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Differential equation

Reimar H Leike, Torsten A Enßlin
Most simulation schemes for partial differential equations (PDEs) focus on minimizing a simple error norm of a discretized version of a field. This paper takes a fundamentally different approach; the discretized field is interpreted as data providing information about a real physical field that is unknown. This information is sought to be conserved by the scheme as the field evolves in time. Such an information theoretic approach to simulation was pursued before by information field dynamics (IFD). In this paper we work out the theory of IFD for nonlinear PDEs in a noiseless Gaussian approximation...
March 2018: Physical Review. E
Romain Modeste Nguimdo
Although the plethora real-life systems modeled by nonlinear systems with two independent time delays, the algebraic expressions for determining the stability of their fixed points remain the Achilles' heel. Typically, the approach for studying the stability of delay systems consists in finding the bifurcation lines separating the stable and unstable parameter regions. This work deals with the parametric construction of algebraic expressions and their use for the determination of the stability boundaries of fixed points in nonlinear systems with two independent time delays...
March 2018: Physical Review. E
M Kiani, A Abdolali, M Safari
In this article, an analytical approach is presented for the analysis of electromagnetic (EM) scattering from radially inhomogeneous spherical structures (RISSs) based on the duality principle. According to the spherical symmetry, similar angular dependencies in all the regions are considered using spherical harmonics. To extract the radial dependency, the system of differential equations of wave propagation toward the inhomogeneity direction is equated with the dual planar ones. A general duality between electromagnetic fields and parameters and scattering parameters of the two structures is introduced...
March 2018: Physical Review. E
Pedro André Arroyo, Sergio Alonso, Rodrigo Weber Dos Santos
Pattern formation has been widely observed in extended chemical and biological processes. Although the biochemical systems are highly heterogeneous, homogenized continuum approaches formed by partial differential equations have been employed frequently. Such approaches are usually justified by the difference of scales between the heterogeneities and the characteristic spatial size of the patterns. Under different conditions, for example, under weak coupling, discrete models are more adequate. However, discrete models may be less manageable, for instance, in terms of numerical implementation and mesh generation, than the associated continuum models...
March 2018: Physical Review. E
P Sprenger, M A Hoefer, G A El
A notion of hydrodynamic optical soliton tunneling is introduced in which a dark soliton is incident upon an evolving, broad potential barrier that arises from an appropriate variation of the input signal. The barriers considered include smooth rarefaction waves and highly oscillatory dispersive shock waves. Both the soliton and the barrier satisfy the same one-dimensional defocusing nonlinear Schrödinger (NLS) equation, which admits a convenient dispersive hydrodynamic interpretation. Under the scale separation assumption of nonlinear wave (Whitham) modulation theory, the highly nontrivial nonlinear interaction between the soliton and the evolving hydrodynamic barrier is described in terms of self-similar, simple wave solutions to an asymptotic reduction of the Whitham-NLS partial differential equations...
March 2018: Physical Review. E
Enrico Gavagnin, Christian A Yates
Persistence of motion is the tendency of an object to maintain motion in a direction for short time scales without necessarily being biased in any direction in the long term. One of the most appropriate mathematical tools to study this behavior is an agent-based velocity-jump process. In the absence of agent-agent interaction, the mean-field continuum limit of the agent-based model (ABM) gives rise to the well known hyperbolic telegraph equation. When agent-agent interaction is included in the ABM, a strictly advective system of partial differential equations (PDEs) can be derived at the population level...
March 2018: Physical Review. E
Sutapa Mukherji
In this paper, we study a one-dimensional totally asymmetric simple exclusion process with position-dependent hopping rates. Under open boundary conditions, this system exhibits boundary-induced phase transitions in the steady state. Similarly to totally asymmetric simple exclusion processes with uniform hopping, the phase diagram consists of low-density, high-density, and maximal-current phases. In various phases, the shape of the average particle density profile across the lattice including its boundary-layer parts changes significantly...
