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We derive a family of similarity solutions to the nonlinear non-equilibrium Marshak wave problem for an inhomogeneous planar medium which is coupled to a time dependent radiation driving source. We employ the non-equilibrium gray diffusion approximation in the supersonic regime. The solutions constitute a generalization of the non-equilibrium nonlinear solutions that were developed recently for homogeneous media. Self-similar solutions are constructed for a power law time dependent surface temperature, a spatial power law density profile and a material model with power law temperature and density dependent opacities and specific energy density. The extension of the problem to non-homogeneous media enables the existence of similarity solutions for a general power law specific material energy. It is shown that the solutions exist for specific values of the temporal temperature drive and spatial density exponents, which depend on the material exponents. We also illustrate how the similarity solutions take various qualitatively different forms which are analyzed with respect to various parameters. Based on the solutions, we define a set of non-trivial benchmarks for supersonic non-equilibrium radiative heat transfer. The similarity solutions are compared to gray diffusion simulations as well as to detailed implicit Monte-Carlo and discrete-ordinate transport simulations in the optically-thick regime, showing a great agreement, which highlights the benefit of these solutions as a code verification test problem., Comment: Accepted for publication in Physics of Fluids. arXiv admin note: text overlap with arXiv:2401.05138

Communication network engineering in enterprise environments is traditionally a complex, time-consuming, and error-prone manual process. Most research on network engineering automation has concentrated on configuration synthesis, often overlooking changes in the physical network topology. This paper introduces GeNet, a multimodal co-pilot for enterprise network engineers. GeNet is a novel framework that leverages a large language model (LLM) to streamline network design workflows. It uses visual and textual modalities to interpret and update network topologies and device configurations based on user intents. GeNet was evaluated on enterprise network scenarios adapted from Cisco certification exercises. Our results demonstrate GeNet's ability to interpret network topology images accurately, potentially reducing network engineers' efforts and accelerating network design processes in enterprise environments. Furthermore, we show the importance of precise topology understanding when handling intents that require modifications to the network's topology.

Elastoplastic properties of nanocrystalline metals are non-uniform on the scale of the grain size, and this non-uniformity affects macroscopic quantities as, in these systems, a significant part of the material is at or adjacent to a grain boundary. We use molecular dynamics simulations to study the spatial distributions of local elastic moduli in nano-grained pure metals and analyze their dependence on grain size. Calculations are performed for copper and tantalum with grain sizes ranging from 5-20nm. Shear modulus distributions for grain and grain-boundary atoms were calculated. It is shown that the non-crystalline grain boundary has a wide shear-modulus distribution, which is grain-size independent, while grains have a peaked distribution, which becomes sharper with increasing grain size. Average elastic moduli of the bulk, grains, and grain boundary are calculated as a function of grain size. The atomistic simulations show that the reduction of total elastic moduli with decreasing grain size is mainly due to a resulting larger grain-boundary atoms fraction, and that the total elastic moduli can be approximated by a simple weighted average of larger grains elastic moduli and a lower grain-boundary elastic moduli., Comment: Accepted for publication in Physical Review Research

We present a systematic study of the similarity solutions for the Marshak wave problem, in the local thermodynamic equilibrium (LTE) diffusion approximation and in the supersonic regime. Self-similar solutions exist for a temporal power law surface temperature drive and a material model with power law temperature dependent opacity and energy density. The properties of the solutions in both linear and nonlinear conduction regimes are studied as a function of the temporal drive, opacity and energy density exponents. We show that there exists a range of the temporal exponent for which the total energy in the system decreases, and the solution has a local maxima. For nonlinear conduction, we specify the conditions on the opacity and energy density exponents under which the heat front is linear or even flat, and does posses its common sharp character; this character is independent of the drive exponent. We specify the values of the temporal exponents for which analytical solutions exist and employ the Hammer-Rosen perturbation theory to obtain highly accurate approximate solutions, which are parameterized using only two numerically fitted quantities. The solutions are used to construct a set of benchmarks for supersonic LTE radiative heat transfer, including some with unusual and interesting properties such as local maxima and non sharp fronts. The solutions are compared in detail to implicit Monte-Carlo and discrete-ordinate transport simulations as well gray diffusion simulations, showing a good agreement, which highlights their usefulness as a verification test problem for radiative transfer simulations., Comment: Accepted for publications in Physics of Fluids

