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We study how firms respond to online customer reviews in a competitive market where they jostle with one another for sales based on online ratings. The focus of this paper is on how firms can optimally manage their ratings through management response and how review ratings affect the sales and profits of competing firms. We develop a controlled diffusion process to model the coevolution of sales and ratings as a function of the response strategy chosen to maximize profit over time. Our model considers a variety of factors, such as profit margin and customer rating sensitivity, that influence a firm’s effort to manage ratings and subsequently its sales and profits. More response effort needs to be exerted to manage ratings when either the profit margin of a tour is very high or customers are very sensitive to ratings. We estimate our model using data on Ctrip’s tours that include each tour’s sales, reviews, prices, and tour features. We find that consumers anchor their beliefs in the mean market rating and that their purchase decisions depend on the tour’s rating relative to this anchor. Thus, relative, rather than absolute, ratings matter. Our study informs firms on how competition and other primitives impact their efforts to manage ratings and hence profit. Our methodology allowed us to conduct “what-if” analyses, for example, to study what would happen to the review ratings, sales, and profits of a tour if a firm adopted a different response strategy. We were also able to provide turnaround strategies for struggling tours, i.e., factors that a loss-making tour should change if it wishes to make a positive profit. Ultimately, we conducted a competitive analysis that allowed us to modify certain parameters that affect the intensity of competition and hence the sales and the profits of competing tours. Finally, we demonstrate the flexibility of the model by extending it to incorporate multiple state variables that might affect the response strategy. [ABSTRACT FROM AUTHOR]

Nonequilibrium interfacial thermodynamics is formulated in the presence of surface reactions for the study of diffusiophoresis in isothermal systems. As a consequence of microreversibility and Onsager-Casimir reciprocal relations, diffusiophoresis, i.e., the coupling of the tangential components of the pressure tensor to the concentration gradients of solute species, has a reciprocal effect where the interfacial currents of solutes are coupled to the slip velocity. The presence of surface reactions is shown to modify the diffusiophoretic and reciprocal effects at the fluid-solid interface. The thin-layer approximation is used to describe the solution flowing near a reactive solid interface. Analytic formulas describing the diffusiophoretic and reciprocal effects are deduced in the thin-layer approximation and tested numerically for the Poiseuille flow of a solution between catalytic planar surfaces. [ABSTRACT FROM AUTHOR]

We develop a nonlocal Nernst-Planck model for reaction and diffusion in multicomponent ionic systems. We apply the model to the one-dimensional liquid junction problem, in which two electrolytic solutions of different ionic concentrations are brought into contact via a permeable membrane. Transport of ions through the membrane induces an electric field which is modeled using two separate nonlocal conditions: charge conservation and Gauss' law. We inve1064s that the net charge at each point in the domain is zero, by considering four different initial scenarios. Charge conservation and Gauss' law yield similar results for most practical scenarios in which the initial condition satisfies strict electroneutrality. However, Gauss' law has two important advantages over charge conservation: (i) it is numerically more stable and can be applied even when the concentration of all the charged species drops to zero and (ii) computationally, it is significantly cheaper. Further, this study provides insights on the prescription of electroneutrality conditions necessary to handle the physics of evolving charges in nonlocal peridynamic models that are aimed at modeling nonlocal reaction-diffusion or corrosion-type processes. [ABSTRACT FROM AUTHOR]

We have carried out molecular dynamics simulations using NAMD to study the diffusivity of Na and Cl ions across a POPC lipid bilayer membrane. We show that an imbalance of positively and negatively charged ions on either side of the membrane leads to the diffusion of ions and water molecules. We considered the cases of both weak and very strong charge imbalance across the membrane. The diffusion coefficients of the ions have been determined from the mean square displacements of the particles as a function of time. We find that for strong electrochemical gradients, both the Na and Cl ions diffuse rapidly through pores in the membrane with diffusion coefficients up to ten times larger than in water. Rather surprisingly, we found that although the Na ions are the first to begin the permeation process due to the lower potential barrier that they experience compared to the Cl ions, the latter complete the permeation across the barrier more quickly due to their faster diffusion rates. [ABSTRACT FROM AUTHOR]

