Arbitrary Density Research Articles

A novel vector potential random flow generation method for synthesizing divergence-free homogeneous isotropic turbulence with arbitrary spectra

A novel method, known as the vector potential random flow generation (VPRFG) method, is introduced for synthesizing divergence-free homogeneous isotropic turbulence with arbitrary spectra. First, the proposed approach employs the random-flow-generation-based method to create a vector potential field. Subsequent application of the curl operation to this field produces a turbulent flow that inherently satisfies the divergence-free condition. In the formulas of the proposed method, we explicitly impose arbitrary homogeneous isotropic three-dimensional spatial cross-spectral density (CSD) and Taylor's frozen hypothesis. This ensures that the generated turbulence conforms to prescribed statistical characteristics, including energy spectra, one-dimensional spatial power spectral density (PSD), temporal PSD, spatial coherence function, turbulent kinetic energy, and Reynolds stress. Additionally, the theoretical accuracy of the proposed method is validated through numerical examples, employing the von Kármán energy spectrum as the target value. Finally, large eddy simulations of homogeneous isotropic temporal-decaying box turbulence generated by the VPRFG method demonstrate a close alignment with the experimental results.

Time-dependent properties of run-and-tumble particles: Density relaxation.

We characterize collective diffusion of hardcore run-and-tumble particles (RTPs) by explicitly calculating the bulk-diffusion coefficient D(ρ,γ) for arbitrary density ρ and tumbling rate γ, in systems on a d-dimensional periodic lattice. We study two minimal models of RTPs: Model I is the standard version of hardcore RTPs introduced in [Phys. Rev. E 89, 012706 (2014)10.1103/PhysRevE.89.012706], whereas model II is a long-ranged lattice gas (LLG) with hardcore exclusion, an analytically tractable variant of model I. We calculate the bulk-diffusion coefficient analytically for model II and numerically for model I through an efficient Monte Carlo algorithm; notably, both models have qualitatively similar features. In the strong-persistence limit γ→0 (i.e., dimensionless ratio r_{0}γ/v→0), with v and r_{0} being the self-propulsion speed and particle diameter, respectively, the fascinating interplay between persistence and interaction is quantified in terms of two length scales: (i) persistence length l_{p}=v/γ and (ii) a "mean free path," being a measure of the average empty stretch or gap size in the hopping direction. We find that the bulk-diffusion coefficient varies as a power law in a wide range of density: D∝ρ^{-α}, with exponent α gradually crossing over from α=2 at high densities to α=0 at low densities. As a result, the density relaxation is governed by a nonlinear diffusion equationwith anomalous spatiotemporal scaling. In the thermodynamic limit, we show that the bulk-diffusion coefficient-for ρ,γ→0 with ρ/γ fixed-has a scaling form D(ρ,γ)=D^{(0)}F(ρav/γ), where a∼r_{0}^{d-1} is particle cross sectionand D^{(0)} is proportional to the diffusion coefficient of noninteracting particles; the scaling function F(ψ) is calculated analytically for model II (LLG) and numerically for model I. Our arguments are independent of dimensions and microscopic details.

Investigation of Excess Thermo‐Acoustic Behavior of Binary Liquid Mixture with Various Temperatures Using Ultrasonic Technique

AbstractUltrasonic methods have been very fruitful in studying the physical properties of binary liquid combinations. In this present study, the thermoacoustic behavior of benzyl propionate with dimethyl sulfoxide (DMSO) is observed using ultrasound, density, and viscosity at different temperatures between 308 and 328 K with a phase of 10 °C. Benzyl propionate is a sweet‐smelling liquid that is used in the botanical and fruit fragrance industries, as well as in the flavoring of organic products. DMSO is a dipolar aprotic, naturally soluble compound used for slow drug synthesis, device synthesis, and drug delivery to the body. Estimated values such as adiabatic compressibility, intermolecular free length, internal pressure, and free volume are determined from arbitrary ultrasonic velocity, density, and viscosity data. The same excess parameters of adiabatic compressibility, intermolecular free length, internal pressure, and free volume support finding the nature of the reaction. The sort of interactions has been accounted for utilizing these qualities. In the present work, benzyl propionate with dimethyl sulfoxide has been characterized by using ultrasonic waves and since this wave is a well‐known tool for NDT, so the mixture is properly characterized. These thermoacoustic parameters with different concentrations of DMSO at different temperatures have been used to study the complex formation and binding through intermolecular forces.