March 2018: Physical Review. E
S I Denisov, T V Lyutyy, V V Reva, A S Yermolenko
We study the temperature dependence of the drift velocity of single-domain ferromagnetic particles induced by the Magnus force in a dilute suspension. A set of stochastic equations describing the translational and rotational dynamics of particles is derived, and the particle drift velocity that depends on components of the average particle magnetization is introduced. The Fokker-Planck equation for the probability density of magnetization orientations is solved analytically in the limit of strong thermal fluctuations for both the planar rotor and general models...
March 2018: Physical Review. E
Hyun-Myung Chun, Xavier Durang, Jae Dong Noh
We investigate the low mass limit of Langevin dynamics for a charged Brownian particle driven by a magnetic Lorentz force. In the low mass limit, velocity variables relaxing quickly are coarse-grained out to yield effective dynamics for position variables. Without the Lorentz force, the low mass limit is equivalent to the high friction limit. Both cases share the same Langevin equation that is obtained by setting the mass to zero. The equivalence breaks down in the presence of the Lorentz force. The low mass limit cannot be achieved by setting the mass to zero...
March 2018: Physical Review. E
Guillaume Dechristé, Jérôme Fehrenbach, Elena Griseti, Valérie Lobjois, Clair Poignard
BACKGROUND: Since several decades, the experiments have highlighted the analogy of fusing cell aggregates with liquid droplets. The physical macroscopic models have been derived under incompressible assumptions. The aim of this paper is to provide a 3D model of growing spheroids, which is more relevant regarding embryo cell aggregates or tumor cell spheroids. METHODS: We extend the past approach to a compressible 3D framework in order to account for the tumor spheroid growth...
May 15, 2018: Journal of Theoretical Biology
Raimund M Kovacevic
In this paper we analyze two stochastic versions of one of the simplest classes of contagion models, namely so-called SIS models. Several formulations of such models, based on stochastic differential equations, have been recently discussed in literature, mainly with a focus on the existence and uniqueness of stationary distributions. With applicability in view, the present paper uses the Fokker-Planck equations related to SIS stochastic differential equations, not only in order to derive basic facts, but also to derive explicit expressions for stationary densities and further characteristics related to the asymptotic behaviour...
2018: Central European Journal of Operations Research
Stephen J Merrill, Balamurugan Pandiyan
Thyroid autoimmunity is characterized by a large number of identified factors, and determining the relative importance of genetics and environment, for instance, can be difficult. In addition, the definition and progression of the individual diseases can also be challenging, and questions such as "when to begin treatment" or even "should treatment be begun" can be problematic. One approach to handling situations in which there are many factors is utilizing mathematical modeling. In a model, quantities that are clinically measurable are related through equations, based on known and inferred relationships between the systems involved...
June 1, 2018: Frontiers in Bioscience (Landmark Edition)
Bhuvaneswari Gurumurthy, Jason A Griggs, Amol V Janorkar
The ability of a tissue-engineered scaffold to regenerate functional tissues depends on its mechanical and biochemical properties. Though the commonly used collagen scaffolds have good biochemical properties, they fail due to their poor mechanical and physical properties. We have reinforced the collagen matrix with elastin-like polypeptide (ELP) to improve the mechanical and physical properties and optimized the composite composition using a novel statistical method of response surface methodology (RSM). RSM used a central composite design to correlate the 2 input factor variables (collagen and ELP concentrations) and 3 output objectives (tensile strength, elastic modulus, and toughness) using a second order polynomial equation...
May 2, 2018: Journal of the Mechanical Behavior of Biomedical Materials
Typhanye V Dyer, Maria R Khan, Rotrease Regan, Nina T Harawa, LaRon E Nelson, Leo Wilton, Lei Wang, Lili Peng, San San Ou, Steve Shoptaw
BACKGROUND: Black men who have sex with men (BMSM); some who also have sex with women (BMSMW), account for over 70% of new HIV infections in the US representing an elevated HIV risk in this group, also informing risks for HIV transmission to other BMSM and female sexual partners. SETTINGS: We examined trajectories of self-reported substance use, HIV-related sexual risk behaviors and psychosocial vulnerabilities among BMSMW versus BMSM over a one-year study period...