Ca2+ signals are ubiquitous. One of the key factors for their versatility is the variety of spatio-temporal distributions that the cytosolic Ca2+ can display. In most cell types Ca2+ signals not only depend on Ca2+ entry from the extracellular medium but also on Ca2+ release from internal stores, a process which is in turn regulated by cytosolic Ca2+ itself. The rate at which Ca2+ is transported, the fraction that is trapped by intracellular buffers, and with what kinetics are thus key features that affect the time and spatial range of action of Ca2+ signals. The quantification of Ca2+ diffusion in intact cells is quite challenging because the transport rates that can be inferred using optical techniques are intricately related to the interaction of Ca2+ with the dye that is used for its observation and with the cellular buffers. In this paper, we introduce an approach that uses Fluorescence Correlation Spectroscopy (FCS) experiments performed at different conditions that in principle allows the quantification of Ca2+ diffusion and of its reaction rates with unobservable (non-fluorescent) Ca2+ buffers. To this end, we develop the necessary theory to interpret the experimental results and then apply it to FCS experiments performed in a set of solutions containing Ca2+, a single wavelength Ca2+ dye, and a non-fluorescent Ca2+ buffer. We show that a judicious choice of the experimental conditions and an adequate interpretation of the fitting parameters can be combined to extract information on the free diffusion coefficient of Ca2+ and of some of the properties of the unobservable buffer. We think that this approach can be applied to other situations, particularly to experiments performed in intact cells. [ABSTRACT FROM AUTHOR]

Lyotropic Liquid Crystals (LLCs) are a class of lipid-based membranes with a strong potential for drug-delivery employment. The characterization and control of their transport properties is a central issue in this regard, and has recently prompted a notable volume of research on the topic. A promising experimental approach is provided by the so-called diffusion setup, where the drug molecules diffuse from a feeding chamber filled with water to a receiving one passing through a LLC. In the present work we provide a theoretical framework for the proper description of this setup, and validate it by means of targeted experiments. Due to the inhomogeneity of the system, a rich palette of different diffusion dynamics emerges from the interplay of the different time- and lengthscales thereby present. Our work paves the way to the employment of diffusion experiments to quantitatively characterize the transport properties of LLCs, and provides the basic tools for device diffusion setups with controlled kinetic properties. [ABSTRACT FROM AUTHOR]

Introduction: Talquite consists of alternating three-layer bundles with weak Van der Waals bonds between them. The octahedral layer is located between two tetrahedral layers. It is used as an adsorbent for heavy metals in aqueous solution. Objective: To determine kinetic model, effective diffusivity and isotherms corresponding to the adsorption in the heterogeneous mass system of Cd (II) and Talquita ion in aqueous solution at temperatures of 298 and 333 K. Materials and Methods: A physical and chemical characterization of the adsorbent is performed. The kinetic, diffusive and equilibrium study of ion adsorption is carried out at 298 and 333 K. The adsorption processes are carried out with 150 rpm stirring on an AGU-10 Bunsen mechanical stirrer. Pseudo-first order, pseudo-second order, Elovich, liquid film diffusion, intraparticle diffusion, Bangham model, and effective diffusion models are instrumented. For isothermal balance studies, the Langmuir, Freundlich, Dubinin-Radushkevich, BET, Redlich, Toth and Flory-Huggins isotherms are implemented. Concentrations are determined by Atomic Absorption Spectroscopy. Results and Discussion: The pseudo-first order kinetic model has better adjust to the adsorption kinetics at two studied temperatures. The isothermal models of BET at 298 K and Flory-Huggins at 333 K have the better adjust to the adsorption of Cd (II) ions in aqueous solution. Conclusions: Talquite has moderate adsorption capacities for Cd (II) ions in aqueous solution. [ABSTRACT FROM AUTHOR]

In this work, we study diffusion of gases in porous amorphous carbon at high temperatures using equilibrium molecular dynamics simulations. Microporous and mesoporous carbon structures are computationally generated using liquid quench method and reactive force fields. Motivated by the need to understand high temperature diffusivity of light weight gases like H2, O2, H2O, and CO in amorphous carbon, we investigate the diffusion behavior as function of two important parameters: (a) the pore size and (b) the concentration of diffusing gases. The effect of pore size on diffusion is studied by employing multiple realizations of the amorphous carbon structures in microporous and mesoporous regimes, corresponding to densities of 1 g/cm³ and 0.5 g/cm³, respectively. A detailed analysis of the effect of gas concentration on diffusion in the context of these two porosity regimes is presented. For the microporous structure, we observe that predominantly, a high diffusivity results when the structure is highly anisotropic and contains wide channels between the pores. On the other hand, when the structure is highly homogeneous, significant molecule-wall scattering leads to a nearly concentration-independent behavior of diffusion (reminiscent of Knudsen diffusion). The mesoporous regime is similar in behavior to the highly diffusive microporous carbon case in that diffusion at high concentration is governed by gas-gas collisions (reminiscent of Fickian diffusion), which transitions to a Knudsen-like diffusion at lower concentration. [ABSTRACT FROM AUTHOR]

The temperature-dependent diffusion coefficient of interstitial helium in zirconium carbide (ZrC) matrix is calculated based on the transition state theory. The microscopic parameters in the activation energy and prefactor are obtained from first-principles total energy and phonon frequency calculations including the all atoms. The obtained activation energy is 0.78 eV, consistent with experimental value. Besides, we evaluated the influence of C and Zr vacancies as the perturbation on helium diffusion, and found the C vacancy seems to confine the mobility of helium and the Zr vacancy promotes helium diffusion in some extent. These results provide a good reference to understand the behavior of helium in ZrC matrix. [ABSTRACT FROM AUTHOR]

