Particle Approximation Research Articles

Why heterogeneous cloud particles matter. Iron-bearing species and cloud particle morphology affect exoplanet transmission spectra

The possibility of observing spectral features in exoplanet atmospheres with space missions like the James Webb Space Telescope (JWST) and Atmospheric Remote-sensing Infrared Exoplanet Large-survey (ARIEL) necessitates the accurate modelling of cloud particle opacities. In exoplanet atmospheres, cloud particles can be made from multiple materials and be considerably chemically heterogeneous. Therefore, assumptions on the morphology of cloud particles are required to calculate their opacities. The aim of this work is to analyse how different approaches to calculate the opacities of heterogeneous cloud particles affect the optical properties of cloud particles and how this may influence the interpretation of data observed by JWST and future missions. We calculated cloud particle optical properties using seven different mixing treatments: four effective medium theories (EMTs; Bruggeman, Landau-Lifshitz-Looyenga (LLL), Maxwell-Garnett, and Linear), core-shell, and two homogeneous cloud particle approximations. We conducted a parameter study using two-component materials to study the mixing behaviour of 21 commonly considered cloud particle materials for exoplanets. To analyse the impact on observations, we studied the transmission spectra of HATS-6b, WASP-39b, WASP-76b, and WASP-107b. Materials with large refractive indices, like iron-bearing species or carbon, can change the optical properties of cloud particles when they comprise less than 1<!PCT!> of the total particle volume. The mixing treatment of heterogeneous cloud particles also has an observable effect on transmission spectroscopy. Assuming core-shell or homogeneous cloud particles results in less muting of molecular features and retains the cloud spectral features of the individual cloud particle materials. The predicted transit depths for core-shell and homogeneous cloud particle materials are similar for all planets used in this work. If EMTs are used, cloud spectral features are broader and the cloud spectral features of the individual cloud particle materials are not retained. Using LLL leads to fewer molecular features in transmission spectra than when using Bruggeman.

Gaussian smoothed particle hydrodynamics: A high-order meshfree particle method

Smoothed particle hydrodynamics (SPH) has attracted significant attention in recent decades, and exhibits special advantages in modeling complex flows with multiphysics processes and complex phenomena. Its accuracy depends heavily on the distribution of particles, and will generally be lower if the particles are distributed non-uniformly. A high-order SPH scheme is proposed in the present work for simulating both compressible and incompressible flows. It uses a Gaussian quadrature rule to perform the particle approximation of SPH by introducing Gaussian nodes. Unfortunately, the Gaussian nodes hardly overlap with SPH particles due to the Lagrangian feature, and thus we use a high-order interpolation method to obtain the corresponding physical quantities at the Gaussian nodes. The accuracy and robustness of the proposed Gaussian SPH are demonstrated by several numerical tests, including the Sod problem, Poiseuille flow, Couette flow, cavity flow, Taylor–Green vortex and dam break flow, and a convergence analysis is also conducted to evaluate the effects of particle resolution and distribution for reconstructing a given function. The simulation results for each test case are in good agreements with the available analytical, experimental or numerical results, showing that the proposed Gaussian SPH method is accurate and reliable but expensive for simulating compressible and incompressible flow problems.

Gedanken experiments to destroy a black hole by a test particle: Multiply charged black hole with higher derivative corrections

We investigate a gedanken experiment to destroy an extremally charged black hole by dropping a test particle, provided that there are multiple U(1) gauge fields coupled with each other through higher derivative interactions. It is known that the Coulomb repulsion prevents a test particle that would break the extremal condition from falling into an extremal black hole and therefore the black hole cannot be destroyed. We extend this observation to include higher derivative corrections. Although the extremal condition is modified by the higher derivative interactions, we find that the repulsive force induced by the higher derivative couplings is responsible for preventing a test particle that would break the modified extremal condition to reach the event horizon. Thus, we confirm that the weak cosmic censorship conjecture holds for extremally charged black holes even in the presence of higher derivative corrections, as long as the test particle approximation is justified. Published by the American Physical Society 2024

A hydrodynamic approach to reproduce multiple spinning vortices in horizontally rotating three-dimensional liquid helium-4