General vorticity‐streamfunction formulation for incompressible binary flow with arbitrary density ratio

AbstractThe classical vorticity‐streamfunction formulation (VSF) can avoid the difficulty in the calculation of pressure gradient term of the Navier Stokes equation via eliminating pressure gradient term from the theoretical basis. Within this context we propose a general VSF, together with redefined vorticity and streamfunction, so as to realize numerically stable and reliable simulations of binary fluids with an arbitrary density contrast. By incorporating the interface‐tracking phase‐field model based on the conservative Allen‐Cahn equation [Phys. Rev. E 94, 023311 (2016)], the binary flow simulation framework is established. Numerical tests are conducted using the Lattice Boltzmann method (LBM), which is usually regarded as an easy‐to‐use tool for solving the Navier–Stokes equation but generally suffers from the drawback of not being capable of enforcing incompressibility. The LBM herein functions as a numerical tool for solving the vorticity transport equation, the streamfunction equation, and the conservative Allen‐Cahn equation. Three two‐dimensional benchmark cases, i.e., the Capillary wave, the Rayleigh–Taylor instability, and the droplet splashing on a thin liquid film, are discussed in detail to verify the present methodology. Results show good agreements with both analytical predictions and literature data, as well as good numerical stability in terms of high density ratio and high Reynolds number. Overall, the general VSF inherits the intrinsic superiority of the classical VSF in enforcing incompressibility, and offers a useful and reliable alternative for binary flow modeling.

Numerical model for linear stimulated Raman scattering in inhomogeneous plasmas

Numerical model for calculating convective gains and absolute thresholds of stimulated Raman scattering (SRS) in inhomogeneous plasmas is constructed based on the Fourier-space method. The model is valid for arbitrary density profiles and scattering geometries, including both backscattering and side scattering. It is shown that 90 deg side scatter has a lower absolute threshold than other scattering geometries. Backscatter, on the other hand, has a relatively large absolute threshold under conventional direct-drive ignition conditions. For a parabolic density profile, the absolute threshold of backscatter decreases dramatically at the peak of parabola, but is still much larger than that of side scatter. We also discuss the absolute thresholds of side scatter under different density profiles, showing not big differences with the linear density profile as well as the analytic formulas. Convective gains, however, are sensitive to the density profiles and collisional damping. The k-space numerical model is verified via analytic formulas and real-space envelope model, and it offers us new perspective on the scattering angles compared with previous models for SRS.

Fundamental limits of parasitoid-driven host population suppression: Implications for biological control.

Parasitoid wasps are increasingly being used to control insect pest populations, where the pest is the host species parasitized by the wasp. Here we use the discrete-time formalism of the Nicholson-Bailey model to investigate a fundamental question-are there limits to parasitoid-driven suppression of the host population density while still ensuring a stable coexistence of both species? Our model formulation imposes an intrinsic self-limitation in the host's growth resulting in a carrying capacity in the absence of the parasitoid. Different versions of the model are considered with parasitism occurring at a developmental stage that is before, during, or after the growth-limiting stage. For example, the host's growth limitation may occur at its larval stage due to intraspecific competition, while the wasps attack either the host egg, larval or pupal stage. For slow-growing hosts, models with parasitism occurring at different life stages are identical in terms of their host suppression dynamics but have contrasting differences for fast-growing hosts. In the latter case, our analysis reveals that wasp parasitism occurring after host growth limitation yields the lowest pest population density conditioned on stable host-parasitoid coexistence. For ecologically relevant parameter regimes we estimate this host suppression to be roughly 10-20% of the parasitoid-free carrying capacity. We further expand the models to consider a fraction of hosts protected from parasitism (i.e., a host refuge). Our results show that for a given host reproduction rate there exists a critical value of protected host fraction beyond which, the system dynamics are stable even for high levels of parasitism that drive the host to arbitrary low population densities. In summary, our systematic analysis sheds key insights into the combined effects of density-dependence in host growth and parasitism refuge in stabilizing the host-parasitoid population dynamics with important implications for biological control.

