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In this chapter, we consider probabilistic drift-diffusion models and Bayesian inference frameworks to address this issue, assisting better social human decision-making. We provide details of the models, as well as representative numerical examples, and discuss the decision-making process with a representative example of the escape route decision-making phenomena by further developing the drift-diffusion models and Bayesian inference frameworks. In the latter context, we also give a review of recent developments in human collective decision-making and its applications with brain network models. Furthermore, we provide illustrative numerical examples to discuss the role of neuromodulation, reinforcement learning in decision-making processes. Finally, we call attention to existing challenges, open problems, and promising approaches in studying social dynamics and collective human decision-making, including those arising from nonequilibrium considerations of the associated processes., Comment: 39 pages,10 pages

Working memory (WM) has been intensively used to enable the temporary storing of information for processing purposes, playing an important role in the execution of various cognitive tasks. Recent studies have shown that information in WM is not only maintained through persistent recurrent activity but also can be stored in activity-silent states such as in short-term synaptic plasticity (STSP). Motivated by important applications of the STSP mechanisms in WM, the main focus of the present work is on the analysis of the effects of random inputs on a leaky integrate-and-fire (LIF) synaptic conductance neuron under STSP. Furthermore, the irregularity of spike trains can carry the information about previous stimulation in a neuron. A LIF conductance neuron with multiple inputs and coefficient of variation (CV) of the inter-spike-interval (ISI) can bring an output decoded neuron. Our numerical results show that an increase in the standard deviations in the random input current and the random refractory period can lead to an increased irregularity of spike trains of the output neuron., Comment: 14 pages, 11 figures. arXiv admin note: substantial text overlap with arXiv:2202.09482

The modelling of human crowd behaviors offers many challenging questions to science in general. Specifically, the social human behavior consists of many physiological and psychological processes which are still largely unknown. To model reliably such human crowd systems with complex social interactions, stochastic tools play an important role for the setting of mathematical formulations of the problems. In this work, using the description based on an exclusion principle, we study a statistical-mechanics-based lattice gas model for active-passive population dynamics with an application to human crowd behaviors. We provide representative numerical examples for the evacuation dynamics of human crowds, where the main focus in our considerations is given to an interacting particle system of active and passive human groups. Furthermore, our numerical results show that the communication between active and passive humans strongly influences the evacuation time of the whole population even when the "faster-is-slower" phenomenon is taken into account. Finally, to provide an additional inside into the problem, a stationary state of our model is analyzed via current representations and heat map techniques., Comment: 11 figures, 21 pages

Pattern formation is a visual understanding of the dynamics of complex systems. Patterns arise in many ways, such as the segmentation of animals, bacterial colonies during growth, vegetation, chemical reactions, etc. In most cases, the long-range diffusion occurs, and the usual reaction-diffusion (RD) model can not capture such phenomena. The nonlocal RD model, on the other hand, can fill the gap. Analytical derivation of the amplitude equations (AE) for an RD system is a valuable tool to predict the pattern selections, in particular, the stationary Turing patterns when they occur. In this paper, we analyze the conditions for the Turing bifurcation for the nonlocal model and also derive the AE for the nonlocal RD model near the Turing bifurcation threshold to describe the reason behind the pattern selections. This derivation of the AE is not only limited to the nonlocal prey-predator model, as shown in our representative example but also can be applied to other nonlocal models near the Turing bifurcation threshold. The analytical prediction agrees with numerical simulation near the Turing bifurcation threshold. Moreover, the analytical and numerical results fit each other well even more remote from the Turing bifurcation threshold for the small values of the nonlocal parameter but not for the higher values., Comment: 21 pages, 7 figures

Stochastic dynamic models have been extensively used for the description of processes with uncertainties arising in the operations research, behavioral sciences, and many other application areas. A large class of the problems from these domains is characterized by the necessity to deal with several distinct groups of populations, which are usually labeled as "active" and "passive". Motivated by important applications of queueing networks and neuroscience, the main focus of the present work is on the analysis of reflecting stochastic dynamics of such mixed populations. We develop a general mathematical modeling framework to describe the reflecting stochastic dynamics for active-passive populations. The analysis of this model is carried out via a combination of low- and high-delity results obtained from the solution of the underlying coupled system of SDEs and from the simulations with a statistical-mechanics-based lattice gas model, where we employ a kinetic Monte Carlo procedure. We provide details of the queueing theory and neuronal models and discuss a relationship between reflecting SDEs and a model of queueing theory via a limit theorem. Furthermore, we present several representative numerical examples, and discuss an intrinsic interconnection between active and passive particles in the underlying stochastic process. Finally, possible extensions of the proposed methodology have been highlighted., Comment: 25 pages, 9 figures

