Rigid Sphere Model Research Articles

Analytical investigation of vesicle dynamics via the modified Riemann-Liouville fractional derivative: Mittag-Leffler function solution and comparative analysis with Caputo's derivative.

The solution of fractional differential equations is a significant focus of current research, given their prevalence in various fields of application. This paper introduces an innovative exploration of vesicle dynamics using Jumarie's modified Riemann-Liouville fractional derivative within a five-dimensional fractional rigid sphere model. The study reveals an exact solution through the Mittag-Leffler function, providing a deep understanding of intricate vesicle dynamics, including alternative motions, such as tank-treading with over-damped and under-damped vesicle oscillations, respectively, TT-OD and TT-UD. A comparative analysis with Caputo's derivative emphasizes the effectiveness of these fractional derivatives, contributing not only to theoretical insights but also practical implications in applied mathematics and biophysical systems. The findings advance our understanding of complex vesicle behaviors, particularly in mimicking real cell-like behaviors, and pave the way for further research and applications in the field.

Effect of surfactant on dynamics and gas-liquid mass transfer for single carbon dioxide bubbles

In carbonation reaction, the impact of surfactants on the movement and mass transfer behavior of carbon dioxide bubbles were crucial for the production of high-quality silicon dioxide products. The study employed the Matlab image processing system to investigate the shapes, motion velocities, and rise path of single carbon dioxide bubbles within varying concentrations of cetyltrimethyl ammonium bromide (CTAB) solutions. This exploration aimed to elucidate the effect of CTAB on the movement and mass transfer coefficient (MTRC) of single carbon dioxide bubbles. Alterations in the CTAB solution concentration and bubble sizes significantly influenced the mass transfer and movement characteristics of single carbon dioxide bubbles. The conclusion was drawn through the computation of the MTRC of single carbon dioxide bubbles in deionized water and CTAB solutions: the addition of CTAB significantly reduced the mass transfer efficiency of carbon dioxide in deionized water, with the MTRC of CTAB solutions decreasing as the solution concentration increased. Utilizing the stagnant cap model, it can be concluded that CTAB's reduction of the MTRC of carbon dioxide was attributed to the high viscosity of the medium, low bubble velocity, stable flow conditions, and intensified adsorption degree of CTAB molecules at the gas-liquid interface. According to the significant periodic trajectories of single carbon dioxide bubbles in the stable range, the correlation between the trajectories of compressible bubbles in surfactant solution and mass transfer in liquid phase was established, and the previous method based on rigid sphere model was modified. The paper proposed the mechanism of CTAB's influence on single carbon dioxide bubbles, offering crucial theoretical insights into the industrial application of surfactants in the carbonation process for producing silicon dioxide.

Numerical simulation of rime ice accretion on airfoil using rigid sphere model

A 2D/3D numerical model for rime ice shape prediction is developed by combining the rigid sphere model (RSM) and computational fluid dynamics (CFD), and its characteristics are investigated. In the RSM, the ice accretion is modeled based on first principles with little physical modeling. The ice particle on an airfoil is described as a rigid sphere, and the ice shape is represented as a collection of rigid spheres. We use a non-body-fitted hierarchical Cartesian grid-based CFD solver so that complex ice shape represented by RSM can be handled. The tree data of the hierarchical Cartesian grid is also used for fast search of droplet positions. In addition, multiple ice particles are modeled as one large particle to reduce the number of trajectory calculations. The sensitivity of several parameters in the calculation is studied in 2D. Subsequently, 3D ice accretion analysis on NACA0012 airfoil using the RSM is performed for the first time. The simulation results are compared with those of the wind-tunnel experiments conducted at NASA. Although the RSM is a simple ice accretion model, reliable results are obtained in both 2D and 3D calculations.

Exploring the interplay between memory effects and vesicle dynamics: A five‐dimensional analysis using rigid sphere models and mapping techniques

AbstractThe memory effect in vesicle dynamics refers to the persistence of shape changes in lipid vesicles, a type of lipid bilayer membrane that mimics some features of real cells, particularly red blood cells (RBCs). To study this effect, a fractional rigid sphere model in five dimensions has been investigated, which maps the dynamics of a vesicle using the Caputo operator. This model provides new insights into the mechanisms behind the memory effect as well as the emergence of two other motions, namely, tank‐treading with underdamped and tank‐treading with overdamped vesicle oscillations, in addition to the tank‐treading mode where the vesicle rotates about its axis while maintaining a constant shape. Overall, this work represents a significant advance in our understanding of vesicle dynamics and has important implications for understanding the behavior of RBCs.