As one of the most important tasks in image processing, texture analysis is related to a class of mathematical models that characterize the spatial variations of an image. In this paper, in order to extract features of interest, we propose a reaction diffusion based model which uses the variational approach. In the first place, we describe the mathematical model, then, aiming to simulate the latter accurately, we suggest an efficient numerical scheme. Thereafter, we compare our method to literature findings. Finally, we conclude our analysis by a number of experimental results showing the robustness and the performance of our algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we study diffusion equations involving Hadamard-type time-fractional derivatives related to ultra-slow random models. We start our analysis using the abstract fractional Cauchy problem, replacing the classical time derivative with the Hadamard operator. The stochastic meaning of the introduced abstract differential equation is provided, and the application to the particular case of the fractional heat equation is then discussed in detail. The ultra-slow behaviour emerges from the explicit form of the variance of the random process arising from our analysis. Finally, we obtain a particular solution for the nonlinear Hadamard-diffusive equation. [ABSTRACT FROM AUTHOR]

The anisotropic 3D equation describing the pointlike particles diffusion in slender impermeable tubes of revolution with cross section smoothly depending on the longitudinal coordinate is the object of our study. We use singular perturbations approach to find the rigorous asymptotic expression for the local particles concentration as an expansion in the ratio of the characteristic transversal and longitudinal diffusion relaxation times. The corresponding leading-term approximation is a generalization of well-known Fick-Jacobs approximation. This result allowed us to delineate the conditions on temporal and spatial scales under which the Fick-Jacobs approximation is valid. A striking analogy between solution of our problem and the method of inner-outer expansions for low Knudsen numbers gas kinetic theory is established. With the aid of this analogy we clarify the physical and mathematical meaning of the obtained results. [ABSTRACT FROM AUTHOR]

Silver iodide (AgI-V) is an archetypical ionic compound for studying the formation mechanism of a superionic state. Previous studies have proven that superionic AgI with high ionic conductivity greater than 0.1 Ω-1cm-1 could only be obtained at high temperatures. We show in this paper that high pressure could also induce the superionic state in AgI even at ambient temperature. Using electrochemical impedance spectroscopy, we investigated Ag+ ions diffusing in rock-salt structured AgI-III and KOH-type AgI-V under high pressures and directly observed the superionic state in AgI-V. The diffusion coefficient of AgI-V is ∼3.4 × 10-4-8.6 × 10-4 cm²/s in the investigated pressure range of 12-17 GPa, comparable with those of superionic α-AgI and AgI-III′. By analyzing the half infinite length Warburg diffusion process, two parameters α and β, which closely relate to the disordered state of Ag+ ions, have been determined and it was suggested that Ag+ ions in AgI-V become disordered. The ionic conductivity of AgI-V is three orders of magnitude higher than that of AgI-III, and has reached around 0.1 Ω-1cm-1. Evidence for all three, the diffusion coefficient, α and β, and conductivity have proven that AgI-V is a superionic conductor at ambient temperature. [ABSTRACT FROM AUTHOR]

The dynamics properties of a new "next generation" model asphalt system that represents SHRP AAA-1 asphalt using larger molecules than past models is studied using molecular simulation. The system contains 72 molecules distributed over 12 molecule types that range from nonpolar branched alkanes to polar resins and asphaltenes. Molecular weights range from 290 to 890 g/mol. All-atom molecular dynamics simulations conducted at six temperatures from 298.15 to 533.15 K provide a wealth of correlation data. The modified Kohlrausch-Williams-Watts equation was regressed to reorientation time correlation functions and extrapolated to calculate average rotational relaxation times for individual molecules. The rotational relaxation rate of molecules decreased significantly with increasing size and decreasing temperature. Translational self-diffusion coefficients followed an Arrhenius dependence. Similar activation energies of ~42 kJ/mol were found for all 12 molecules in the model system, while diffusion prefactors spanned an order of magnitude. Viscosities calculated directly at 533.15 K and estimated at lower temperatures using the Debye-Stokes-Einstein relationship were consistent with experimental data for asphalts. The product of diffusion coefficient and rotational relaxation time showed only small changes with temperature above 358.15 K, indicating rotation and translation that couple self-consistently with viscosity. At lower temperatures, rotation slowed more than diffusion. [ABSTRACT FROM AUTHOR]

The article presents the discussion on Nicu Boboc memorial volume. Topics include convolution and Riesz capacities, 3-D stochastic vorticity equations, and the heat equation for the Dirichlet fractional Laplacian; and showing Wasserstein distance for heating semigroups of diffusion processes on Riemannian manifolds and stochastic wave equation with fractional Gaussian random noise.