Piezoelectric materials are employed in a wide range of sensing devices. At present, the vast majority of piezoelectric materials used for industrial applications are ceramic and exhibit a high lead content in their composition. However, the development of lead-free piezoelectric materials is attracting great attention in recent years, with the aim of enabling technologies that are environmentally friendly. This paper discusses the computational design of microstructured lead-free polymer-based piezoelectric nanocomposites suitable for production by 3D printing. Results are presented and further analyzed for various configurations using BaTiO3 inclusions in polymeric matrices enriched with the addition of carbon nanotubes (CNT). By incorporating carbon nanotubes in the matrix, we anticipate a quite significant improvement in the piezoelectric response of the composite, through simultaneous hardening of the matrix and improvement in its permittivity. Ministerio de Economía y Competitividad de España y el Fondo Europeo de Desarrollo Regional (FEDER) RTI2018-094945-B-C21 Ministerio de Economía y Competitividad de España y el Fondo Europeo de Desarrollo Regional (FEDER) DPI2017-89162-R

An odd number of zigzag edges in armchair graphene nanoribbons and their mechanical properties (e.g., Young's modulus, Poisson ratio and shear modulus) have potential interest for bandgap engineering in graphene based optoelectronic devices. In this paper, we consider armchair graphene nanoribbons passivated with hydrogen at the armchair edges and then apply the strain for tuning the bandgaps. Using density functional theory calculations, our study finds that the precise control of strain can allow tuning the bandgap from semiconductor to mettalic and then again switching back to semiconductor. In addition, we also show that the strained graphene nanoribbon passivated with hydrogen molecules can have large out-of-plane deformations demonstrating the properties of relaxed shape graphene. We express the strain induced by hydrogen in terms of binding energy. Finally, we characterise the effect of strain on the mechanical properties that can be used for making straintronic devices based on graphene nanoribbons., Comment: 7 pages and 7 figures

Piezoelectric materials are employed in a wide range of sensing devices. At present, the vast majority of piezoelectric materials used for industrial applications are ceramic and exhibit a high lead content in their composition. However, the development of lead-free piezoelectric materials is attracting great attention in recent years, with the aim of enabling technologies that are environmentally friendly. This paper discusses the computational design of microstructured lead-free polymer-based piezoelectric nanocomposites suitable for production by 3D printing. Results are presented and further analyzed for various configurations using BaTiO3 inclusions in polymeric matrices enriched with the addition of carbon nanotubes (CNT). By incorporating carbon nanotubes in the matrix, we anticipate a quite significant improvement in the piezoelectric response of the composite, through simultaneous hardening of the matrix and improvement in its permittivity. El desarrollo de este trabajo ha sido posible gracias al apoyo financiero del Ministerio de Economía y Competitividad de España y el Fondo Europeo de Desarrollo Regional (FEDER), en el marco de los proyectos RTI2018-094945-B-C21 y DPI2017-89162-R.

A nonlocal-in-time problem for the abstract Schr��dinger equation is considered. By exploiting the linear nature of nonlocal condition we derive an exact representation of the solution operator under assumptions that the spectrum of Hamiltonian is contained in the horizontal strip of complex plane. The derived representation permits us to establish the necessary and sufficient conditions for the problem's well-posedness and the existence of its mild, strong solutions. Furthermore, we present new sufficient conditions for the existence of solution which extend the available results to the case when some nonlocal parameters are unbounded. Two examples are provided., 19 pages, 2 examples, 2 figures

We study the influence of ripple waves originating from the electromechanical effects on spin relaxation caused by electromagnetic fields in armchair and zigzag graphene nanoribbons (GNRs). By utilizing analytical expressions supported by numerical simulations, we show that it is possible to tune the spin flip behaviors ON and OFF due to ripple waves in GNRs for potential applications in straintronic devices. This finding is similar to recently made observations on the design of spintronic devices in III-V semiconductor quantum dots, where the sign change in the effective Land$\mathrm{\acute{e}}$ $g$-factor can be engineered with the application of gate controlled electric fields. In particular, we show that the tuning of spin extends to larger widths for the armchair GNRs than for the zigzag GNRs. Here we also report that the relaxation rate vanishes like $L^5$., Comment: 8 pages and 7 figures