Vibro-Impact Response Analysis of Collision with Clearance: A Tutorial

A collision with clearance causes obvious nonlinearity in structures, and dynamic response analysis plays an important role in predicting the mechanical performance of the structure. The general form of the nonlinear dynamic equation of a structure and the clearance modeling method are introduced, and the clearance-caused nonlinear term is expressed by nonlinear impact forces. Different clearance collision models of local nonlinear structures are presented. The relationships between different impact forces and clearances are analyzed by two rigid sphere models. The solution methods of the nonlinear dynamic equation are compared by a vibro-impact response, such as the Newmark-β method combined with the Newton–Raphson method, generalized α method and precise integration method. The single degree of freedom model is adopted to compare the efficiency of the different numerical integration algorithms. Taking the beam structure model as a case study, the accurate nonlinear collision model with clearance is established by using the impact force model with high accuracy, and the accuracy of the model is verified by comparing the reference model with the numerical model.

Laser cluster interaction in ambient magnetic fields for accelerating electrons in two stages without external injection

In the few-cycle pulse regime of laser-cluster interaction (intensity >10^{16},text{ W/cm}^{2}, wavelength > 780 nm), laser absorption is mostly collisionless and may happen via anharmonic resonance (AHR) process in the overdense (cluster) plasma potential. Many experiments, theory and simulation show average absorbed energy per cluster-electron ({mathcal {E}_A}) close to the electron’s ponderomotive energy (U_mathrm {p}) in the collisionless regime. In this work, by simple rigid sphere model (RSM) and detailed particle-in-cell (PIC) simulation, we show enhanced {mathcal {E}_A}approx 30–70U_mathrm {p}—a 15–30 fold increase—with an external (crossed) magnetic field near the electron-cyclotron resonance (ECR). Due to relativistic mass increase, electrons quickly deviate from the standard (non-relativistic) ECR, but time-dependent relativistic-ECR (RECR) happens which also contributes to enhanced {mathcal {E}_A}. Here laser is coupled to electrons in two stages, i.e, AHR and ECR/RECR. To probe further we retrieve the phase-difference Delta psi between the driving electric field and corresponding velocity component for each electron (in PIC and RSM). We find absorption by electron via AHR happens in a very short interval Delta tau for less than half a laser period where Delta psi remains close to pi (necessary condition for maximum laser absorption) and then Delta psi drops to its initial pi /2 (meaning no absorption) after such short-lived AHR. On the contrary, auxiliary magnetic field near the ECR modifies AHR scenario inside the cluster and also helps maintaining the required phase Delta psi approx pi for the liberated cluster-electron accompanied by frequency matching for ECR/RECR for a prolonged Delta tau (which covers 50–60% of the laser pulse through pulse maxima) even after AHR—leading to jump in {mathcal {E}_A}approx 30–70U_mathrm {p}. We note that to realize the second stage of enhanced energy coupling via ECR/RECR, the first stage via AHR is necessary.

GPU-Accelerated Target Strength Prediction Based on Multiresolution Shooting and Bouncing Ray Method

The application of the traditional planar acoustics method is limited due to the low accuracy when computing the echo characteristics of underwater targets. Based on the concept of the shooting and bouncing ray which considers multiple reflections on the basic of the geometrics optics principle, this paper presents a more efficient GPU-accelerated multiresolution grid algorithm in the shooting and bouncing ray method (SBR) to quickly predict the target strength value of complex underwater targets. The procedure of the virtual aperture plane generation, ray tracing, scattered sound field integral and subdividing the divergent ray tubes are all implemented on the GPU. Particularly, stackless KD-tree traversal is adopted to effectively improve the ray-tracing efficiency. Experiments on the rigid sphere, cylinder and corner reflector model verify the accuracy of GPU-based multiresolution SBR. Besides, the GPU-based SBR is more than 750 times faster than the CPU version because of its tremendous computing capability. Further, the proposed accelerated GPU-based multiresolution SBR improves runtime performance at least 2.4 times that of the single resolution GPU-based SBR.