From ray to spray: augmenting amplitudes and taming fast oscillations in fully numerical neutrino codes

In this note we describe how to complement the neutrino evolution matrix calculated at a given energy and trajectory with additional information which allows to reliably extrapolate it to nearby energies or trajectories without repeating the full computation. Our method works for arbitrary matter density profiles, can be applied to any propagation model described by an Hamiltonian, and exactly guarantees the unitarity of the evolution matrix. As a straightforward application, we show how to enhance the calculation of the theoretical predictions for experimentally measured quantities, so that they remain accurate even in the presence of fast neutrino oscillations. Furthermore, the ability to “move around” a given energy and trajectory opens the door to precise interpolation of the oscillation amplitudes within a grid of tabulated values, with potential benefits for the computation speed of Monte-Carlo codes. We also provide a set of examples to illustrate the most prominent features of our approach.

Bubbles of cosmology in AdS/CFT

Gravitational effective theories associated with holographic CFTs have cosmological solutions, which are typically big-bang/big-crunch cosmologies. These solutions are not asymptotically AdS, so they are not dual to finite-energy states of the CFT. However, we can find solutions with arbitrarily large spherical bubbles of such cosmologies embedded in asymptotically AdS spacetimes where the exterior of the bubble is Schwarzschild-AdS. In this paper, we explore such solutions and their possible CFT dual descriptions. Starting with a cosmological solution with Λ < 0 plus arbitrary matter density, radiation density, and spatial curvature, we show that a comoving bubble of arbitrary size can be embedded in a geometry with AdS-Schwarzschild exterior across a thin-shell domain wall comprised of pressureless matter. We show that in most cases (in particular, for arbitrarily large bubbles with an arbitrarily small negative spatial curvature) the entropy of the black hole exceeds the (radiation) entropy in the cosmological bubble, suggesting that a faithful CFT description is possible. We show that unlike the case of a de Sitter bubble, the Euclidean continuation of these cosmological solutions is sensible and suggests a specific construction of CFT states dual to the cosmological solutions via Euclidean path integral.

Relaxation method for Mie–Grüneisen type equations of state

Mie–Grüneisen type equations of state (EOS) are widely used to describe the thermodynamics of solids, liquids, and gases in a variety of physics problems, including shock wave dynamics in condensed materials and the thermodynamic behavior of dense gases generated by detonation waves. The Jones–Wilkins–Lee (JWL), Cochran–Chan, and original Mie–Grüneisen EOSs are relevant examples. However, these EOSs present several major difficulties. First, their range of validity is limited because these EOSs are fitted to a reference curve and tolerate only small deviations from that curve. The second difficulty lies in the complexity of the mathematical formulations, affecting the efficiency of pressure relaxation solvers. These two difficulties give rise to a third. Under extreme flow conditions, computational failures are quite common. Methods for “extending” the equations of state are often used to continue the computations. For example, below a certain arbitrary density, the JWL EOS is sometimes extended to the ideal-gas EOS. A fundamentally new method is presented in this work. It consists of using the much simpler Noble–Abel-stiffened-gas EOS as a predictor, to close the corresponding flow model. A thermodynamic relaxation step follows the prediction step. The solution is projected onto the target EOS, in this case the Mie–Grüneisen EOS, with the help of additional transport equations. Therefore, the flow model is an extended version, much more efficient for numerical resolution. This method solves the three problems above by extending the validity domain of the thermodynamic formulation, making the relaxation solvers much faster, and dramatically increasing the robustness of computations.

Dispersion Characteristics of Low-Frequency Electron Waves in a Magnetoactive Plasma of Arbitrary Density

The article studies waves in a collisionless magnetoactive plasma with frequencies much lower than the electron cyclotron frequency at an arbitrary ratio between the electron plasma and cyclotron frequencies. A general dispersion relation is obtained for the wave frequency as a function of the wave vector and the ratio of the plasma frequency to the cyclotron frequency. This relation is a bicubic equation with respect to frequency. Based on this equation, the existence domains of various wave modes depending on the specified parameter, their group velocity, polarization, and energy density are studied. Special attention is paid to low-frequency whistler waves in a low-density plasma, since, among the propagating wave modes existing in the specified range of parameters, whistler waves have the highest refractive index and play an important role in theresonant interaction of waves and particles.

Dispersion Characteristics of Low-Frequency Electron Waves in a Magnetoactive Plasma of Arbitrary Density

Dispersion Characteristics of Low-Frequency Electron Waves in a Magnetoactive Plasma of Arbitrary Density

Asymptotic expected T‐functionals of random polytopes with applications to Lp$L_p$ surface areas

AbstractAn asymptotic formula is proved for the expected T‐functional of the convex hull of independent and identically distributed random points sampled from the Euclidean unit sphere in according to an arbitrary positive continuous density. As an application, the approximation of the sphere by random polytopes in terms of surface area differences is discussed.