In this work, we analyze in detail the problem of piston driven shock waves in planar media. Similarity solutions to the compressible hydrodynamics equations are developed, for a strong shock wave, generated by a time dependent pressure piston, propagating in a non-homogeneous planar medium consisting of an ideal gas. Power law temporal and spatial dependency is assumed for the piston pressure and initial medium density, respectively. The similarity solutions are written in both Lagrangian and Eulerian coordinates. It is shown that the solutions take various qualitatively different forms according to the value of the pressure and density exponents. We show that there exist different families of solutions for which the shock propagates at constant speed, accelerates or slows down. Similarly, we show that there exist different types of solutions for which the density near the piston is either finite, vanishes or diverges. Finally, we perform a comprehensive comparison between the planar shock solutions and Lagrangian hydrodynamic simulations, by setting proper initial and boundary conditions. A very good agreement is reached, which demonstrates the usefulness of the analytic solutions as a code verification test problem.

Similarity solutions to the nonlinear non-equilibrium Marshak wave problem with a time dependent radiation driving source are presented. The radiation transfer model used is the gray, non-equilibrium diffusion approximation in the supersonic regime. These solutions constitute an extension of existing non-equilibrium supersonic Marshak wave solutions which are linear, to the nonlinear regime, which prevails in realistic high energy density systems. The generalized solutions assume a material model with power law temperature dependent opacities and a material energy density which is proportional to the radiation energy density, as well as a surface radiation temperature drive which obeys a temporal power-law. The solutions are analyzed in detail and it is shown that they take various qualitatively different forms according to the values of the opacity exponents. The solutions are used to construct a set of standardized benchmarks for supersonic non-equilibrium radiative heat transfer, which are nontrivial but straightforward to implement. These solutions are compared in detail to implicit Monte-Carlo and discrete-ordinate transport simulations as well gray diffusion simulations, showing a good agreement, which demonstrates the usefulness of these solutions as a code verification test problem.

We resolve a long standing question regarding the suitable effective diffusion coefficient of the spherically-symmetric transport equation, which is valid at long times. To that end, we generalize a transport solution in three dimensions for homogeneous media, to include general collisional properties, including birth-death events and linearly anisotropic scattering. This is done by introducing an exact scaling law relating the Green function of the pure-scattering case with the general collision case, which is verified using deterministic and Monte-Carlo simulations. Importantly, the effective diffusion coefficient is identified by inspecting the transport solution at long times., Comment: 9 pages, 4 figures

We consider the solutions of the Guderley problem, consisting of a converging and diverging hydrodynamic shock wave in an ideal gas with a power law initial density profile. The self-similar solutions, and specifically the reflected shock coefficient, which determines the path of the reflected shock, are studied in detail, for cylindrical and spherical symmetries and for a wide range of values of the adiabatic index and the spatial density exponent. Finally, we perform a comprehensive comparison between the analytic solutions and Lagrangian hydrodynamic simulations, by setting proper initial and boundary conditions. A very good agreement between the analytical solutions and the numerical simulations is obtained. This demonstrates the usefulness of the analytic solutions as a code verification test problem., Comment: Accepted for publication in Physics of Fluids

We consider the solutions of the Guderley problem, consisting of an imploding strong shock wave in an ideal gas with a power law initial density profile. The self-similar solutions, and specifically the similarity exponent which determines the behavior of the accelerating shock, are studied in detail, for cylindrical and spherical symmetries and for a wide range of the adiabatic index and the spatial density exponent. We then demonstrate how the analytic solutions can be reproduced in Lagrangian hydrodynamic codes, thus demonstrating their usefulness as a code validation and verification test problem.