An integro-differential diffusion equation with linear force, based on the continuous time random walk model, is considered. The equation generalizes the ordinary and fractional diffusion equations. Analytical expressions for transition probability density, mean square displacement, and intermediate scattering function are presented. The mean square displacement and intermediate scattering function can fit well the simulation data of the temperature-dependent translational dynamics of nitrogen atoms of elastin for a wide range of temperatures and various scattering vectors. Moreover, the numerical results are also compared with those of a fractional diffusion equation. [ABSTRACT FROM AUTHOR]

Copyright of Cybernetics & Systems Analysis / Kibernetiki i Sistemnyj Analiz is the property of V.M. Glushkov Institute of Cybernetics of NAS of Ukraine and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Cybernetics & Systems Analysis / Kibernetiki i Sistemnyj Analiz is the property of V.M. Glushkov Institute of Cybernetics of NAS of Ukraine and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This article examines asymptotic mean-square stability analysis of stochastic linear theta (SLT) scheme for n-dimensional stochastic delay differential equations (SDDEs). We impose some conditions on drift and diffusion terms, which admit that the diffusion coefficient can be highly nonlinear and does not necessarily satisfy a linear growth or global Lipschitz condition. We prove that the proposed scheme is asymptotically mean square stable if the employed stepsize is smaller than a given and easily computable upper bound. In particular, based on our investigation in the case θ ∈ [1/2, 1], the stepsize is arbitrary. Eventually, numerical examples are given to demonstrate the effectiveness of our work. [ABSTRACT FROM AUTHOR]

This article presents a mathematical model of a diffusion absorption refrigerator (DAR) equipped with a shell-tube vapor generator. The DAR is charged with 3 fluids: ammonia, water and hydrogen. The modeling was based on using mass and energy balances in control volumes to simulate operations DAR. The model is composed of 14 interconnected distinct parts that allow to calculate: poor and rich concentrations of the solutions, the heating in the generator and the heating transfer in the other components, the mass flow rate of solution in several part of the system, as well as the temperature and pressure. The model also allows to simulate the homogenization of vapors, to predict the rectification process final location, the condensed ammonia fraction, the heat losses in the condenser and in the other components. These phenomena haven't been quantified in other diffusion absorption refrigerator models. The present model's validation was achieved by comparing the model results with results obtained experimentally in a commercial refrigerator with 80 W of nominal electric power. The model designing allows new DARs. [ABSTRACT FROM AUTHOR]

Abstract In this work, we study the existence and uniqueness of the solution to the stochastic differential equation of the double Heston model which is defined by two independent variance processes with non-Lipschitz diffusions. Besides, we present a Monte Carlo algorithm based on the Euler discretization method to price the Lookback options under this model. [ABSTRACT FROM AUTHOR]

Abstract This paper deals with a parameter robust numerical method for solving a nonlinear singularly perturbed elliptic reaction–diffusion problem. Existence and uniqueness of a solution to a nonlinear difference scheme are established. The uniform convergence of the nonlinear difference scheme on piecewise uniform and log-meshes is established. Numerical experiments are presented. [ABSTRACT FROM AUTHOR]

Abstract This paper is concerned with the tropical model with temperature-dependent diffusion on the barotropic mode in R 2 × R +. We prove the existence of the global strong solution under the initial data ‖ u 0 ‖ H s 2 + ‖ v 0 ‖ H s 2 + ‖ θ 0 ‖ H s 2 with s > 1 is suitably small. [ABSTRACT FROM AUTHOR]

This paper is concerned with diffusive approximations of some numerical schemes for several linear (or weakly nonlinear) kinetic models which are motivated by wide-range applications, including radiative transfer or neutron transport, run-and-tumble models of chemotaxis dynamics, and Vlasov-Fokker-Planck plasma modeling. The well-balanced method applied to such kinetic equations leads to time-marching schemes involving a "scattering S-matrix", itself derived from a normal modes decomposition of the stationary solution. One common feature these models share is the type of diffusive approximation: their macroscopic densities solve drift-diffusion systems, for which a distinguished numerical scheme is Il'in/Scharfetter-Gummel's "exponential fitting" discretization. We prove that these well-balanced schemes relax, within a parabolic rescaling, towards such type of discretization by means of an appropriate decomposition of the S-matrix, hence are asymptotic preserving. [ABSTRACT FROM AUTHOR]

This paper deals with a non-self-adjoint differential operator which is associated with a diffusion process with random jumps from the boundary. Our main result is that the algebraic multiplicity of an eigenvalue is equal to its order as a zero of the characteristic function $\unicode[STIX]{x1D6E5}(\unicode[STIX]{x1D706})$. This is a new criterion for determining the multiplicities of eigenvalues for concrete operators. [ABSTRACT FROM AUTHOR]