Tristochastic operations and products of quantum states

The notion of convolution of two probability vectors, corresponding to a coincidence experiment can be extended to a family of binary operations determined by (tri)stochastic tensors, to describe Markov chains of a higher order. The problem of associativity, commutativity, and the existence of neutral elements and inverses for such operations acting on classical states is analyzed. For a more general setup of multi-stochastic tensors, we present the characterization of their probability eigenvectors. Similar results are obtained for the quantum case: we analyze tristochastic channels, which induce binary operations defined in the space of quantum states. Studying coherifications of tristochastic tensors we propose a quantum analogue of the convolution of probability vectors defined for two arbitrary density matrices of the same size. Possible applications of this notion to construct schemes of error mitigation or building blocks in quantum convolutional neural networks are discussed.

Thermo-Field Dynamics Approach to Photo-induced Electronic Transitions Driven by Incoherent Thermal Radiation.

The effects of thermal light-matter interaction on the dynamics of photo-induced electronic transitions in molecules are investigated using a novel first principles approach based on the thermo-field dynamics description of both the molecular vibrational modes and of the radiation field. The developed approach permits numerically accurate simulations of quantum dynamics of electronic/excitonic systems coupled to nuclear and photonic baths kept at different temperatures. The baths can be described by arbitrary spectral densities and can have any system-bath coupling strengths. In agreement with the results obtained previously by less rigorous methods, we show that the excitation process obtained by the continuous interaction with the suddenly turned-on thermal radiation field creates a mixed ensemble having a nonnegligible component consisting of a superposition of vibronic eigenstates which can sustain coherent oscillations for relatively long times. The results become especially relevant for the dynamics of electronic transitions upon sunlight excitation. Analytical results based on time-dependent perturbation theory support the numerical simulations and provide a simple interpretation of the time evolution of quantum observables.

Stationary response analysis for a linear system under non-Gaussian random excitation by the equivalent non-Gaussian excitation method and the Hermite moment model

An approximate analytical method is developed to obtain the stationary response probability density and mean upcrossing rate for a linear system subjected to non-Gaussian random excitation. The random excitation is a stationary stochastic process prescribed by an arbitrary first-order probability density and a class of power spectral density with a bandwidth parameter, and is described by an Itô stochastic differential equation. In the proposed method, the equivalent non-Gaussian excitation method is first utilized to derive a closed set of moment equations for the system response. The exact solutions of response moments up to the fourth order are calculated from the moment equations. Next, using the response moments, the Hermite moment model is built for the stationary displacement response, and its probability density function is obtained through the model. Finally, the mean upcrossing rate of the displacement is determined from the response probability distribution by making two approximations that the displacement and velocity of the system are independent and the velocity is Gaussian. The proposed method can be used for any excitation probability density and bandwidth parameter value as long as the skewness and kurtosis of the response are within the applicable range of the Hermite moment model. In illustrative examples, the proposed method is applied to linear systems under random excitations with two-types of non-Gaussian probability densities. The effectiveness of the method is demonstrated by comparing the analytical results with the pertinent Monte Carlo simulation results while widely varying the bandwidth ratio between the excitation spectral density and the frequency response function of the system. Moreover, the effect of excitation non-Gaussianity on the mean upcrossing rate is discussed. It is shown that for small bandwidth ratio, the crossing rate differs considerably depending on the excitation probability density. The difference due to the excitation distribution decreases monotonically as the bandwidth ratio increases, and the crossing rate becomes almost the same as that in the case of Gaussian excitation when the bandwidth ratio is large.

Steady states of two-dimensional granular systems are unique, stable, and sometimes satisfy detailed balance

Understanding the structural evolution of granular systems is a long-standing problem. A recently proposed theory for such dynamics in two dimensions predicts that steady states of very dense systems satisfy detailed-balance. We analyse analytically and numerically the steady states of this theory in systems of arbitrary density and report the following. (1) We discover that all such dynamics almost certainly possess only one physical steady state, which may or may not satisfy detailed balance. (2) We show rigorously that, if a detailed balance solution is possible then it is unique. The above two results correct an erroneous conjecture in the literature. (3) We show rigorously that the detailed-balance solutions in very dense systems are globally stable, extending the local stability found for these solutions in the literature. (4) In view of recent experimental observations of robust detailed balance steady states in very dilute cyclically sheared systems, our results point to a self-organisation of process rates in dynamic granular systems.