A method for the calculation of elastic constants in the NVT ensamble, using molecular dynamics (MD) simulation with a realistic many-body embedded-atom-model (EAM) potential, is studied in detail. It is shown that in such NVT MD simulations, the evaluation of elastic constants is robust and accurate, as it gives the elastic tensor in a single simulation which converges using a small number of time steps and particles. These results highlight the applicability of this method in: (i) the calculation of local elastic constants of non-homogeneous crystalline materials and (ii) in the calibration of interatomic potentials, as a fast and accurate alternative to the common method of explicit deformation, which requires a set of consistent simulations at different conditions. The method is demonstrated for the calculation of the elastic constants of copper in the temperature range of 0-1000K, and results agree with the target values used for the potential calibration. The various contributions to the values of the elastic constants, namely, the Born, stress fluctuation and ideal gas terms, are studied as a function of temperature., Comment: Accepted for publication in Physical Review E

Analytic solutions to the nonlinear radiation diffusion equation with an instantaneous point source for a non-homogeneous medium with a power law spatial density profile, are presented. The solutions are a generalization of the well known solutions for a homogeneous medium. It is shown that the solutions take various qualitatively different forms according to the value of the spatial exponent. These different forms are studied in detail for linear and non linear heat conduction. In addition, by inspecting the generalized solutions, we show that there exist values of the spatial exponent such the conduction front has constant speed or even accelerates. Finally, the various solution forms are compared in detail to numerical simulations, and a good agreement is achieved., Comment: The following article has been accepted for publication in Physics of Fluids

In hot dense plasmas of intermediate or high-Z elements in the state of local thermodynamic equilibrium, the number of electronic configurations contributing to key macroscopic quantities such as the spectral opacity and equation of state, can be enormous. In this work we present systematic methods for the analysis of the number of relativistic electronic configurations in a plasma. While the combinatoric number of configurations can be huge even for mid-Z elements, the number of configurations which have non negligible population is much lower and depends strongly and non-trivially on temperature and density. We discuss two useful methods for the estimation of the number of populated configurations: (i) using an exact calculation of the total combinatoric number of configurations within superconfigurations in a converged super-transition-array (STA) calculation, and (ii) by using an estimate for the multidimensional width of the probability distribution for electronic population over bound shells, which is binomial if electron exchange and correlation effects are neglected. These methods are analyzed, and the mechanism which leads to the huge number of populated configurations is discussed in detail. Comprehensive average atom finite temperature density functional theory (DFT) calculations are performed in a wide range of temperature and density for several low, mid and high Z plasmas. The effects of temperature and density on the number of populated configurations are discussed and explained.

Smart city is one of the most known Internet of Things (IoT) applications. The smart city services improve user's daily lives. However, security and privacy issues are slowing down their adoption. In addition, the characteristics of IoT devices, applications and users make security implementation of the considered applications a challenging task. To address these issues, we present, in this paper, a new context-aware security and privacy architecture for the IoT. Thanks to the "as a service" approach, this new architecture will be user-centric. It will also support known context-aware security issues: dynamicity, flexibility. In addition, it will address mobility, customization of security and privacy services, and support for generic IoT applications, particularly for smart city. To do so, a knowledge plane allowing effective management of context-awareness is proposed. A security and privacy plane allowing better implementation of context-aware security and privacy mechanisms is also proposed. This will be done through dynamic composition of context-based micro services. The role of the different components of these two planes are also described.

This work extends the variance reduction method for the pricing of possibly path-dependent derivatives, which was developed in (Genin and Tankov, 2016) for exponential L\'evy models, to affine stochastic volatility models (Keller-Ressel, 2011). We begin by proving a pathwise large deviations principle for affine stochastic volatility models. We then apply a time-dependent Esscher transform to the affine process and use Varadhan's lemma, in the fashion of (Guasoni and Robertson, 2008) and (Robertson, 2010), to approximate the problem of finding the Esscher measure that minimises the variance of the Monte-Carlo estimator. We test the method on the Heston model with and without jumps to demonstrate the numerical efficiency of the method.

We prove a large deviations principle for the class of multidimensional affine stochastic volatility models considered in (Gourieroux, C. and Sufana, R., J. Bus. Econ. Stat., 28(3), 2010), where the volatility matrix is modelled by a Wishart process. This class extends the very popular Heston model to the multivariate setting, thus allowing to model the joint behaviour of a basket of stocks or several interest rates. We then use the large deviation principle to obtain an asymptotic approximation for the implied volatility of basket options and to develop an asymptotically optimal importance sampling algorithm, to reduce the number of simulations when using Monte-Carlo methods to price derivatives.

