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In the realm of fluid dynamics, a curious and counterintuitive phenomenon is Stokes' paradox. While Stokes equations -- used for modeling slow and steady flows -- lead to a meaningful solution to the problem of slow and steady flow past a sphere, they fail to yield a non-trivial solution to the problem of slow and steady flow past an infinitely long cylinder (a two-dimensional problem essentially); this is referred to as Stokes' paradox. We revisit this paradox in the context of rarefied gas flows by means of the method of fundamental solutions (MFS). To this end, we adopt an extended hydrodynamic model, referred to as the CCR model, consisting of the balance equations for the mass, momentum and energy and closed with the coupled constitutive relations. We determine an analytic solution of the CCR model for the problem and compare it with the MFS-based numerical solution. Apart from addressing flow past a circular cylinder, we aim to showcase the capability of the MFS to predict the flow past other objects in two dimensions for which the analytic solutions do not exist. For that, we investigate the problem of rarefied gas flow past an infinitely long semicircular cylinder., Comment: 28 Pages, 16 figures

In this study, we enhance the Maximum Entropy Deep Inverse Reinforcement Learning (MEDIRL) framework, targeting its application in human robot interaction (HRI) for modeling pedestrian behavior in crowded environments. Our work is grounded in the pioneering research by Fahad, Chen, and Guo, and aims to elevate MEDIRL's efficacy in real world HRI settings. We replicated the original MEDIRL model and conducted detailed ablation studies, focusing on key model components like learning rates, state dimensions, and network layers. Our findings reveal the effectiveness of a two dimensional state representation over three dimensional approach, significantly improving model accuracy for pedestrian behavior prediction in HRI scenarios. These results not only demonstrate MEDIRL's enhanced performance but also offer valuable insights for future HRI system development, emphasizing the importance of model customization to specific environmental contexts. Our research contributes to advancing the field of socially intelligent navigation systems, promoting more intuitive and safer human robot interactions., Comment: 14 pages, 13 figures

The inability of the Navier-Stokes-Fourier equations to capture rarefaction effects motivates us to adopt the extended hydrodynamic equations. In the present work, a hydrodynamic model, which consists of the conservation laws closed with the recently propounded coupled constitutive relations (CCR), is utilized. This model is referred to as the CCR model and is adequate for describing moderately rarefied gas flows. A numerical framework based on the method of fundamental solutions is developed to solve the CCR model for rarefied gas flow problems in quasi two dimensions. To this end, the fundamental solutions of the linearized CCR model are derived in two dimensions. The significance of deriving the two-dimensional fundamental solutions is that they cannot be deduced from their three-dimensional counterparts that do exist in literature. As applications, the developed numerical framework based on the derived fundamental solutions is used to simulate (i) a rarefied gas flow between two coaxial cylinders with evaporating walls and (ii) a temperature-driven rarefied gas flow between two non-coaxial cylinders. The results for both problems have been validated against those obtained with the other classical approaches. Through this, it is shown that the method of fundamental solutions is an efficient tool for addressing quasi two-dimensional multiphase microscale gas flow problems at a low computational cost. Moreover, the findings also show that the CCR model solved with the method of fundamental solutions is able to describe rarefaction effects, like transpiration flows and thermal stress, generally well., Comment: 18 pages, 15 figures

Experimental and theoretical studies on millimetre-sized droplets suggest that at low Reynolds number the difference between the drag force on a circulating water droplet and that on a rigid sphere is very small (less than 1 %) (LeClair et al., J. Atmos. Sci., vol. 29, 1972, pp. 728-740). While the drag force on a spherical liquid droplet at high viscosity ratios (of the liquid to the gas), is approximately the same as that on a rigid sphere of the same size, the other quantities of interest (e.g. the temperature) in the case of a rarefied gas flow over a liquid droplet differ from the same quantities in the case of a rarefied gas flow over a rigid sphere. The goal of this article is to study the effects of internal motion within a spherical microdroplet/nanodroplet -- such that its diameter is comparable to the mean free path of the surrounding gas -- on the drag force and its overall dynamics. To this end, the problem of a slow rarefied gas flowing over an incompressible liquid droplet is investigated analytically by considering the internal motion of the liquid inside the droplet and also by accounting for kinetic effects in the gas. Detailed results for different values of the Knudsen number, the ratio of the thermal conductivities and the ratio of viscosities are presented for the pressure and temperature profiles inside and outside the liquid droplet. The results for the drag force obtained in the present work are in good agreement with the theoretical and experimental results existing in the literature., Comment: 39 pages, 15 figures

