Asymmetric Boundary Conditions Research Articles

A Riemann–Hilbert approach for the focusing and defocusing mKdV equation with asymmetric boundary conditions in Few-Cycle Pulses

A Riemann–Hilbert approach for the focusing and defocusing mKdV equation with asymmetric boundary conditions in Few-Cycle Pulses

A Riemann–Hilbert approach for the focusing and defocusing mKdV equation with asymmetric boundary conditions in Few-Cycle Pulses

A Riemann–Hilbert approach for the focusing and defocusing mKdV equation with asymmetric boundary conditions in Few-Cycle Pulses

Jetting bubbles observed by x-ray holography at a free-electron laser: internal structure and the effect of non-axisymmetric boundary conditions

In this work, we study the jetting dynamics of individual cavitation bubbles using x-ray holographic imaging and high-speed optical shadowgraphy. The bubbles are induced by a focused infrared laser pulse in water near the surface of a flat, circular glass plate, and later probed with ultrashort x-ray pulses produced by an x-ray free-electron laser (XFEL). The holographic imaging can reveal essential information of the bubble interior that would otherwise not be accessible in the optical regime due to obscuration or diffraction. The influence of asymmetric boundary conditions on the jet’s characteristics is analysed for cases where the axial symmetry is perturbed and curved liquid filaments can form inside the cavity. The x-ray images demonstrate that when oblique jets impact the rigid boundary, they produce a non-axisymmetric splash which grows from a moving stagnation point. Additionally, the images reveal the formation of complex gas/liquid structures inside the jetting bubbles that are invisible to standard optical microscopy. The experimental results are analysed with the assistance of full three-dimensional numerical simulations of the Navier–Stokes equations in their compressible formulation, which allow a deeper understanding of the distinctive features observed in the x-ray holographic images. In particular, the effects of varying the dimensionless stand-off distances measured from the initial bubble location to the surface of the solid plate and also to its nearest edge are addressed using both experiments and simulations. A relation between the jet tilting angle and the dimensionless bubble position asymmetry is derived. The present study provides new insights into bubble jetting and demonstrates the potential of x-ray holography for future investigations in this field.

Statistical analysis of coupled oscillations with a single fixed endpoint and its application to carbon nanomaterials

Squared deviations from the equilibrium positions of one-dimensional coupled harmonic oscillators with fixed and free endpoints are calculated, and the time averages are expressed as a function of the initial displacements and velocities. Furthermore, we consider the averages of squared deviations over an ensemble of initial displacements and velocities, which distribute based on a product of the same distribution functions with variances of the initial coordinates σx2 and velocities σv2 , respectively. We demonstrate that the mean squared deviation linearly increases as the oscillator separates further from the fixed endpoint because of the asymmetrical boundary conditions, and that the increase rate depends only on σv2 and not on σx2 . This simple statistical property of harmonic oscillation is similarly observed in the oscillations of a graphene sheet and carbon nanotube in molecular dynamics simulations, in which the interacting forces are nonlinear.

The effect of external magnetic field on the instability of THz plasma waves in nanoscale graphene field-effect transistors

Abstract The instability of plasma waves in the channel of field-effect transistors will cause the electromagnetic waves with THz frequency. Based on a self-consistent quantum hydrodynamic model, the instability of THz plasmas waves in the channel of graphene field-effect transistors has been investigated with external magnetic field and quantum effects. We analyzed the influence of weak magnetic fields, quantum effects, device size, and temperature on the instability of plasma waves under asymmetric boundary conditions numerically. The study results show that the magnetic fields, quantum effects, and the thickness of the dielectric layer between the gate and the channel can increase the radiation frequency. Additionally, we observed that increase in temperature leads to a decrease in both oscillation frequency and instability increment. The numerical results and accompanying images obtained from our simulations provide support for the above conclusions.