Given a one-dimensional downwards transient diffusion process $X$ , we consider a random time $\unicode[STIX]{x1D70C}$ , the last exit time when $X$ exits a certain level $\ell$ , and detect the optimal stopping time for it. In particular, for this random time $\unicode[STIX]{x1D70C}$ , we solve the optimisation problem $\inf _{\unicode[STIX]{x1D70F}}\mathbb{E}[\unicode[STIX]{x1D706}(\unicode[STIX]{x1D70F}-\unicode[STIX]{x1D70C})_{+}+(1-\unicode[STIX]{x1D706})(\unicode[STIX]{x1D70C}-\unicode[STIX]{x1D70F})_{+}]$ over all stopping times $\unicode[STIX]{x1D70F}$. We show that the process should stop optimally when it runs below some fixed level $\unicode[STIX]{x1D705}_{\ell }$ for the first time, where $\unicode[STIX]{x1D705}_{\ell }$ is the unique solution in the interval $(0,\unicode[STIX]{x1D706}\ell)$ of an explicitly defined equation. [ABSTRACT FROM AUTHOR]

Abstract Based on fractal theory (FT) and fractional calculus (FC), a new fractally fractional diffusion model (FFDM) of composite dual-porosity has been developed to evaluate performance of multiple fractured horizontal wells (MFHWs) with stimulated reservoir volume (SRV) in tight gas reservoirs (TGRs). More specifically, FT is used to characterize the complex and heterogeneous fracture network (FN) both inside and outside of SRV, while anomalous behavior of diffusion processes both inside and outside of SRV is quantified by applying the temporal fractional derivatives. The FFDM is then solved by the Laplace transformation, line source function, the numerical discrete method, and superposition principle. The transient pressure responses are then inversely converted from Laplace domain into real time domain with the Stehfest algorithm, and the FFDM is also validated, and type curves are generated as well. Flow stages are subsequently identified together with analysis on characteristics of the type curves, especially the anomalous features different with those generated from the conventional Euclidean model. Sensitivity analyses of some related parameters have also been discussed as well. And the FFDM is then also matched with the real field well-testing data of a MFHW with SRV in a TGR. The proposed FFDM provides a new understanding of the performance of MFHWs with SRV in TGRs, which can be used to interpret the field pressure data more accurately and appropriately. Graphical abstract The SRV includes the main hydraulic fractures, the Euclidean matrix, and the fractal micro-fractures, while the USRV contains the Euclidean matrix and the fractal natural fractures. The flow of the gas in SRV and USRV follows the temporal fractional anomalous diffusion. By discretizing the main hydraulic fractures and applying the Laplace transformation, line source function, and superposition principle, we can obtain the pressure responses of a MFHW with SRV in a tight gas reservoir. Flow regime diagnostics and the characteristics analysis of type curves are accomplished, especially the anomalous characteristics. Image 1 Highlights • Fractal theory is used to describe the complex fracture network both in the SRV and USRV. • The anomalous diffusion both in the SRV and USRV is considered by employing the fractional derivatives. • A new FFDM of composite dual-porosity for MFHWs with SRV in tight gas reservoirs has been developed. • The PTA is then studied in depth, especially the anomalous characteristics different from that of conventional model. [ABSTRACT FROM AUTHOR]

Abstract We provide an existence result for stationary fractional mean field game systems, with fractional exponent greater than 1/2. In the case in which the coupling is a nonlocal regularizing potential, we obtain existence of solutions under general assumptions on the Hamiltonian. In the case of local coupling, we restrict to the subcritical regime, that is the case in which the diffusion part of the operator dominates the Hamiltonian term. We consider both the case of local bounded coupling and of local unbounded coupling with power-type growth. In this second regime, we impose some conditions on the growth of the coupling and on the growth of the Hamiltonian with respect to the gradient term. [ABSTRACT FROM AUTHOR]

The weak–strong uniqueness for renormalized solutions to reaction–cross-diffusion systems in a bounded domain with no-flux boundary conditions is proved. The system generalizes the Shigesada–Kawasaki–Teramoto population model to an arbitrary number of species. The diffusion matrix is neither symmetric nor positive definite, but the system possesses a formal gradient-flow or entropy structure. No growth conditions on the source terms are imposed. It is shown that any renormalized solution coincides with a strong solution with the same initial data, as long as the strong solution exists. The proof is based on the evolution of the relative entropy modified by suitable cutoff functions. [ABSTRACT FROM AUTHOR]

