Infinite Wall Research Articles

The Lambert diffuse reflection model revisited.

The Lambert diffuse reflection model is used widely in computerized prediction of sound in rooms as well as for outdoor scenarios. One seemingly surprising consequence of the model was pointed out by Borish [J. Audio Eng. Soc. 34, 539-545 (1986)]: A diffusely reflecting, non-absorbing wall seems to give a 3 dB stronger reflection than a specularly reflecting wall for a source and receiver along the same plane normal. Similar observations have been made by others, and it is usually commented that the two reflection types distribute the reflected energy in different directions. The aspect of energy conservation does not seem to have been sorted out entirely. It is shown here that the difference between an omnidirectional receiver, like a microphone, and a surface element receiver, which can give the total reflected power, explains the claim. Analytic solutions and numerical evaluations of the well-known integrals for a single infinite wall confirm that energy conservation is indeed maintained and also lead to a spatial distribution of the Lambert reflection strength, which differs substantially from the previously published values. The special case can serve as a useful benchmark test of implementations of diffuse reflections, which follow Lambert's law.

Effect of electrical field on pulsation characteristics of laser-induced cavitation bubble

An experimental platform for laser-induced cavitation under the action of an electric field was built, and the bubble pulsation under two different conditions of infinite domain and solid wall was experimentally studied. The effects of voltage, laser energy, and liquid viscosity on bubble pulsation and the difference in the effect of voltage on bubble induced by different laser energies and bubble pulsation in different viscous liquids were explored. It is found that the size, velocity and period of bubble pulsation in infinite domain increase with the increase of laser energy, and the law is similar at the solid wall. When the voltage is applied, the size and period of bubble pulsation in infinite domain decrease with the increase of voltage, the bubble expansion speed decreases with the increase of voltage, but the bubble collapse speed increases with the increase of voltage. The diameter and velocity of bubble pulsation in infinite domain decrease with the increase of liquid viscosity, while the whole pulsation period of bubble increases with the increase of viscosity. Due to the damping effect of liquid, the effect of electric field on the bubble pulsation with higher viscosity is low.

Interactive Digital Poetry and Experimental Prospects: A Study of the Works of Digital Poet Mushtaq Abbas Ma'an

Interactive digital literature offers parallel worlds between linguistic text based on the eloquence of letters, their energy, and digital interactive text based on visual, kinetic, chromatic, and auditory elements, enriched by the participation of the receiver who becomes an explorer. This literature is the product of significant cognitive developments. In this research, we aim to examine experimentation in the works of digital poet Mushtaq Abbas Ma'an and the evolution of his tools, starting with his first collection, "Digital Verses of Some of Which Are Blue," through his second collection, "The Infinite Fire Wall," to his latest collection, “Ancient pain with enduring echoes.” which combines printed text and interactive digital work in a pioneering and remarkable experiment within its field. We will focus on the key foundations of both works, noting the poet's openness to experimentation. We will delve deeper into the study of the last collection, which encapsulates the creative process, to analyze the evolution of the poet's perspective on interactive digital poetry, the development of his tools, and his digital experience. To achieve this goal, the research will follow the following plan: Phase One: Digital Verses of Some of Which Are Blue and the Experimentation Adventure. Phase Two: The Infinite Fire Wall and Continuation After a Break. Phase Three: Ancient pain with enduring echoes and the Completion of the Digital Experiment.

Wall modes and the transition to bulk convection in rotating Rayleigh-Bénard convection