This paper reports a three-dimensional (3D) simulation of a rotating liquid helium-4, using a two-fluid model with spin-angular momentum conservation. Our model was derived from the particle approximation of an inviscid fluid with residual viscosity. Despite the fully classical mechanical picture, the resulting system equations were consistent with those of the conventional two-fluid model. We consider bulk liquid helium-4 to be an inviscid fluid, assuming that the viscous fluid component remains at finite temperatures. As the temperature decreased, the amount of the viscous fluid component decreased, ultimately becoming a fully inviscid fluid at absolute zero. Weak compressibility is assumed to express the volume change because some helium atoms do not render fluid owing to Bose–Einstein condensations or change states because of local thermal excitation. One can solve the governing equations for an incompressible fluid using explicit smoothed-particle hydrodynamics, simultaneously reproducing density fluctuations and describing the fluid in a many-particle system. We assume the following fluid–particle duality: a hydrodynamic interfacial tension between the inviscid and viscous components or a local interaction force between two types of fluid particles. The former can be induced in the horizontal direction when non-negligible non-uniformity of the particles occurs during forced two-dimensional rotation, and the latter is non-negligible when the former is negligible. We performed a large-scale simulation of 3D liquid helium forced to rotate horizontally using 32 graphics processing units. Compared with the low-resolution calculation using 2.4 × 106 particles, the high-resolution calculation using 19.6 × 106 particles showed spinning vortices close to those of the theoretical solution. We obtained a promising venue to establish a practical simulation method for bulk liquid helium-4.

Application of Improved SPH Method in Solving Time Fractional Schrödinger Equation

In this paper, a pure meshless method for solving the time fractional Schrödinger equation (TFSE) based on KDF-SPH method is presented. The method is used for the first time to numerically solve the TFSE. The method utilizes the finite difference method (FDM) to approximate the time fractional-order derivative defined in the Caputo sense. The spatial derivatives are discretized by the KDF-SPH meshless method. Expressions for the kernel approximation and the particle approximation are provided. To ensure the validity and flexibility of the numerical calculations, we conducted numerical simulations of one- and two-dimensional linear/nonlinear time Schrödinger equations (1D/2D TFLSE/TF-NLSE) in both bounded and unbounded regions. We also examined nonlinear time fractional Schrödinger equations that lack analytical solutions and compared our method with other meshless methods. Numerical results show that the proposed method can approximate to the second-order precision in space, which verifies the effectiveness and accuracy of the proposed method.

From Bulk to one-dimensional MoS2 nanochains: evolution of electronic, mechanical, and optical properties

We theoretically investigate the stability of a MoS2 nanochain, reporting its electronic, mechanical, and optical properties. The nanochain presents a semiconductor structure with a minute band gap of 67m eV compared to the larger gap bulk and monolayer structures. It is more malleable, enduring a maximum compressive (tensile) strain of 6% (6.5%). It is dynamically stable, showing no negative frequencies along its Brillouin zone (BZ) path. The nanochain is thermally stable at 300K, making it possible to synthesize as a freestanding structure. The optical properties of the bulk, monolayer, and 1D MoS2 materials are evaluated using the time-dependent density functional perturbation theory (TDDFPT) and compared to those determined via the independent particle approximation (IPA). Along the nanochain’s periodic x direction, the reflectivity retains a maximum value of ∼68% in the infrared (IR) region. Furthermore, its optical conductivity also exhibits a peak within the IR regime. These two features make such nanochains suitable as coating materials in applications involving infrared radiation or can even be exploited as conductive substrates in near-IR devices.

Opinion formation on evolving network: the DPA method applied to a nonlocal cross-diffusion PDE-ODE system

Abstract We study a system of nonlocal aggregation cross-diffusion PDEs that describe the evolution of opinion densities on a network. The PDEs are coupled with a system of ODEs that describe the time evolution of the agents on the network. Firstly, we apply the Deterministic Particle Approximation (DPA) method to the aforementioned system in order to prove the existence of solutions under suitable assumptions on the interactions between agents. Later on, we present an explicit model for opinion formation on an evolving network. The opinions evolve based on both the distance between the agents on the network and the ’attitude areas’, which depend on the distance between the agents’ opinions. The position of the agents on the network evolves based on the distance between the agents’ opinions. The goal is to study radicalisation, polarisation and fragmentation of the population while changing its open-mindedness and the radius of interaction.