Fuel cells, batteries, and thermochemical and other energy conversion devices involve the transport of a number of (electro-) chemical species through distinct materials so that they can meet and react at specified multi-material interfaces. Therefore, morphology or arrangement of these different materials can be critical in the performance of an energy conversion device. In this paper, we study a model problem motivated by a solar-driven thermochemical conversion device that splits water into hydrogen and oxygen. We formulate the problem as a system of coupled multi-material reaction-diffusion equations where each species diffuses selectively through a given material and where the reaction occurs at multi-material interfaces. We introduce a phase-field formulation of the optimal design problem and numerically study selected examples. [ABSTRACT FROM AUTHOR]

Abstract The purpose of this paper is to study the existence of steady state in a linear cross-diffusion predator–prey model with Beddington–DeAngelis functional response. The proofs mainly rely on Fixed point index theory and analytical techniques. [ABSTRACT FROM AUTHOR]

In this article, we investigate the pricing and convergence of general non-affine non-Gaussian GARCH-based discretely sampled variance swaps. Explicit solutions for fair strike prices under two different sampling schemes are derived using the extended Girsanov principle as the pricing kernel candidate. Following standard assumptions on time-varying GARCH parameters, we show that these quantities converge respectively to fair strikes of discretely and continuously sampled variance swaps that are constructed based on the weak diffusion limit of the underlying GARCH model. An empirical study which relies on a joint estimation using both historical returns and VIX data indicates that an asymmetric heavier tailed distribution is more appropriate for modelling the GARCH innovations. Finally, we provide several numerical exercises to support our theoretical convergence results in which we further investigate the effect of the quadratic variation approximation for the realized variance, as well as the impact of discrete versus continuous-time modelling of asset returns. [ABSTRACT FROM AUTHOR]

Surface diffusion coefficients may be estimated by fitting solutions of a diffusion model to batch kinetic data. For non-linear systems, a numerical solution of the diffusion model's governing equations is generally required. We report here the application of the classic Langmuir kinetics model to extract surface diffusion coefficients from batch kinetic data. The use of the Langmuir kinetics model in lieu of the conventional surface diffusion model allows derivation of an analytical expression. The parameter estimation procedure requires determining the Langmuir rate coefficient from which the pertinent surface diffusion coefficient is calculated. Surface diffusion coefficients within the 10−9 to 10−6 cm2/s range obtained by fitting the Langmuir kinetics model to experimental kinetic data taken from the literature are found to be consistent with the corresponding values obtained from the traditional surface diffusion model. The virtue of this simplified parameter estimation method is that it reduces the computational complexity as the analytical expression involves only an algebraic equation in closed form which is easily evaluated by spreadsheet computation. [ABSTRACT FROM AUTHOR]

We present a novel numerical scheme for the valuation of options under a well‐known jump‐diffusion model. European option pricing for such a case satisfies a 1 + 2 partial integro‐differential equation (PIDE) including a double integral term, which is nonlocal. The proposed approach relies on nonuniform meshes with a focus on the discontinuous and degenerate areas of the model and applying quadratically convergent finite difference (FD) discretizations via the method of lines (MOL). A condition for observing the time stability of the fully discretized problem is given. Also, we report results of numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper, we study the well‐known Degn‐Harrison reaction diffusion model. We are concerned with the local and global asymptotic stability of the system. Weaker conditions than those of previous studies are derived and validated using Matlab computer simulations. [ABSTRACT FROM AUTHOR]

This paper analyzes the optimal reinsurance strategy for insurers with a generalized mean-variance premium principle. The surplus process of the insurer is described by the diffusion model which is an approximation of the classical Cramér-Lunderberg model. We assume the dynamic VaR constraints for proportional reinsurance. We obtain the closed form expression of the optimal reinsurance strategy and corresponding survival probability under proportional reinsurance. [ABSTRACT FROM AUTHOR]

Highlights · Formulated the conditional model for diffusion-controlled FRP. · Developed smoothing methods for gel, glass and cage effects. · Proposed adaptive smoothing strategy for dynamic optimization of FRP. · Presented numerical case studies for efficiency demonstration. Abstract With the increase of conversion and viscosity, a batch free radical polymerization (FRP) may encounter complicated phenomena, including the gel, glass, and cage effects. These effects normally lead to a conditional modeling formulation described by a set of differential-algebraic equations (DAEs). Discontinuous gradient exists at model switches triggered by occurrence of the effects, which cause difficulty for dynamic optimization on the batch process. To deal with the discontinuity, interior-point smooth approximations are proposed to describe the model switches at the occurrence of the effects. An adaptive smoothing strategy, which can efficiently balance the efficiency of optimization and the accuracy of the approximated model, is proposed for the dynamic optimization. To show the effectiveness of this smoothing strategy, case studies for optimal operating profiles in a polymerization process of methyl methacrylate are conducted. Good computational performance is achieved with the proposed strategy. [ABSTRACT FROM AUTHOR]