We investigate states of rapidly rotating Rayleigh-Bénard convection in a cylindrical cell over a range of Rayleigh numbers 3×105≤Ra≤5×109 and Ekman numbers 10−6≤Ek≤10−4 for Prandtl number Pr=0.8 and aspect ratios 1/5≤Γ≤5 using direct numerical simulations. We characterize, for perfectly insulating sidewall boundary conditions, the first transition to convection via wall mode instability and the nonlinear growth and instability of the resulting wall mode states, including a secondary transition to time dependence. We show how the radial structure of the vertical velocity uz and the temperature T is captured well by the linear eigenfunctions of the wall mode instability where the radial width of uz is δuz∼Ek1/3r/H whereas δT∼e−kr (k is the wave number of a laterally infinite wall mode state). The disparity in spatial scales for Ek=10−6 means that the heat transport is dominated by the radial structure of uz since T varies slowly over the radial scale δuz. We further describe how the transition to a state of bulk convection is influenced by the presence of the wall mode states. We use temporal and spatial scales as measures of the local state of convection and the Nusselt number Nu as representative of global transport. Our results elucidate the evolution of the wall state of rotating convection and confirm that wall modes are strongly linked with the boundary zonal flow being the robust remnant of nonlinear wall mode states. We also show how the heat transport (Nu) contributions of wall modes and bulk modes are related and discuss approaches to disentangling their relative contributions. Published by the American Physical Society 2024

Domain walls in Horndeski gravity

The Horndeski gravity yields domain wall solutions that connect asymmetric vacua for a certain region of parameters. In the thin wall limit there exist BPS domain walls that connect stable vacua. That is, the false vacua in this theory follows the same effect obtained in supergravity vacua, i.e., it does not decay according to Coleman-de Luccia theory and the BPS solutions interpolating different vacua, e.g., non-degenerate AdS vacua, are static infinite planar domain walls separating vacua associated with different spacetimes.

Peculiarities for domain walls in Taub coordinates

In the present letter the infinite domain wall geometry in GR (Vilenkin in Phys Rev D 23:852, 1981; Vilenkin in Phys Lett B 133:177, 1983; Ipser and Sikivie in Phys Rev D 30:712, 1984) is reconsidered in Taub coordinates (Taub in Ann Math 53:472, 1951). The use of these coordinates makes explicit that the regions between the horizons and the wall and the outer ones are flat. By use of these coordinates, it is suggested that points inside the horizon and outside never communicate each other. The wall is seen on the left and the right side as contracting and expanding portions of spheres and a plane singularity, which is the imprint the contracting and expanding domain wall. Particles of each region will never reach this imprint. In addition, at some point during the evolution of the system, four curious holes inside the space time appear, growing at the speed of light. This region is not parameterized by the standard Taub coordinates, and the boundary of this hole adsorbs all the particles that intersect it. The boundary of these holes are composed by points which in the coordinates of [1–3] are asymptotic, in the sense that they correspond to trajectories tending to infinite values of the time or space like coordinates, while the proper time elapsed for the travel is in fact finite. This is not paradoxical, as the coordinates [1–3] are not to be identified with the true lengths or proper time on the space time. The correct interpretation of the boundary is particularity relevant when studying scattering of quantum fields approaching the domain wall. A partial analysis about this issue is done in the last section.

On the Exponential Decay of Strongly Interacting Cold Atoms from a Double-Well Potential

In this article, we study an exponential decay for the gas of bosons with strong repulsive delta interactions from a double-well potential. We consider an exactly solvable model comprising an infinite wall and two Dirac delta barriers. We explore its features both within the exact method and with the resonance expansion approach. The study reveals the effect of the splitting barrier on the decay rate in dependence on the number of particles. Among other things, we find that the effect of the splitting barrier on the decay rate is most pronounced in systems with odd particle numbers. During exponential decay, the spatial correlations in an internal region are well captured by the “radiating state”.

Partial confinement effects on the performance of a flapping foil power generator

The impacts of partial confinement on the power extraction performance of a flapping foil generator at a Reynolds number of 1100 are numerically studied using an immersed boundary–lattice Boltzmann method. Four confinement levels are implemented with two thin plates of finite size symmetrically placed at the distance of 1.5, 2, 3, and 4 foil chord length from the neutral position of the flapping foil. Parametric studies on plate lengths varying from 10 to 50 foil chord lengths at the four confinement levels are conducted. The results show that the power-extraction efficiency increases nearly monotonically with the upstream plate lengths while the impact of the downstream plate lengths is much less significant, indicating that upstream confinement is the dominant factor influencing the power-extraction performance. Contrary to the performance improvement observed in studies on the effect of infinite walls, the efficiency decreases dramatically with the decrease in the distance from the plates to the foil. The reasons for the dramatically decreased performance due to confinement effects are found. First, the interactions between the boundary layer of the plates and leading edge vortices formed on the foil reduce the size of the low-pressure region on the suction surface of the foil, leading to reductions in lift forces and consequently to major reductions in the extracted power. In addition, large mass flow deficits between the finite plates are observed when the distance between the two plates is small, indicating substantial reductions in potential power that can be extracted from the inflow.