May 10, 2018: Journal of Acquired Immune Deficiency Syndromes: JAIDS
R J Seager, Andrew J Acevedo, Fabian Spill, Muhammad H Zaman
The processes of dissolution and fragmentation have high relevance in pharmaceutical research, medicine, digestive physiology, and engineering design. Experimentally, dissolution and fragmentation are observed to occur simultaneously, yet little is known about the relative importance of each of these processes and their impact on the dissolution process as a whole. Thus, in order to better explain these phenomena and the manner in which they interact, we have developed a novel mathematical model of dissolution, based on partial differential equations, taking into consideration the two constituent processes of surface area-dependent diffusive mass removal and physical fragmentation of the solid particles, and the basic physical laws governing these processes...
May 16, 2018: Scientific Reports
D Crevillén-García
Time-consuming numerical simulators for solving groundwater flow and dissolution models of physico-chemical processes in deep aquifers normally require some of the model inputs to be defined in high-dimensional spaces in order to return realistic results. Sometimes, the outputs of interest are spatial fields leading to high-dimensional output spaces. Although Gaussian process emulation has been satisfactorily used for computing faithful and inexpensive approximations of complex simulators, these have been mostly applied to problems defined in low-dimensional input spaces...
April 2018: Royal Society Open Science
Zhiqiang Li, Tingxue Xu, Junyuan Gu, Qi Dong, Linyu Fu
This paper presents a quantitative reliability modelling and analysis method for multi-state elements based on a combination of the Markov process and a dynamic Bayesian network (DBN), taking perfect repair, imperfect repair and condition-based maintenance (CBM) into consideration. The Markov models of elements without repair and under CBM are established, and an absorbing set is introduced to determine the reliability of the repairable element. According to the state-transition relations between the states determined by the Markov process, a DBN model is built...
April 2018: Royal Society Open Science
Daniel S Kosov
We present a theoretical approach to solve the Markovian master equation for quantum transport with stochastic telegraph noise. Considering probabilities as functionals of a random telegraph process, we use Novikov's functional method to convert the stochastic master equation to a set of deterministic differential equations. The equations are then solved in the Laplace space, and the expression for the probability vector averaged over the ensemble of realisations of the stochastic process is obtained. We apply the theory to study the manifestations of telegraph noise in the transport properties of molecular junctions...
May 14, 2018: Journal of Chemical Physics
X-L Wang, J-M Lei, Y Yuan, L Feng, Y Ning, Y-F Liu
OBJECTIVE: Acute heart failure (AHF) is one of the most commonly seen clinical cases, with a high rate of re-hospitalization and mortality. AHF can be divided into two categories based on the systolic function of the left ventricle, which are heart failure with reduced ejection fraction (HFREF) and heart failure with preserved ejection fraction (HFPEF). Pathogenesis and treatment of the two are quite different. In this article we attempted to explore the value of combined use of clinical and laboratory indicators in the differential diagnosis of AHFREF and AHFPEF...
April 2018: European Review for Medical and Pharmacological Sciences
Wenhui Hu, Wenzhu Huang, Zuquan Hu, Zhu Zeng
Dendritic cells (DCs) are the most potent and specialized antigen-presenting cells (APCs) currently known, which play a crucial role in initiating and amplifying both the innate and adaptive immune responses. During the process of immune function, migration ability of DCs and the number of effector T cells which activated by DCs are closely related to the efficiency of immune function. However, because of the complexity of immune system, in the immune response process caused by the skin chronic inflammatory, much is still unknown about the dynamic changes of cell count with time...
October 1, 2017: Sheng Wu Yi Xue Gong Cheng Xue za Zhi, Journal of Biomedical Engineering, Shengwu Yixue Gongchengxue Zazhi
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