The paper is concerned with the construction of a cubic spline wavelet basis on the unit interval and an adaptation of this basis to the first-order homogeneous Dirichlet boundary conditions. The wavelets have four vanishing moments and they have the shortest possible support among all cubic spline wavelets with four vanishing moments corresponding to B-spline scaling functions. We provide a rigorous proof of the stability of the basis in the space L 2 (0 , 1) or its subspace incorporating boundary conditions. To illustrate the applicability of the constructed bases, we apply the wavelet-Galerkin method to option pricing under the double exponential jump-diffusion model and we compare the results with other cubic spline wavelet bases and with other methods. [ABSTRACT FROM AUTHOR]

We study a PDE model for dynamics of susceptible-infected interactions. The dispersal of susceptibles is via diffusion and repellent taxis as they move away from the increasing density of infected. The diffusion of infected is a nonlinear, possibly degenerating term in nondivergence form. We prove the existence of so-called weak-strong solutions in 1D for a positive susceptible initial population. For dimension N ≥ 2 and nonnegative susceptible initial density we show the existence of supersolutions. Numerical simulations are performed for different scenarios and illustrate the space-time behaviour of solutions. [ABSTRACT FROM AUTHOR]

Highlights • Examined twenty-seven scans from four participants at three sites across three years. • Hierarchical clustering performed on anatomical, diffusion, and functional connectivity. • Data clustered by participant rather than scanner across all modalities. • MRI data is individually identifying even across multiple scanners and time. • Provides strong support for collapsing data across multiple sites. Abstract Multi-center MRI studies can enhance power, generalizability, and discovery for clinical neuroimaging research in brain disorders. Here, we sought to establish the utility of a clustering algorithm as an alternative to more traditional intra-class correlation coefficient approaches in a longitudinal multi-center human phantom study. We completed annual reliability scans on 'travelling human phantoms'. Acquisitions across sites were harmonized prospectively. Twenty-seven MRI sessions were available across four participants, scanned on five scanners, across three years. For each scan, three metrics were extracted: cortical thickness (CT), white matter fractional anisotropy (FA), and resting state functional connectivity (FC). For each metric, hierarchical clustering (Ward's method) was performed. The cluster solutions were compared to participant and scanner using the adjusted Rand index (ARI). For all metrics, data clustered by participant rather than by scanner (ARI > 0.8 comparing clusters to participants, ARI < 0.2 comparing clusters to scanners). These results demonstrate that hierarchical clustering can reliably identify structural and functional scans from different participants imaged on different scanners across time. With increasing interest in data-driven approaches in psychiatric and neurologic brain imaging studies, our findings provide a framework for multi-center analytic approaches aiming to identify subgroups of participants based on brain structure or function. [ABSTRACT FROM AUTHOR]

Abstract The study of influence maximization (IM) has attracted many scholars in recent years due to its import practical values. Given a social network, it aims at finding a subset of k individuals as seed nodes which can trigger the maximum influence cascade through the network under a predefined diffusion model. Kempe et al. first formulated influence maximization as a discrete optimization problem and proved its NP-hardness and submodularity, based on which they further proposed a greedy approach with guaranteed solution accuracy. Unfortunately, the greedy algorithm was also known for its extremely low time efficiency. To solve this problem more efficiently, many research works were proposed in recent years. However, these studies either make sacrifices in solution accuracy or require huge memory consumption. Besides, only a handful of research works can handle mega-scale networks with millions of nodes and edges. To solve this problem both efficiently and effectively, in this paper we propose IMPC: an influence maximization framework based on multi-neighbor potential in community networks. In our approach the influence diffusion process is divided into two phases: (i) multi-neighbor potential based seeds expansion; and (ii) intra-community influence propagation. Based on this framework we derive an objective function to evaluate the overall influence as a combination of the influence during the two phases. We theoretically prove that the objective function is submodular and design an efficient greedy algorithm to find the seed nodes. We evaluate the performance of our framework on eight real-world networks which scale up to millions of nodes and hundreds of millions of edges. Experimental results show that our approach can significantly outperform other state-of-the-art algorithms in terms of time and space efficiency with no compromise on solution accuracy. Highlights • We propose the IMPC framework to solve the influence maximization problem. • Based on IMPC, we propose an efficient greedy algorithm to find the seed nodes. • We propose two techniques to further accelerate our algorithm. • Experiments on eight real-world networks show the superiority of our approach. [ABSTRACT FROM AUTHOR]