Examining the Applicability of Direct Analytic Method (DAM) to Normal Modes of Poloidal Oscillations Under Symmetric and Asymmetric Boundary Conditions

AbstractA working Direct Analytic Method (DAM) model is envisaged to explain the normal modes of poloidal Alfven waves in the Earth's magnetosphere. The model solves the ideal, cold, magnetohydrodynamic (MHD) equations associated with transverse components of the magnetic perturbations in a dipolar magnetic field. DAM model is used to study the transverse poloidal waves in different regions of magnetosphere characterized by their L‐value and different plasma variability. The plasma density distribution is assumed to be governed by the standard power law, 1/rm, where r is the geocentric distance of any point of interest on the field line and m is the density index. The eigen frequencies and spatial structures are obtained analytically under different ideal ionospheric boundary conditions and the results are compared with the numerical solutions to establish the validity of the model. DAM, being an analytic model, is used to explain the distinctive structural features of transverse poloidal waves which are obtained under different boundary conditions, for different density indices. Furthermore, the application of the analytic model in the computation of eigen frequency as well as plasma density is demonstrated under different observational scenario.

On-Chip Integration of a Plasmonic FET Source and a Nano-Patch Antenna for Efficient Terahertz Wave Radiation.

Graphene-based Field-Effect Transistors (FETs) integrated with microstrip patch antennas offer a promising approach for terahertz signal radiation. In this study, a dual-stage simulation methodology is employed to comprehensively investigate the device's performance. The initial stage, executed in MATLAB, delves into charge transport dynamics within a FET under asymmetric boundary conditions, employing hydrodynamic equations for electron transport in the graphene channel. Electromagnetic field interactions are modeled via Finite-Difference Time-Domain (FDTD) techniques. The second stage, conducted in COMSOL Multiphysics, focuses on the microstrip patch antenna's radiative characteristics. Notably, analysis of the S11 curve reveals minimal reflections at the FET's resonant frequency of 1.34672 THz, indicating efficient impedance matching. Examination of the radiation pattern demonstrates the antenna's favorable directional properties. This research underscores the potential of graphene-based FETs for terahertz applications, offering tunable impedance matching and high radiation efficiency for future terahertz devices.

Transient heat transfer in concentric cylinders using periodic boundary condition and asymmetric heat generation applied to thermal plug and abandonment of oil wells

When a well does not fulfil its objectives, it is repurposed or permanently plugged, a shift in budget from revenue to Plug and Abandonment (P&A) expenditures occurs. New technologies being developed for P&A make use of a powerful heat emitter for melting the surrounding of the well forming a solid plug after the cool down. However, there is a gap in understanding the heat transport process in the well and much need for appropriate mathematical tools and solutions for estimating the effectiveness of Thermal P&A. The thermal analysis of the process requires eigenvalues in polar coordinates, which return only real quantities due to its implicitly dependence on the angular eigenvalues. Here, a hybrid analytical/numerical method is applied to an asymmetric transient heat conduction problem. The oil well is conceived as a 2-D multi-layer disc cast in polar coordinates, where the Separation of Variables Method (SVM) was applied to achieve a closed-form solution. Asymmetric boundary conditions of first, second and third kind can be implemented utilizing the proposed framework. A Finite Volume Method (FVM) numerical solution was produced for code verification. Lastly, research results show that temperature levels arising from the thermite reaction throughout the composite cylinder domain in radial and azimuthal ranges are enough for surpassing the melting point of the production tube steel. The results evidenced the thermal efficiency of the TP&A procedure and suggested that the production column may be destroyed by fusion, thus reducing tamponing expenses significantly.

An Improved Lax-Wendroff Scheme for Two-Dimensional Transient Thermal Simulation

The stability and accuracy of explicit high-order finite difference (HOFD) algorithms have been research hotspots in different fields. To improve the stability and accuracy of the HOFD algorithms in thermal simulations, we present a Lax-Wendroff high-order finite difference (LHOFD) algorithm to solve the 2D transient heat transfer equation in this paper and develop an improved LHOFD (IHOFD) algorithm to improve the stability of the LHOFD algorithm. The formulas of the general high-order central FD (HOCFD) coefficients and the truncation error coefficient as well as the high-order non-central FD (HONFD) coefficients and the truncation error coefficient of the fourth-order spatial derivative are derived concisely in a different way. Furthermore, a unified analytical formula of the general HOCFD and HONFD coefficients, which can calculate the spatial derivative of any integer order, is derived. A new strategy of combination with the HOCFD and HONFD approximations under the same high-order accuracy as the internal computational domain is proposed to calculate the mixed derivatives of the boundary domains with high accuracy, no additional computational cost, and easy implementation. Then, the accuracy analysis, stability analysis, and comparative analysis of numerical simulation results obtained by the LHOFD and IHOFD algorithms with the exact solution show the correctness and validity of the proposed algorithms and their stability formulas, and the advantages of the proposed algorithms. The proposed algorithms are valid under both symmetric and asymmetric boundary conditions. The stability factor of the LHOFD algorithm is slightly higher than that of the conventional algorithm. The stability factor of the IHOFD algorithm is twice that of the conventional algorithm, and the maximum absolute error of the thermal simulation is within 0.015 (°C).