Solving a class of Fredholm integral equations of the first kind via Wasserstein gradient flows

Solving Fredholm equations of the first kind is crucial in many areas of the applied sciences. In this work we consider integral equations featuring kernels which may be expressed as scalar multiples of conservative (i.e. Markov) kernels and we adopt a variational point of view by considering a minimization problem in the space of probability measures with an entropic regularization. Contrary to classical approaches which discretize the domain of the solutions, we introduce an algorithm to asymptotically sample from the unique solution of the regularized minimization problem. As a result our estimators do not depend on any underlying grid and have better scalability properties than most existing methods. Our algorithm is based on a particle approximation of the solution of a McKean–Vlasov stochastic differential equation associated with the Wasserstein gradient flow of our variational formulation. We prove the convergence towards a minimizer and provide practical guidelines for its numerical implementation. Finally, our method is compared with other approaches on several examples including density deconvolution and epidemiology.

Energy and Z dependence of low velocity Nq+ ion induced M X-ray relative intensities for some heavy elements

The intensity ratios, IMk/IMn (exp)(k = ξ, γ, m1; n = total, αβ), for some heavy elements, 70Yb, 79Au, 81Tl, 82Pb and 83Bi induced by 1000 keV−1750 keV Nq+ (q = 4, 5) ions have been measured in order to investigate their dependence on the projectile energy and atomic number of the respective target elements. The measured intensity ratios have been compared with two sets of values calculated using the Mj (j = 1–5) sub-shell ionization cross sections based on the ECPSSR-UA model, the X-ray emission rates based on the Dirac-Hartree Slater (DHS) model, two sets of the fluorescence and Coster-Kronig yields based on the DHS model and those evaluated by McGuire employing non-relativistic Hartree-Slater model. Significant differences have been observed between the present measured IMk/IMαβ (exp) (k = ξ, γ, m1) intensity ratios and those calculated using independent particle approximation (IPA) models based single atomic vacancy state physical parameters.

Unveiling the Electronic Structure of SnS for Photocatalytic Applications: A DFT Approach†

AbstractPhotocatalytic materials are of great scientific interest due to their potential applications in sustainable energy sources. Band gap and optical absorption of the materials are two core characteristics for photocatalysis that eventually depend on electronic structure. In order to accurately compute (predict) the electronic‐scale properties of a crystalline solid using first principles calculations, which might be costly to measure experimentally, large‐scale atomic level calculation frameworks have been made possible through the use of density functional theory (DFT). We have used DFT with many body perturbation theory (MBPT) by solving the bethe‐salpeter equation (BSE) to priorly predict the properties of bulk tin sulfide (SnS) as it meets the necessary requirements for photocatalytic applications. We fixed the DFT band gap underestimation by including the Hubbard parameter (U) and used projector augmented wave pseudo‐potentials with generalized‐gradient approximation (GGA) to calculate the electronic and optical properties of SnS. Optical properties were computed using independent particle approximation (IPA) and BSE with DFT+U wave functions. Our theoretical results align with experimental data for this material, demonstrating the potential for further research in validating experimental results with theoretical approximations and empirical relations.

Meshless Generalized Finite Difference Method Based on Nonlocal Differential Operators for Numerical Simulation of Elastostatics

This study proposes an innovative meshless approach that merges the peridynamic differential operator (PDDO) with the generalized finite difference method (GFDM). Based on the PDDO theory, this method introduces a new nonlocal differential operator that aims to reduce the pre-assumption required for the PDDO method and simplify the calculation process. By discretizing through the particle approximation method, this technique proficiently preserves the PDDO’s nonlocal features, enhancing the numerical simulation’s flexibility and usability. Through the numerical simulation of classical elastic static problems, this article focuses on the evaluation of the calculation accuracy, calculation efficiency, robustness, and convergence of the method. This method is significantly stronger than the finite element method in many performance indicators. In fact, this study demonstrates the practicability and superiority of the proposed method in the field of elastic statics and provides a new approach to more complex problems.

