some unique features, such as: i) additional bolus administration from anesthesiologist, ii) variable time-delays introduced by data window averaging when poor signal quality is detected, iii) drug trapping from heterogeneous tissue diffusion in high body mass index patients. We successfully reproduced the clinical expected effects of various drugs interacting among the anesthetic and hemodynamic states. Our work is uniquely defined in current state of the art and first of its kind for this application of dose management problem in anesthesia. This simulator provides the research community with accessible tools to allow a systematic design, evaluation and comparison of various control algorithms for multi-drug dosing optimization objectives in anesthesia.

A kind of anomalous diffusion and heat transfer on a comb structure with anisotropic relaxation are studied, which can be used to model many problems in bio-logic and nature in fractal porous media. The Hausdorff derivative is introduced and new governing equations is formulated in view of fractal dimension. Numerical solutions are obtained and the Fox H-function analytical solutions is given for special cases. The particles spatial-temporal evolution and the mean square displacement vs. time are presented. The effects of backbone and finger relaxation parameters, and the time fractal parameter are discussed. Results show that the mean square displacement decreases with the increase of backbone parameter or the decrease of finger relaxation parameter in a short of time, but they have little effect on mean square displacement in a long period. Particularly, the mean square displacement has time dependence in the form of t?/2 (0 < ? ? 1)when t>?, which indicates that the diffusion is an anomalous sub-diffusion and heat transfer.