Performance improvement and thermomechanical analysis of a novel asymmetrical annular thermoelectric generator

Enhancing thermoelectric performance hinges on optimizing the geometry of thermoelectric legs. In this study, we present a novel asymmetrical annular thermoelectric generator (ATEG) in which the proportions of P-type and N-type legs are meticulously balanced. We construct a one-dimensional analytical model tailored to this ATEG. Utilizing this model, we derive the relationship governing thermal-electrical impedance matching in an asymmetrical ATEG and formulate a general expression for optimizing the asymmetry coefficient. We explore the influence of various thermal boundary conditions on optimal impedance matching, ideal annular leg parameters, and the optimal asymmetry coefficient. Our findings reveal that thermal boundary conditions significantly affect the optimal load ratio. Furthermore, in comparison to traditional ATEGs, our proposed asymmetrical ATEG with the optimized structure exhibits a remarkable 16.2 % increase in output power while maintaining the same material volume. Additionally, we perform a three-dimensional numerical analysis of the asymmetrical ATEG using Comsol. Our research findings indicate that introducing the asymmetric structure leads to higher maximum thermal stress on the legs. Interestingly, the study of asymmetric thermal boundary conditions highlights that improving heat transfer between the ATEG and the cooler yields higher mechanical reliability compared to enhancing heat transfer between the ATEG and the heat source.

Numerical analysis of non-Fourier heat conduction dynamics in the composite layer

This paper presents the numerical analysis of non-Fourier heat conduction in thin composite layers under asymmetrical boundary conditions. In the thermal barriers such as steam and gas turbine blades, thin film coating are used to protect the blade from thermal damage. The coating on the blades are very short in length. Heat conduction across thin composite layer with short time is examined using a finite element approach. With this very small duration with the finite speed of the thermal wave, the Fourier mode of heat conduction is disappeared due to the infinite speed of the thermal wave assumption. Therefore, analyzing the non-Fourier heat conduction in thin layers is essential. The developed model is executed in Python using Newmark's scheme and the constant average acceleration method to predict the temperature variation and temperature contours. The present model is validated with an experimental and numerical solution with good agreement. Besides, the temperature distribution across the composite layer with the entire length of the substrate and the coating for different thermal conductivity values, thermal diffusivity, and relaxation time are examined. It is noted that when the dimensionless

Asymmetric Periodic Boundary Conditions for All-Atom Molecular Dynamics and Coarse-Grained Simulations of Nucleic Acids.

Periodic boundary conditions are commonly applied in molecular dynamics simulations in the microcanonical (NVE), canonical (NVT), and isothermal-isobaric (NpT) ensembles. In their simplest application, a biological system of interest is placed in the middle of a solvation box, which is chosen 'sufficiently large' to minimize any numerical artifacts associated with the periodic boundary conditions. This practical approach brings limitations to the size of biological systems that can be simulated. Here, we study simulations of effectively infinitely long nucleic acids, which are solvated in the directions perpendicular to the polymer chain, while periodic boundary conditions are also applied along the polymer chain. We study the effects of these asymmetric periodic boundary conditions (APBC) on the simulated results, including the mechanical properties of biopolymers and the properties of the surrounding solvent. To get some further insights into the advantages of using the APBC, a coarse-grained worm-like chain model is first studied, illustrating how the persistence length can be extracted from the local properties of the polymer chain, which are less affected by the APBC than some global averages. This is followed by all-atom molecular dynamics simulations of DNA in ionic solutions, where we use the APBC to investigate sequence-dependent properties of DNA molecules and properties of the surrounding solvent.