A wide-band based weighted-sum-of-gray-gases model for participating media: Application to [formula omitted]-[formula omitted] mixtures with or without soot

The presence of participating gases and soot in combustion processes often makes the thermal radiation the main mechanism of heat transfer due to the elevated temperatures involved. The accurate solution of the radiative transfer equation (RTE) through the line-by-line (LBL) integration in engineering applications is in general still impracticable due to the high computational effort required to account for the millions of spectral lines that characterize the absorption coefficient of a gas. Global spectral models, such as the weighted-sum-of-gray-gases (WSGG) model, are attempts to replace the LBL integration with low computational cost and satisfactory accuracy. In the present study, an improvement of the WSGG model through a partition of the spectrum is proposed. The spectrum is divided into a set of ranges in which the standard methodology of the WSGG model is applied to determine the gray gases coefficients in these bands. This is the central aspect of what is named here a wide-band based WSGG (WBW) model, which consists firstly of determining the emittance of each band from the HITEMP 2010 database, then obtaining the pressure-absorption coefficients and the temperature-dependent coefficients. The total radiative heat flux and radiative heat source are obtained by the summation of the contribution of each band individually. For soot, a gray gas approach is considered for each band via Planck-mean absorption coefficients. A set of 1D problems consisting of two infinite parallel black walls, filled with a non-isothermal and non-homogeneous gaseous mixture of water vapor, carbon dioxide and soot, is solved. The results show that, especially in cases where the thermal radiation of soot is dominant, the maximum deviations obtained with the proposed method in relation to the LBL solution reduce by almost three times compared to other global WSGG models in the literature, in addition to decreasing by 40% the number of equations that need to be solved.

Effects of natural convection flow of fractional Maxwell hybrid nanofluid by finite difference method

Heat transfer phenomenon occurs in a wide range of industrial and engineering problems. In this framework, investigating the heat transfer behavior using an efficient mathematical tool is the hot research area in the research community. Therefore, we discussed the impact of fractional Maxwell hybrid nanofluid on heat transfer under the effects of Joules Heating, Magnetic field, and viscous dissipation via porous Medium with Caputo time fractional derivative. We have considered an infinite vertical wall with adaptable temperature moving with jerked motion along -direction. Water is taken as base fluid and nano-sized particles of Copper (Cu) & Alumina are used for the preparation of nanofluid. The governing equations of nonlinear Caputo time fractional model are converted into dimensionless form. A finite difference scheme is developed and applied successfully to get numerical solutions to the problem and to examine the influence of Maxwell hybrid nanofluid, physical parameters, and fractional parameters on velocity and temperature profiles. It can also be observed that the extended finite difference algorithm is very efficient and gives the accurate solution of the discussed model. It can be extended for more numerous types of heat transfer problems arising in physical nature with complex geometry.

Analysis of quantum decay law: is quantum tunneling really exponential?

The exponential decay law is well established since its first derivation in 1928; however, it is not exact but only an approximate description. In recent years some experimental and theoretical indications for non-exponential decay have been documented. First we solve analytically the time-dependent Schrödinger equation in one dimension for a potential consisting of an infinite wall plus a rectangular barrier with finite width and also a cut harmonic oscillator potential by considering it as a sequence of square potentials. Then using the staggered Leap-Frog method, we solve the time-dependent Schrödinger equation for the cut harmonic oscillator potential. In both methods, time dependence of the survival probability of the particle and the decay parameter \( \lambda \) are analyzed. The results exhibit non-exponential behavior for survival probability at short and intermediate times.