In this paper, we consider European and American option pricing problems under regime switching jump diffusion models which are formulated as a system of partial integro-differential equations (PIDEs) with fixed and free boundaries. For free boundary problem arising in pricing American option, we use operator splitting method to deal with early exercise feature of American option. For developing a numerical technique we employ localized radial basis function generated finite difference (RBF-FD) approximation to overcome the ill-conditioning and high density issues of discretized matrices. The proposed method leads to linear systems with tridiagonal and diagonal dominant matrices. Also, in this paper the convergence and consistency of the proposed method are discussed. Numerical examples presented in the last section illustrate the robustness and practical performance of the proposed algorithm for pricing European and American options. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we investigate the heat transport across Germanium Silicon interface using an enhanced ballistic-diffusive equation (EBDE), where we introduce the temperature jump boundary condition coupled with a thermal boundary resistance (TBR) and an effective thermal conductivity model. This paper focuses on the thermal transport of sub-23 nm Ge/Si thin films. The present model is aimed to describe the ballistic-diffusive phonon transport across Ge/Si interface. We have found that the temperature jump occurs in the interface due to phonon-boundary interactions. In addition, the interfacial heat transport is influenced by the surface roughness effect. The prediction of the suggested EBDE model are in good accordance with analytical method reported in the literature. The proposed model shows excellent agreement with the phonon Boltzmann transport equation (BTE) approach and Monte Carlo simulation (MC). Further, the analytic model for the effective thermal conductivity (ETC) is in strong agreement with experimentally based approach and also the theoretical model. Graphical abstract Image Highlights • An enhanced ballistic-diffusive model is developed for heat transport across the interface scattering between nanomaterials. • An excellent agreement with experimental results and Monte Carlo simulation. • Investigation of phonon-surface scattering in nanostructures. • This work help research optimization of interface quality. [ABSTRACT FROM AUTHOR]

In the present work, the soil gas radon survey has been carried out for locating the trend of soil radon in the foothills of Siwalik which is covered with lithology of Pliocene unconsolidated deposits. Soil gas radon concentration and mass exhalation rate have been studied in natural soil samples of Udhampur district, Jammu and Kashmir, India using active measurement technique RAD7 and smart RnDuo monitor. The sampling measurements were chosen according to suitability of the area. Few of the locations are near the Main Boundary Thrust (MBT) and tectonically active lineaments, having reasonably high concentration of soil gas radon. The soil gas radon concentration in 15 locations of studied area has been measured at different depths (30, 45 and 60 cm) and the overall soil gas concentration was found to vary from 0.14 to 61.01 kBq m−3, respectively. This large variation in radon content might be due to radioactive nature of the bedrocks present in different geological structure. Soil pore diffusion model have been used to observe the relation between experimentally and theoretically determined soil gas radon concentrations in the studied region. [ABSTRACT FROM AUTHOR]

Common methods for measuring soil denitrification in situ include monitoring the accumulation of 15N-labelled N2 and N2O evolved from 15N-labelled soil nitrate pool in closed chambers that are placed on the soil surface. Gas diffusion is considered to be the main transport process in the soil. Because accumulation of gases within the chamber decreases concentration gradients between soil and chamber over time, the surface efflux of gases decreases as well and gas production rates are underestimated if calculated from chamber concentrations without consideration of this mechanism. Moreover, concentration gradients to the non-labelled subsoil exist, inevitably causing downward diffusion of 15N labelled denitrification products. A numerical 3-D model for simulating gas diffusion in soil was used in order to determine the significance of this source of error. Results show that subsoil diffusion of 15N-labelled N2 and N2O - and thus potential underestimation of denitrification derived from chamber fluxes - increases with chamber deployment time as well as with increasing soil gas diffusivity. Simulations based on the range of typical soil gas diffusivities of unsaturated soils showed that the fraction of N2 and N2O evolved from 15N-labelled NO3 that is not emitted at the soil surface during one hour chamber closing is always significant with values up to > 50% of total production due to accumulation in the pore space of the 15N-labelled soil and diffusive flux to the unlabelled subsoil. Empirical coefficients to calculate denitrification from surface fluxes were derived by modelling multiple scenarios with varying soil water content. Field experiments with arable silt loam soil for measuring denitrification with the 15N gas flux method were conducted to obtain direct evidence for the incomplete surface emission of gaseous denitrification products. We compared surface fluxes of 15N2 and 15N2O from 15N-labelled micro-plots confined by cylinders using the closed chamber method with cylinders open or closed at the bottom, finding 37% higher surface fluxes with bottom closed. Modeling fluxes of this experiment confirmed this effect, however with a higher increase in surface flux of 89%. From our model and experimental results we conclude that field surface fluxes of 15N-labelled N2 and N2O severely underestimate denitrification rates if calculated from chamber accumulation only. The extent of this underestimation increases with closure time. Underestimation also occurs during laboratory incubations in closed systems due to pore space accumulation of 15N-labelled N2 and N2O. Due to this bias in past denitrification measurements, denitrification in soils might be more relevant than assumed to date. Corrected denitrification rates can be obtained by estimating subsurface flux and storage with our model. The observed deviation between experimental and modeled subsurface flux revealed the need for refined model evaluation which must include assessment of the spatial variability in diffusivity and production and the spatial dimension of the chamber. [ABSTRACT FROM AUTHOR]