Nonlocal approximation of nonlinear diffusion equations

We show that degenerate nonlinear diffusion equations can be asymptotically obtained as a limit from a class of nonlocal partial differential equations. The nonlocal equations are obtained as gradient flows of interaction-like energies approximating the internal energy. We construct weak solutions as the limit of a (sub)sequence of weak measure solutions by using the Jordan-Kinderlehrer-Otto scheme from the context of 2-Wasserstein gradient flows. Our strategy allows to cover the porous medium equation, for the general slow diffusion case, extending previous results in the literature. As a byproduct of our analysis, we provide a qualitative particle approximation.

Optimal transport with nonlinear mobilities: A deterministic particle approximation result

Abstract We study the discretisation of generalised Wasserstein distances with nonlinear mobilities on the real line via suitable discrete metrics on the cone of N ordered particles, a setting which naturally appears in the framework of deterministic particle approximation of partial differential equations. In particular, we provide a Γ-convergence result for the associated discrete metrics as N → ∞ {N\to\infty} to the continuous one and discuss applications to the approximation of one-dimensional conservation laws (of gradient flow type) via the so-called generalised minimising movements, proving a convergence result of the schemes at any given discrete time step τ > 0 {\tau>0} . This the first work of a series aimed at sheding new lights on the interplay between generalised gradient-flow structures, conservation laws, and Wasserstein distances with nonlinear mobilities.

Concentration of measure for graphon particle system

Abstract We study heterogeneously interacting diffusive particle systems with mean-field-type interaction characterized by an underlying graphon and their finite particle approximations. Under suitable conditions, we obtain exponential concentration estimates over a finite time horizon for both 1- and 2-Wasserstein distances between the empirical measures of the finite particle systems and the averaged law of the graphon system.

Probability measures on path space for rectilinear damped pressureless Euler-Poisson equations

We show global existence of a measure-valued solution to the Cauchy problem for the rectilinear Euler-Poisson equations, which govern flow of pressureless dust experiencing linear damping in the gravitational field generated by its own mass, and a given background charge field modeling exterior gravitational force. The velocity of the dust is a Borel measurable function, and the distribution of mass is given by time-dependent probability measures on the real line. Upon adapting the method established in Hynd (2020) [25], we obtain the solution by construction of a probability measure on the path space, through approximation of finite sticky particles.

The effect of Ficoll 70 on thermally-induced and chemically-induced conformational transitions of an RTX protein is quantitatively accounted for by a unified excluded volume model.

A unified excluded volume model based upon the effective hard particle approximation is developed and used to quantitatively model previously published experimental measurements of the effect of adding high concentrations of an "inert" polymer, Ficoll 70, on conformational transitions of the toxin protein RCL that are induced by addition of calcium at constant temperature or by increasing temperature in the absence and presence of high calcium concentrations. The best-fit of this model, which accounts quantitatively for all of the published data to within experimental precision, yields an estimate of the volume of solution excluded to Ficoll by each of four identified conformational states of RCL: H - the most compact conformation adopted in the limits of high calcium concentration and low temperature, H* - the conformation adopted in the limits of high calcium concentration and high temperature, A - the conformation adopted in the limits of low (or no) calcium at low temperature, and A* - the conformation adopted in the limits of low calcium and high temperature. Ficoll exclusion volumes increase in the order H < H* < A < A*. These results are discussed in the context of the physiological functions of the RTX proteins, which are involved in the secretion process and the calcium-induced folding of bacterial virulence factors.