Cavity-induced chiral edge currents and spontaneous magnetization in two-dimensional electron systems

We consider a laterally confined two-dimensional electron gas (2DEG), placed inside a gyrotropic cavity. Splitting of the circularly polarized electromagnetic modes leads to the emergence of the ground state spontaneous magnetization, anomalous Hall effect and chiral edge currents in 2DEG. We examine the dependence of the magnetization and edge current density on the system size for two particular cases of the confining potential: infinite wall and parabolic potentials. We show that paramagnetic and diamagnetic contributions to the edge currents have qualitatively different dependence on the system size. These findings pave the route to the design quantum electrodynamic engineering of the material properties of the mesoscopic electron systems.

Investigations of Couette Flow Unsteady Radiative Convective Heat Transfer in a Vertical Channel Using the Generalized Method of Lines (MOL)

This study describes a very efficient and fast numerical solution method for the non-steady free convection flow with radiation of a viscous fluid between two infinite vertical parallel walls. The method of lines (MOL) is used together with the Runge-Kutta ODE Matlab solver to investigate this problem numerically. The presence of radiation adds more stiffness and numerical complexity to the problem. A complete derivation in dimensionless form of the governing equations for momentum and energy is also included. A constant heat flux condition is applied at the left wall and a transient numerical solution is obtained for different values of the radiation parameter (<i>R</i>). The results are presented for dimensionless velocity, dimensionless temperature and Nusselt number for different values of the Prandtl number (<i>Pr</i>), Grashof number (<i>Gr</i>), and the radiation parameter (<i>R</i>). As expected, the results show that the convection heat transfer is high when the Nusselt number is high and the radiation parameter is low. It is also shown that the solution method used is simple and efficient and could be easily adopted to solve more complex problems.

Dark sector domain walls could explain the observed planes of satellites

The observed 'planes of satellites' around the Milky Way and other nearby galaxies are notoriously difficult to explain under the ΛCDM paradigm. Here, we propose an alternative solution: domain walls arising in theories with symmetry-breaking scalar fields coupled to matter. Because of the matter coupling, satellite galaxies experience fifth forces as they pass through domain walls, leading to a subset of satellites with orbits confined to the domain wall plane. We demonstrate this effect using simple simulations of a toy model comprising point-like satellites and an infinite domain wall, and explore the efficacy of various planarity metrics in detecting this effect. We believe this is the first potential 'new physics' explanation for the observed planes of satellites which does not do away with dark matter.

Simulating local fields in carbon nanotube-reinforced composites for infinite strip with voids

A numerical simulation of the thermal properties is conducted for an isotropic and homogeneous infinite strip composite reinforced by carbon nanotubes (CNTs) and containing voids. The CNTs can be uniformly or randomly distributed but are non-overlapping. We model the CNTs as thin perfectly conducting elliptic inclusions and assume the voids to be of circular shape and act as barriers to heat flow. We also impose isothermal conditions on the external boundaries by assuming the lower infinite wall to be a heater under a given temperature, and the upper wall to be a cooler that can be held at a lower fixed temperature. The mathematical model, which takes the form of a mixed Dirichlet–Neumann problem, is solved by applying the boundary integral equation with the generalized Neumann kernel. We illustrate the performance of the proposed method through several numerical examples including the case of the presence of a large number of CNTs and voids.

Joule heating in squeezed flow of hybrid nanomaterial via FDM with Cattaneo–Christov (C–C) heat flux

PurposeThis study aims to explore the combined impacts of velocity and thermal slips on hybrid nanomaterial (GO+Ag+kerosene oil) bounded between two parallel infinite walls (plates). Both the walls are separated by a distance. The upper wall is subjected to squeezing with velocity, while the lower wall stretches with velocity. A uniform magnetic field acts normally to the flow. Moreover, heat transmission is analyzed in the presence of Joule heating. Heat transport characteristics are investigated by imposing the Cattaneo–Christov (C–C) heat flux model. The behavior of velocities, skin friction and temperature under sundry variables are examined graphically.Design/methodology/approachThe obtained partial differential equations (PDEs) related to the considered problem are nondimensionalized by choosing appropriated variables. These nondimensional PDEs are then solved by the numerical technique, finite difference method (FDM). For implementation of this method, the obtained nondimensional PDEs are converted into finite difference equations (FDEs) using forward difference (FD) toolkits.FindingsVelocity of the hybrid nanomaterial decreases with higher Hartman number and velocity slip parameter, while it increases with increase in Reynolds and squeezing numbers. Temperature of the hybrid nanomaterial increases for large Hartman number, Eckert number and squeezing parameter, while it is reduced by higher thermal slip parameter, thermal relaxation time parameter and nanoparticle volume fractions for graphene oxide (GO) and silver (Ag). Skin friction is controlled through higher Reynolds number, while it intensifies with nanoparticle volume fractions for GO and Ag.Originality/valueHere, the authors have investigated 2D flow of hybrid nanomaterial bounded between two parallel walls. The lower and upper walls are subjected to stretching and squeezing, respectively. The authors guarantee that all outcomes and numerical technique (FDM) results are original, neither submitted nor published in any journal before.