Intending to solve the decade old problem of solar opacity, we report substantial photoabsorption uncertainty due to the effect of ion-ion correlations. By performing detailed opacity calculations of the solar mixture, we find that taking into account the ionic structure changes the Rosseland opacity near the convection zone by about 10%. We also report about 15% difference in the Rosseland opacity for iron, which was recently measured at the Sandia Z facility, where the temperature reached that prevailing in the convection zone boundary while the density is 2.5 times lower. Finally, we propose a method to measure opacities at solar temperatures and densities that were never reached in the past via laboratory radiation flow experiments, by using plastic foams doped with permilles of dominant photon absorbers in the Sun. The method is advantageous for an experimental study of solar opacities that may lead to a resolution of the solar problem., Comment: Accepted for publication in ApJ

The calculation of line widths constitutes theoretical and computational challenges in the calculation of opacities of hot dense plasmas. Opacity models use line broadening approximations that are untested at stellar interior conditions. Moreover, calculations of atomic spectra of the sun, indicate a large discrepancy in the K-shell line widths between several atomic codes and the OP. In this work, the atomic code STAR is used to study the sensitivity of solar opacities to line-broadening. Variations in the solar opacity profile, due to an increase of the Stark widths resulting from discrepancies with OP, are compared, in light of the solar opacity problem, with the required opacity variations of the present day sun, as imposed by helioseismic and neutrino observations. The resulting variation profile, is much larger than the discrepancy between different atomic codes, agrees qualitatively with the missing opacity profile, recovers about half of the missing opacity nearby the convection boundary and has a little effect in the internal regions. Since it is hard to estimate quantitatively the uncertainty in the Stark widths, we show that an increase of all line widths by a factor of about 100 recovers quantitatively the missing opacity. These results emphasize the possibility that photoexcitation processes are not modeled properly, and more specifically, highlight the need for a better theoretical characterization of the line broadening phenomena at stellar interior conditions and of the uncertainty due to the way it is implemented by atomic codes., Comment: Version accepted for publication in ApJ

A new opacity model based on the Super-Transition-Array (STA) method for the calculation of monochromatic opacities of local thermodynamic equilibrium plasmas, was developed. The atomic code, named STAR (STA-Revised), is described and used to calculate spectral opacities for a solar model implementing the recent AGSS09 composition. Calculations are carried throughout the solar radiative zone. The relative contributions of different chemical elements and atomic processes to the total Rosseland mean opacity are analyzed in detail. Monochromatic opacities and charge state distributions were compared with the widely used Opacity-Project (OP) code, for several elements near the radiation-convection interface. STAR Rosseland opacities for the solar mixture show a very good agreement with OP and the OPAL opacity code, throughout the radiation zone. Finally, an explicit STA calculation of the full AGSS09 photospheric mixture, including all heavy metals was performed. It was shown that due to their extremely low abundance, and despite being very good photon absorbers, the heavy elements do not affect the Rosseland opacity., Comment: Accepted for publication (ApJ). Revised version, please use the numbers in this version

In this paper we consider the pricing of options on interest rates such as caplets and swaptions in the L\'evy Libor model developed by Eberlein and \"Ozkan (2005). This model is an extension to L\'evy driving processes of the classical log-normal Libor market model (LMM) driven by a Brownian motion. Option pricing is significantly less tractable in this model than in the LMM due to the appearance of stochastic terms in the jump part of the driving process when performing the measure changes which are standard in pricing of interest rate derivatives. To obtain explicit approximation for option prices, we propose to treat a given L\'evy Libor model as a suitable perturbation of the log-normal LMM. The method is inspired by recent works by Cern\'y, Denkl and Kallsen (2013) and M\'enass\'e and Tankov (2015). The approximate option prices in the L\'evy Libor model are given as the corresponding LMM prices plus correction terms which depend on the characteristics of the underlying L\'evy process and some additional terms obtained from the LMM model.