Approximate Gibbsian structure in strongly correlated point fields and generalized Gaussian zero ensembles

AbstractGibbsian structure in random point fields has been a classical tool for studying their spatial properties. However, exact Gibbs property is available only in a relatively limited class of models, and it does not adequately address many random fields with a strongly dependent spatial structure. In this work, we provide a very general framework for approximate Gibbsian structure for strongly correlated random point fields, including those with a highly singular spatial structure. These include processes that exhibit strong spatial rigidity, in particular, a certain one‐parameter family of analytic Gaussian zero point fields, namely the ‐GAFs, that are known to demonstrate a wide range of such spatial behavior. Our framework entails conditions that may be verified via finite particle approximations to the process, a phenomenon that we call an approximate Gibbs property. We show that these enable one to compare the spatial conditional measures in the infinite volume limit with Gibbs‐type densities supported on appropriate singular manifolds, a phenomenon we refer to as a generalized Gibbs property. Our work provides a general mechanism to rigorously understand the limiting behavior of spatial conditioning in strongly correlated point processes with growing system size. We demonstrate the scope and versatility of our approach by showing that a generalized Gibbs property holds with a logarithmic pair potential for the ‐GAFs for any value of . In this vein, we settle in the affirmative an open question regarding the existence of point processes with any specified level of rigidity. In particular, for the ‐GAF zero process, we establish the level of rigidity to be exactly , a fortiori demonstrating the phenomenon of spatial tolerance subject to the local conservation of moments. For such processes involving complex, many‐body interactions, our results imply that the local behavior of the random points still exhibits 2D Coulomb‐type repulsion in the short range. Our techniques can be leveraged to estimate the relative energies of configurations under local perturbations, with possible implications for dynamics and stochastic geometry on strongly correlated random point fields.

Optimization of the sensitivity of the magnetoimpedance sensor of small magnetic fields by methods of sequential approximation and swarm of particles

The use of multiparametric optimization of an unknown discrete function in the development of applied solutions for physical systems is considered. Such optimization is practically implemented in real time using modern data transfer protocols at high speed and continuously increasing computing power. To optimize the sensitivity of a modern magnetic sensor based on high-frequency magnetoimpedance in ferromagnetic microconducts, an iterative method of global maximum search, the particle swarm algorithm, has been applied. The output signal of the sensor depends non-linearly on both the internal magnetic properties of the microcircuit and the excitation mode, which requires a certain calibration to establish optimal excitation parameters. The sensor output signals for various excitation parameters and external magnetic fields were measured using an automated installation. The results of the search for the global maximum by the sequential approximation method and the particle swarm method presented in the paper demonstrate the effectiveness of the search algorithm used, the particle swarm algorithm turned out to be the most effective, since it found the global maximum more accurately. With different excitation parameters, the algorithm has always determined the maximum sensitivity when varying the three main parameters of the excitation signal: frequency, amplitude and constant component. The results obtained can be applied in the development of highly sensitive intelligent magnetic sensors and systems based on them.

Black Phosphorene/MoS2 van der Waals heterostructure: Electronic and optical properties

In this study, we use density functional theory to calculate the optical and electronic properties of a black-phosphorene/MoS2 stack. We have considered different exchange–correlation functionals to account for the effects of van der Waals interaction and examined the impact of stacking order/layers alignment on the opto-electronic properties. Our findings reveal that the heterostructure exhibits a reduction in band gap and a modification of optical properties compared to single monolayers. The optical response was evaluated using an independent particle approximation to get the dielectric function’s imaginary part, which showed a strong absorption peak in the visible and ultraviolet regions. This feature could be helpful for optoelectronic applications. Nonetheless, the stacking order has a negligible effect on the electronic and optical properties of the BP/MoS2 bilayer.

P-wave Sommerfeld enhancement near threshold: a simplified approach

The calculation of P-wave Sommerfeld enhancement in processes with unstable particles in the final state is known to be divergent. In a complete description, where resonant (on-shell unstable particles) and non-resonant contributions are included, it has been shown that results are finite. For most beyond the Standard Model applications, these complete calculations are not readily available. In this work, we are interested in the near-threshold region and we consider only the resonant contribution. In this case, we provide a simplified prescription to compute the P-wave Sommerfeld enhancement in the narrow-width approximation of the unstable particle that directly eliminates divergences. We show that we can define a finite resonant contribution without the inclusion of the non-resonant processes in a way similar to the usual S-wave Sommerfeld enhancement.