A collocation method for the Williams equation with Chebyshev polynomials

The linearized problem of gas flow in plane channel with infinite walls has been solved in the kinetic approximation. The flow in the channel is caused by a constant pressure gradient parallel to the walls of the channel. The Williams equation has been used as a basic equation, and the boundary condition has been set in terms of the diffuse reflection model. The collocation method for Chebyshev polynomials has been applied to construct the solution of the equation of Williams with the given boundary conditions. The mass flux of the gas in the channel has been calculated.

Analytical solution to the problem of diffusion of the light component of the binary gas mixture in a plane channel

Within the framework of the kinetic approach, an analytical solution to the problem of diffusion of the light component of a binary mixture in a flat channel with infinite parallel walls is constructed. It is assumed that the mass of light component molecules and their concentration is much less than the mass of molecules and the concentration of heavy components. The flow rate of the heavy component is assumed to be zero. The change in the state of a light gas component is described on the basis of the BGK (Bhatnagar, Gross, Kruk) model of the Boltzmann kinetic equation. The diffuse reflection model is used as a boundary condition on the channel walls. The mass velocity profile of the light gas component is constructed. The flow rate of the light gas component per unit channel width is calculated. A comparison with similar results presented in open sources was done.

Acceleration in quantum mechanics and electric charge quantization

In this study, we have discussed the implications of acceleration in quantum mechanics by means of a generalized derivative operator (GDO). A new Schrödinger equation is obtained which depends on the reduced Compton wavelength of the particle. We have discussed its implications in quantum mechanics for different types of potentials mainly the infinite wall potential, the gravitational linear field potential, the Cornell potential and the Coulomb repulsive potential. The corresponding wave functions and discrete energies are modified and differ from the results obtained in the conventional formalism. The major results obtained concerned the large improvement of the ground energy of the electron subject to the gravitational acceleration in addition to Cornell potential and the emergence of quantized electric charge in the theory without including Dirac monopoles or using gauge theories.

Modeling rarefied gas-solid surface interactions for Couette flow with different wall temperatures using an unsupervised machine learning technique.

In rarefied gas flows, discontinuity phenomena such as velocity slip and temperature jump commonly appear in the gas layer adjacent to a solid boundary. Due to the physical complexity of the interactions at the gas-solid interface, particularly in the case of systems with local nonequilibrium state, boundary models with limited number of parameters cannot completely describe the reflection of gas molecules at the boundary. In this work, the Gaussian mixture (GM) model, which is an unsupervised machine learning technique, is employed to construct a statistical gas-solid surface scattering model based on the collisional data obtained from molecular dynamics (MD) simulations. The GM model is applied to study Couette flow for different inert gases (Ar and He) confined between two parallel infinite gold walls at different temperatures. A direct comparison between the results obtained from the GM model and the Cercignani-Lampis-Lord (CLL) scattering kernel against the MD collisional data in terms of the distribution of the predicted postcollisional velocities, and accommodation coefficients has shown that the results from the GM model are an excellent match with the MD results outperforming the CLL scattering kernel. As an example, for He gas, while the predicted energy accommodation coefficient by the CLL model is more than two times higher than the MD predictions, the value computed by the GM model is in excellent agreement with the MD results. This superior performance of the GM model confirms its high potential to derive a generalized boundary condition in systems encountered with highly nonequilibrium and complex gas flow conditions.