Finite-difference time-domain simulations: Verification on head-related transfer functions of a rigid sphere model.

This paper presents a verification procedure for finite-difference time-domain-simulated head-related transfer functions (HRTFs) from a simplified model of a human head, a sphere. The analytic solution required by the code verification is computed with the multipole reexpansion technique and used to estimate convergence rates. A solution verification process follows in which asymptotic predictions are computed. For the HRTFs considered and employed grids, results show that the convergence rates attain the expected first-order accuracy at lower frequencies, after which scattered estimates are observed. Results also reveal that the asymptotic predictions are accurate up to 10 kHz, after which bias is observed.

Elastic Scattering of Slow Electrons by Noble Gases—The Effective Range Theory and the Rigid Sphere Model

We report on an extensive semi-empirical analysis of scattering cross-sections for electron elastic collision with noble gases via the Markov Chain Monte Carlo-Modified Effective Range Theory (MCMC−MERT). In this approach, the contribution of the long-range polarization potential (∼r−4) to the scattering phase shifts is precisely expressed, while the effect of the complex short-range interaction is modeled by simple quadratic expression (the so-called effective range expansion with several adjustable parameters). Additionally, we test a simple potential model of a rigid sphere combined with r−4 interaction. Both models, the MERT and the rigid sphere are based on the analytical properties of Mathieu functions, i.e., the solutions of radial Schrödinger equation with pure polarization potential. However, in contrast to MERT, the rigid sphere model depends entirely upon one adjustable parameter—the radius of a hard-core. The model’s validity is assessed by a comparative study against numerous experimental cross-sections and theoretical phase shifts. We show that this simple approach can successfully describe the electron elastic collisions with helium and neon for energies below 1 eV. The purpose of the present analysis is to give insight into the relations between the parameters of both models (that translate into the cross-sections in the very low energy range) and some “macroscopic” features of atoms such as the polarizability and atomic “radii”.

MODEL REPRESENTATIONS OF THE MELTS STRUCTURE DESCRIPTION BY THE MODEL OF HARD SPHERES

In the article the optimization of the oil and gas enterprise, a complex process both from the technological and from the economic point of view is investigated. It is noted that today the development of methods of mathematical modeling of physical processes, for example, in oil fields on the basis of theoretical research and modern computer technology is absolutely relevant
 One of the ways is to create new or improve existing mathematical models of processes occurring in oil and gas reservoirs, and calculate on their basis the characteristics of the process that optimize production. From this perspective, the study appears particularly relevant liquids in a narrow, purely physical and chemical aspects – namely melt.
 Various fluid models have been proposed to describe the equilibrium and kinetic properties of liquids (melts), as well as to interpret experimental results. Model representations are also used in solving integrodifferential equations that relate distribution functions to interaction potentials. It is noted that integrodifferential equations are a powerful mathematical algorithm for describing inhomogeneous dynamic models, but they depend directly on the efficiency of software that implements the proposed models.
 The model of hard spheres as simple fluid model proposed use. The reasons that allow you to choose this model as optimal were defined. Namely: the presence of analytical expression for the structural factor; application to describe the electronic and atomic properties of melts. The optimal methods for obtaining optimal values for the theoretical calculation of the structural factor of the proposed model were determined.
 As a result of the analysis of existence of correspondence between the calculated and experimental structural factors it is established. This led to the conclusion that the possibility of applying the model of rigid to calculate the equilibrium and kinetic properties of melts exists. It is determined that the model of rigid spheres could be used as an approximation to describe the structure of both one-component and multicomponential melts (liquids).

Distributions of Two Atoms Collisions over the Surface of the Condensed Phase

The processes of heat and mass transfer are closely related to the evaporation of a substance from the surface of the condensed phase. The interaction of outgoing molecules from the surface of the condensed phase with condensed phase molecules plays a fundamental role. A simpler case of evaporation is the departure of atoms from the surface of the condensed phase, i.e. the atoms overcome the potential barrier on the surface of the condensed phase. Depending on the evaporation rate, a Knudsen layer appears above the surface of the condensed phase. In this paper, based on the model of rigid spheres, the density distributions of the collision distances and the average values of the collision distances of two atoms emitted simultaneously from the surface of the condensed phase above the surface are analyzed. Distributions of the collision distance depending on the surface temperature, the size of the potential barrier, and the size of the evaporation area are obtained. Computer experiments were performed using the Monte Carlo method. To obtain the results of numerical simulation, a parallel algorithm adapted to calculations on graphics processors with CUDA technology was developed.