Extending the analysis of the Euler–Bernoulli model for a stochastic static cantilever beam: Theory and simulations

In this paper, we present a comprehensive probabilistic analysis of the deflection of a static cantilever beam based on Euler–Bernoulli’s theory. For the sake of generality in our stochastic study, we assume that all model parameters (Young’s modulus and the beam moment of inertia) are random variables with arbitrary probability densities, while the loads applied on the beam are described via a delta-correlated process. The probabilistic study is based on the calculation of the first probability density function of the solution and the probability density of other key quantities of interest, such as the shear force, and the bending moment, which are treated as random variables too. To conduct our study, we will first calculate the first moments of the solution, which is a stochastic process, and we then will take advantage of the Principle of Maximum Entropy. Furthermore, we will present an algorithm, based on Monte Carlo simulations, that allows us to simulate our analytical development computationally. The theoretical findings will be illustrated with numerical examples where different realistic probability distributions are assumed for each model random parameter.

Quantum entanglement & purity testing: A graph zeta function perspective

We assign an arbitrary density matrix to a weighted graph and associate to it a graph zeta function that is both a generalization of the Ihara zeta function and a special case of the edge zeta function. We show that a recently developed bipartite pure state separability algorithm based on the symmetric group is equivalent to the condition that the coefficients in the exponential expansion of this zeta function are unity. Moreover, there is a one-to-one correspondence between the nonzero eigenvalues of a density matrix and the singularities of its zeta function. Several examples are given to illustrate these findings.

Statistical analysis of randomized pseudo-first/second order kinetic models. Application to study the adsorption on cadmium ions onto tree fern

Adsorption kinetics are commonly modeled using pseudo-first order (PFO) and pseudo-second order (PSO) rate laws. Both models are formulated via differential equations whose coefficients are commonly treated as deterministic quantities, which are calculated from experimental data using regression techniques. In this paper, we propose a full randomization of both models by assuming that all the parameters of the PFO and PSO models are random variables with arbitrary densities. Then, we probabilistically solve both models by determining semi-explicit expressions of the first probability density functions of the corresponding solution stochastic processes, as well as the densities of the time until a fixed adsorbed amount of reactant has been reached for each model too. The analysis is conducted under very general assumptions and is based on extensive application of the so-called Random Variable Transformation (RVT) technique. Finally, we apply all the aforementioned theoretical findings to model the adsorption of cadmium ions onto tree fern, using real data. We compare the results obtained by the randomized PFO and PSO models, using a Bayesian and a randomized version of the least mean square method to assign reasonable densities to model parameters. After comparing the results, the PSO model is selected, and, we then show how the RVT technique can be applied to obtain further key information, such as the second probability density function, of the solution and the covariance function.

Modeling the combined effect of initial density and temperature on the soil–water characteristic curve of unsaturated soils

The soil–water characteristic curve (SWCC) plays an important role in solving the stability and deformation problems of unsaturated soils. In many practical situations, soils are usually experienced by both deformations and thermal conditions. In this interest, the paper proposes a simple and effective model to predict the combined effect of initial density and temperature on the SWCC and to be able to quantify the changes in thermal-hydro-mechanical behavior of unsaturated soils. In the first step, an initial density-dependent SWCC model is presented using the translation principle between particle-size distribution curve and soil–water characteristic curve. In the second part, a non-isothermal model is proposed to predict the effect of temperature on the SWCC. The key to the non-isothermal model is considering five different temperature-dependent functions, which are surface tension, contact angle, particle-size expansion, void ratio, and water density. On the basis of 22 data sets of thermal volume change, this study also developed further a theoretical correlation between void ratio and temperature that is directly related to soil plasticity. It was observed that the value of the thermal void ratio increases as soil plasticity increases, and there is a nonlinear relationship between the plasticity index and the void ratio. Because of this, soils with high plasticity are more susceptible to volume changes caused by temperature fluctuations than soils with low plasticity. A coupled mechanical–thermal model is then produced which is capable to predict separately or simultaneously the effect of temperature and initial density on SWCC. The proposed model is validated against several test data sets available in the literature. The results show that the proposed model has a good performance in predicting the variation in SWCC with arbitrary temperature and initial density.