Determining physically admissible boundary conditions for higher moments in an extended continuum model is recognised as a major obstacle. Boundary conditions for the regularised 26-moment (R26) equations obtained using Maxwell's accommodation model do exist in the literature; however, we show in this article that these boundary conditions violate the second law of thermodynamics and the Onsager reciprocity relations for certain boundary value problems, and, hence, are not physically admissible. We further prove that the linearised R26 (LR26) equations possess a proper $H$-theorem (second-law inequality) by determining a quadratic form without cross-product terms for the entropy density. The establishment of the $H$-theorem for the LR26 equations in turn leads to a complete set of boundary conditions that are physically admissible for all processes and comply with the Onsager reciprocity relations. As an application, the problem of a slow rarefied gas flow past a spherical droplet with and without evaporation is considered and solved analytically. The results are compared with the numerical solution of the linearised Boltzmann equation, experimental results from the literature and/or other macroscopic theories to show that the LR26 theory with the physically admissible boundary conditions provides an excellent prediction up to Knudsen number $\,\lesssim 1$ and, consequently, provides transpicuous insights into intriguing effects, such as thermal polarisation. In particular, the analytic results for the drag force obtained in the present work are in an excellent agreement with experimental results even for very large values of the Knudsen number., Comment: 40 pages, 12 figures

Recently, generative machine-learning models have gained popularity in physics, driven by the goal of improving the efficiency of Markov chain Monte Carlo techniques and of exploring their potential in capturing experimental data distributions. Motivated by their ability to generate images that look realistic to the human eye, we here study generative adversarial networks (GANs) as tools to learn the distribution of spin configurations and to generate samples, conditioned on external tuning parameters, such as temperature. We propose ways to efficiently represent the physical states, e.g., by exploiting symmetries, and to minimize the correlations between generated samples. We present a detailed evaluation of the various modifications, using the two-dimensional XY model as an example, and find considerable improvements in our proposed implicit generative model. It is also shown that the model can reliably generate samples in the vicinity of the phase transition, even when it has not been trained in the critical region. On top of using the samples generated by the model to capture the phase transition via evaluation of observables, we show how the model itself can be employed as an unsupervised indicator of transitions, by constructing measures of the model's susceptibility to changes in tuning parameters., Comment: 15 pages, 4 figures, 3 tables

One prototypical instability in granular flows is the shear-banding instability, in which a uniform granular shear flow breaks into alternating bands of dense and dilute clusters of particles having low and high shear (shear stress or shear rate), respectively. In this work, the shear-banding instability in an arbitrarily inelastic granular shear flow is analyzed through the linear stability analysis of granular hydrodynamic equations closed with Navier--Stokes-level constitutive relations. It is shown that the choice of appropriate constitutive relations plays an important role in predicting the shear-banding instability. A parametric study is carried out to study the effect of the restitution coefficient, channel width and mean density. Two global criteria relating the control parameters are found for the onset of the shear-banding instability., Comment: 21 pages, 11 figures (accepted for publication in Physical Review E)

Various systems of moment equations---consisting of up to (d+3)(d^2+6d+2)/6 moments---in a general dimension d for a dilute granular gas composed of Maxwell molecules are derived from the inelastic Boltzmann equation by employing the Grad moment method. The Navier--Stokes-level constitutive relations for the stress and heat flux appearing in the system of mass, momentum and energy balance equations are determined from the derived moment equations. It has been shown that the moment equations only for the hydrodynamic field variables (density, velocity and granular temperature), stress and heat flux---along with the time-independent value of the fourth cumulant---are sufficient for determining the Navier--Stokes-level constitutive relations in the case of inelastic Maxwell molecules, and that the other higher-order moment equations do not play any role in this case. The homogeneous cooling state of a freely cooling granular gas is investigated with the system of the Grad (d+3)(d^2+6d+2)/6-moment equations and its various subsystems. By performing a linear stability analysis in the vicinity of the homogeneous cooling state, the critical system size for the onset of instability is estimated through the considered Grad moment systems. The results on critical system size from the presented moment theories are found to be in reasonably good agreement with those from simulations., Comment: 55 pages, 13 figures (accepted version)

High-temperature operation of metal-semiconductor-metal (MSM) UV photodetectors fabricated on pulsed laser deposited \b{eta}-Ga2O3 thin films has been investigated. These photodetectors were operated up to 250 {\deg}C temperature under 255 nm illumination. The photo current to dark current (PDCR) ratio of about 7100 was observed at room temperature (RT) while it had a value 2.3 at 250 {\deg}C at 10 V applied bias. A decline in photocurrent was observed from RT to 150 {\deg}C and then it increased with temperature up to 250 {\deg}C. The suppression of the blue band was also observed from 150 {\deg}C temperature which indicated that self-trapped holes in Ga2O3 became unstable. Temperature-dependent rise and decay times of carriers were analyzed to understand the photocurrent mechanism and persistence photocurrent at high temperatures. Coupled electron-phonon interaction with holes was found to influence the photoresponse in the devices. The obtained results are encouraging and significant for high-temperature applications of \b{eta}-Ga2O3 MSM deep UV photodetectors.