Simulation of dendrite collision behavior based on cellular automata-lattice Boltzmann model

In the alloy solidification process, the movement behavior of free dendrites in the melt is one of the key issues in studying the formation process of the alloy solidification structure. The cellular automata-lattice Boltzmann coupling model has become a main numerical model for numerical simulation of solidification microstructure in recent years. In this paper, cellular automata and lattice Boltzmann model for simulating dendrite growth are improved to simulate the movement of equiaxed grains in undercooled melt. In the improved model, the Galilean invariant momentum exchange method is used to calculate the fluid force, the motion equation of the center of mass is solved to calculate the motion displacement of the dendrite, the motion of the dendrite is realized through the dynamic mesh technology, and the rigid sphere model is used to deal with the collision of the dendrite. The settlement of a single dendrite in the undercooled melt of Al-4.7% Cu alloy, the settlement of two round particles in the Newtonian fluid, and the elastic collision of two dendrites are all simulated by this model. The simulation results show that this model can maintain the morphology of dendrites well in the process of calculating dendrite growth motion, and this model can calculate the collision process of irregular dendrites. The movement of dendrite disturbs the melt around it, resulting in a significant change in the concentration of melt around it, which affects the growth of dendrite and aggravates the asymmetry of dendrite growth.

Mode locking phenomena of the current-induced skyrmion-lattice motion in microfabricated MnSi

Using voltage fluctuation spectroscopy, we observe the mode locking phenomena of current-induced skyrmion-lattice motion in microfabricated MnSi. When only a dc electric current is applied, the frequency of the emergent narrow-band noise (NBN) monotonously increases with increasing dc current. By contrast, if an ac electric current is further added, the NBN frequency becomes much less dependent on the dc current when it satisfies a simple integer ratio to the ac current frequency, a hallmark of mode locking. In the mode locked state, the linewidth of the NBN is sharpened, indicating the enhanced coherence of the skyrmion-lattice motion. The overall features of the mode locking phenomena are qualitatively reproduced within the framework of the classical rigid-sphere model.

Analytical-function correction to the Hartmann–Tran profile for more reliable representation of the Dicke-narrowed molecular spectra

The β-corrected Hartmann–Tran profile (HTP) constitutes an approximation of the partially correlated quadratic speed-dependent billiard-ball profile (SDBBP) easily applicable in calculations. We extend the approach originally developed for self-perturbed molecules [Wcisło et al. J. Quant. Spectrosc. Radiat. Transf. 177, 75–91 (2016)] to systems with a wide range of perturber-to-absorber mass ratios, including those relevant for atmospheric studies. This approach combines the computational simplicity of the HTP with the more physically justified rigid-sphere model for velocity-changing collisions. It is important for the analysis of high-resolution spectra influenced by the Dicke-narrowing effect. The β-corrected HTP enables high quality analytical representation of experimental spectra without incurring the high computational cost of more advanced line-shape models. This correction is directly applicable to any other line-shape model based on the hard-collision model for velocity-changing collisions.

On the Contribution of Dispersion Forces to the Linear and Point Energies of Graphene

For two-dimensional structures, the linear and point energies are physical parameters of the same significance as the surface and linear energies, respectively, for three-dimensional bodies. The theory presented in this communication enables one to calculate the contribution of dispersion forces to the local cohesion energy, local linear energy, and point energy of graphene from its microscopic parameters, namely, the lattice spacing, two-dimensional atomic density, and pair interaction potential. The local values are calculated on the basis of the Irving–Kirkwood pressure tensor inside of a plane-parallel empty two-dimensional slit with a finite size extension between two rectangular pieces of graphene lying in the same plane. The calculation is performed for the absolute zero of temperature (when the energy is equivalent to the free energy). The structure of graphene is assumed to be rigid, which entails ignorance of the effect of relaxation upon the separation of the two graphene pieces. The calculation result depends on the direction of graphene boundary line. The line normal to the σ-bonds has been selected for the calculations, with this line corresponding to the natural boundary of graphene. The linear and point energies of graphene are calculated within the model of rigid spheres with dispersion forces and the Lennard—Jones model. It has been found that, near a corner of a rectangular graphene piece, the linear energy becomes a value variable within five distances between atoms in the lattice, thereby making it possible to evaluate the contribution of the dispersion forces to the point energy of graphene.