Effect of spin on the instability of THz plasma waves in field-effect transistors under non-ideal boundary conditions

Terahertz (THz) radiation can be generated due to the instability of THz plasma waves in field-effect transistors (FETs). In this work, we discuss the instability of THz plasma waves in the channel of FETs with spin and quantum effects under non-ideal boundary conditions. We obtain a linear dispersion relation by using the hydrodynamic equation, Maxwell equation and spin equation. The influence of source capacitance, drain capacitance, spin effects, quantum effects and channel width on the instability of THz plasma waves under the non-ideal boundary conditions is investigated in great detail. The results of numerical simulation show that the THz plasma wave is unstable when the drain capacitance is smaller than the source capacitance; the oscillation frequency with asymmetric boundary conditions is smaller than that under non-ideal boundary conditions; the instability gain of THz plasma waves becomes lower under non-ideal boundary conditions. This finding provides a new idea for finding efficient THz radiation sources and opens up a new mechanism for the development of THz technology.

Thermomechanical performance of energy retaining pile influenced by surrounding utility tunnel via the regression tree model

The thermomechanical performance of energy retaining pile differs from that of axisymmetric energy pile due to utility tunnel excavation. This study presents four field tests of energy retaining pile conducted before and after utility tunnel construction. A regression tree (RT) model for predicting the thermally induced stress of energy retaining pile was established based on the measured water temperature, pile temperature and previous stage thermally induced stress to evaluate the effect of shallow buried utility tunnel on the thermomechanical performance of adjacent energy pile. The established thermally induced stress RT prediction model could acceptably predict the thermally induced stress of the future short-team. Surrounding utility tunnel excavation alters the distribution of the axial thermally induced stress. The axial thermomechanical response of the energy retaining pile after utility tunnel construction is approximately 50% that before utility tunnel construction. The asymmetrical boundary conditions cause a limited bending moment of the energy retaining pile at the top or bottom of the utility tunnel, which is not enough to threaten the pile safety. Moreover, the thermal performance of the energy retaining pile slightly increases due to the heat exchange between the pile and the air in the surrounding utility tunnel.

Thermal boundary condition studies in large aspect ratio Rayleigh–Bénard convection

We study the influence of thermal boundary conditions on large aspect ratio Rayleigh–Bénard convection by a joint analysis of experimental and numerical data sets for a Prandtl number Pr=7 and Rayleigh numbers Ra=105−106. The spatio-temporal experimental data are obtained by combined Particle Image Velocimetry and Particle Image Thermometry measurements in a cuboid cell filled with water at an aspect ratio Γ=25. In addition, numerical data are generated by Direct Numerical Simulations (DNS) in domains with Γ=25 and Γ=60 subject to different idealized thermal boundary conditions. Our experimental data show an increased characteristic horizontal extension scaleλ̃ of the flow structures for increasing Ra , which due to an increase of the convective heat transfer also leads to an increase of the Biot number (Bi) at the cooling plate. However, we find the experimental flow structure size to range in any case in between the ones observed for the idealized thermal boundary conditions captured by the simulations: On the one hand, they are larger than in the numerical case with applied uniform temperatures at the plates. On the other hand, they are smaller than in the case of an applied constant heat flux, the latter of which leads to a structure that grows gradually up to the horizontal domain size. We are able to link this observation qualitatively to theoretical predictions for the onset of convection. Furthermore, we study the effect of the asymmetric boundary conditions on the heat transfer. Contrasting experimental and numerical data reveals an increased probability of far-tail events of reversed heat transfer. The successive decomposition of the local Nusselt number Nuloc traces this effect back to the sign of the temperature deviation Θ̃, eventually revealing asymmetries of the heating and cooling plate on the thermal variance of the generated thermal plumes.