In this paper, a detailed analysis of anisotropic effects on the phonon induced spin relaxation rate in III-V semiconductor quantum dots (QDs) is carried out. We show that the accidental degeneracy due to level crossing between the first and second excited states of opposite electron spin states in both isotropic and anisotropic QDs can be manipulated with the application of externally applied gate potentials. In particular, anisotropic gate potentials enhance the phonon mediated spin-flip rate and reduce the cusp-like structure to lower magnetic fields, in addition to the lower QDs radii in III-V semiconductor QDs. In InAs QDs, only the Rashba spin-orbit coupling contributes to the phonon induced spin relaxation rate. However, for GaAs QDs, the Rashba spin-orbit coupling has a contribution near the accidental degeneracy point and the Dresselhaus spin-orbit coupling has a contribution below and above the accidental degeneracy point in the manipulation of phonon induced spin relaxation rates in QDs., Comment: 7 pages, 5 figures

We study the variation in the Land$\acute{\text{e}}$ g-factor of electron spins induced by both anisotropic gate potentials and magnetic fields in InAs quantum dots for possible implementation towards solid state quantum computing. In this paper, we present analytical expressions and numerical simulations of the variation in the Land$\acute{\text{e}}$ g-factor for both isotropic and anisotropic quantum dots. Using both analytical techniques and numerical simulations, we show that the Rashba spin-orbit coupling has a major contribution in the variation of the g-factor with electric fields before the regime, where level crossing or anticrossing occurs. In particular, the electric field tunability is shown to cover a wide range of g-factor through strong Rashba spin-orbit interaction. Another major result of this paper is that the anisotropic gate potential gives quenching effect in the orbital angular momentum that reduces the variation in the E-field and B-field tunability of the g-factor if the area of the symmetric and asymmetric quantum dots is held constant. We identify level crossings and anticrossings of the electron states in the variation of the Land$\acute{\text{e}}$ g-factor. We model the wavefunctions of electron spins and estimate the size of the anticrossing for the spin states $|0,-1,+1/2>$ and $|0,0,-1/2>$ corresponding to a quantum dot that has been recently studied experimentally (Phys. Rev. Lett. \textbf{104}, 246801 (2010))., 9 pages and 8 figures

The synthesis of dsRNA is analyzed using a pathway model with amplifications caused by the aberrant RNAs. The transgene influx rate is assumed time-decaying considering the fact that the number of transgenes can not be infinite. The dynamics of the transgene induced RNA silencing is investigated using a system of coupled nonautonomous ordinary nonlinear differential equations which describe the model phenomenologically. The silencing phenomena are detected after a period of transcription. Important contributions of certain parameters are discussed with several numerical examples.

A numerical model is constructed for modelling macroscale damping effects induced by the first order martensite phase transformations in a shape memory alloy rod. The model is constructed on the basis of the modified Landau-Ginzburg theory that couples nonlinear mechanical and thermal fields. The free energy function for the model is constructed as a double well function at low temperature, such that the external energy can be absorbed during the phase transformation and converted into thermal form. The Chebyshev spectral methods are employed together with backward differentiation for the numerical analysis of the problem. Computational experiments performed for different vibration energies demonstrate the importance of taking into account damping effects induced by phase transformations., Comment: Keywords: martensite transformation, thermo-mechanical coupling, vibration damping, Ginzburg-Landau theory

Many new applications of ferroelastic materials require a better understanding of their dynamics that often involve phase transformations. In such cases, an important prerequisite is the understanding of wave propagation caused by pulse-like loadings. In the present study, a mathematical model is developed to analyze the wave propagation process in shape memory alloy rods. The first order martensite transformations and associated thermo-mechanical coupling effects are accounted for by employing the modified Ginzburg-Landau-Devonshire theory. The Landau-type free energy function is employed to characterize different phases, while a Ginzburg term is introduced to account for energy contributions from phase boundaries. The effect of internal friction is represented by a Rayleigh dissipation term. The resulted nonlinear system of PDEs is reduced to a differential-algebraic system, and Chebyshev's collocation method is employed together with the backward differentiation method. A series of numerical experiments are performed. Wave propagations caused by impact loadings are analyzed for different initial temperatures. It is demonstrated that coupled waves will be induced in the material. Such waves will be dissipated and dispersed during the propagation process, and phase transformations in the material will complicate their propagation patterns. Finally, the influence of internal friction and capillary effects on the process of wave propagation is analyzed numerically., Comment: Keywords: nonlinear waves, thermo-mechanical coupling, martensite transformations, Ginzburg-Landau theory, Chebyshev collocation method