Dynamical resonance shift and unification of resonances in short-pulse laser-cluster interaction

Pronounced maximum absorption of laser light irradiating a rare-gas or metal cluster is widely expected during the linear resonance (LR) when Mie-plasma wavelength $\lambdaM$ of electrons equals the laser wavelength $\lambda$. On the contrary, by performing molecular dynamics (MD) simulations of an argon cluster irradiated by short 5-fs (fwhm) laser pulses it is revealed that, for a given laser pulse energy and a cluster, at each peak intensity there exists a $\lambda$ -- shifted from the expected $\lambdaM$ -- that corresponds to a {\em unified dynamical} LR at which evolution of the cluster happens through very effective unification of possible resonances in various stages, including (i) the LR in the initial time of plasma creation, (ii) the LR in the Coulomb expanding phase in the later time and (iii) anharmonic resonance in the marginally over-dense regime for a relatively longer pulse duration, leading to maximum laser absorption accompanied by maximum removal of electrons from cluster and also maximum allowed average charge states for the argon cluster. Increasing the laser intensity, the absorption maxima is found to shift to a higher wavelength in the band of $\lambda\approx (1-1.5)\lambdaM$ than permanently staying at the expected $\lambdaM$. A naive rigid sphere model also corroborates the wavelength shift of the absorption peak as found in MD and un-equivocally proves that maximum laser absorption in a cluster happens at a shifted $\lambda$ in the marginally over-dense regime of $\lambda\approx (1-1.5)\lambdaM$ in stead of $\lambdaM$ of LR. Present study may find importance for guiding an optimal condition laser-cluster interaction experiment in the short pulse regime.

Calculating the Entropy of Solid and Liquid Metals, Based on Acoustic Data

The entropies of iron, cobalt, rhodium, and platinum are studied for the first time, based on acoustic data and using the Debye theory and rigid-sphere model, from 298 K up to the boiling point. A formula for the melting entropy of metals is validated. Good agreement between the research results and the literature data is obtained.

The Effect of Shape and Concentration on Translational Diffusion of Proteins Measured by PFG NMR

The concentration dependences of self-diffusion coefficient for irregular-shaped fibrinogen, for globular, spheroidal trypsin and α-chymotrypsin were studied by pulsed field gradient nuclear magnetic resonance. The experimental data were analyzed in a view of two known theoretical approaches—the hydrodynamic model of rigid spheres by Tokuyama and Oppenheim and the phenomenological approach based on the frictional formalism of non-equilibrium thermodynamics by Vink. The detailed discussion of their merits and drawbacks is presented. Our results testify that the Vink’s approach is quite universal, providing a satisfactory description of experimental data for proteins of complicated structure and different shape while the model of Tokuyama and Oppenheim is applicable only to proteins of more regular shape.

Thirteen-moment model kinetic equation and its parameters

We propose the generalized model kinetic equation that represents a hybrid of the Shakhov equation and the ellipsoidal statistical Holway equation; this is the thirteen-moment equation. The constants of the equation are expressed at first in the terms of the transport coefficients, namely, the viscosity of a gas, its heat conductivity, and the self-diffusion coefficient. Next, the transport coefficients are expressed in terms of integral brackets; for the molecule–rigid sphere model these coefficients are brought to a number in the first and second approximations.

Revisit the adhesive contact between a nanoscale rigid sphere and an elastic half-space: considering the effect of sphere size

The current paper revisits the adhesive contact between a rigid nanoscale sphere and an elastic half-space. Using analytical solution for traction and a modified numerical scheme, a new simulation is proposed. The adhesive contact is simulated faster and more easily than previous researches. The effect of sphere size is investigated. A modified spherical JKR model and spherical DMT model are proposed. The results are compared with spherical JKR, spherical DMT, and rigid sphere model. The load–approach and contact radius–load relations can be predicted by the modified spherical JKR model for sphere radius larger than 50ɛ. Finally, approximation equations for pull-off force vs. Tabor parameter and jump-in distance vs. Tabor parameter are proposed.