Self-Consistent Positive Streamer-Leader Propagation Model Based on Finite Element Method (FEM) and Voltage Distortion Method (VDM)

Researchers have worked on positive leader propagation models and proposed different theoretical and numerical approaches. The charge simulation method (CSM) has traditionally been chosen to model the quasi-static electric field of each stage of leader propagation. The biggest drawback of the CSM is that the calculation is complicated and time-consuming when dealing with asymmetric electric field structures. On the contrary, the finite element method (FEM) is more suitable and reliable for solving electrostatic field problems with asymmetric and complex boundary conditions, avoiding the difficulties of virtual charge configuration and electric field calculation under complex boundary conditions. This paper modeled a self-consistent streamer-leader propagation model in an inverted rod-plane air gap based on FEM and the voltage distortion method (VDM). The voltage distortion coefficient was analyzed to calculate the streamer length and space charge. The physical dynamic process of the discharge was simulated with the help of COMSOL Multiphysics and MATLAB co-simulation technology. The results show that the initial voltage of the first corona is -1036 kV, close to the experiment value of -1052 kV. The breakdown voltage of -1369 kV is highly consistent with the experimental value of -1365 kV. The largest streamer length is 2.72 m, slightly higher than the experimental value of 2.3 m. The leader velocity is 2.43×104 m/s, close to the experiment value of 2.2×104 m/s. This model has simple calculations and can be used in complex electrode configurations and arbitrary boundary conditions without simplifying the model structure, making the model more flexible.

Electrokinetic cells powered by osmotic gradients: an analytic survey of asymmetric wall potentials and hydrophobic surfaces

Nowadays, the fabrication of microelectromechanical systems has given rise to several studies whose main purpose is to obtain the greater benefit of micro-nano scales, putting special interest in the improvement of the design of such devices. One of several applications is harvesting energy due to electrokinetic phenomena, more specifically, streaming potential. Nonetheless, there is a lack of theoretical studies encompassing coupled asymmetries in both slip conditions and electric potentials (these being associated with the chemical and physical characteristics of the surfaces). By virtue of the previous explanation, ideal assumptions based on the symmetry of some variables must be reconsidered, especially when manufacturing symmetric flat surfaces on a tiny scale is quite difficult to achieve. This work presents a theoretical study in power generation, exploiting streaming potentials produced by an asymmetric membrane which in turn prompts a flux inside a microchannel made of two flat parallel surfaces. The driving force in this electrokinetic battery is the osmotic gradient on both sides of the membrane. The model uses the Debye–Hückel approximation together with the appropriate asymmetric boundary conditions for both slips and potentials on the surfaces. The main variables of interest, such as the dimensionless horizontal velocity component, the pressure field, and the average streaming potential, were estimated.

Rayleigh–Bénard magnetoconvection with asymmetric boundary condition and comparison of results with those of symmetric boundary condition

Rayleigh–Bénard magnetoconvection with asymmetric boundary condition and comparison of results with those of symmetric boundary condition

Comparison of the effect of suction-injection-combination on Rayleigh–Bénard convection in the case of asymmetric boundaries with those of symmetric ones

The effect of suction-injection-combination (SIC) on the linear and weakly nonlinear stability of Rayleigh–Bénard convection is considered in the paper for the cases of symmetric and asymmetric boundary conditions. Using the Maclaurin series with an appropriate number of terms, expression for eigenfunctions is obtained. The linear theory corroborates the results obtained using the chosen eigenfunctions in the limiting case of the no-SIC effect by matching accurately with the exact values concerning the critical Rayleigh number (Rac) and the wave number (αc). It is found that the effect of SIC is to stabilize the system in the case of symmetric boundaries irrespective of SIC being pro-gravity or anti-gravity. However, the effect of SIC is to stabilize/destabilize the system depending on SIC being pro-gravity or anti-gravity in the case of the asymmetric boundaries. We also noted a similar effect in the case of αc wherein a maximum error of order 10−4 was observed. The main novelty of the present work is studying the influence of SIC on the nonlinear dynamics of the considered problem. It is shown that the effect of SIC is to hasten the onset of chaos. Using various indicators (the largest Lyapunov exponent, the time series solution, the amplitude spectrum, and the phase-space plots), the dynamical behavior of the system is analyzed and the influence of SIC on the dynamics is recorded. The change due to the boundary effect and the SIC on the size of convection rolls and the trapping region where the dynamical system evolves within a bound is highlighted in the paper.

The Asymmetric Dynamical Casimir Effect

A mirror with time-dependent boundary conditions will interact with the quantum vacuum to produce real particles via a phenomenon called the dynamical Casimir effect (DCE). When asymmetric boundary conditions are imposed on the fluctuating mirror, the DCE produces an asymmetric spectrum of particles. We call this the asymmetric dynamical Casimir effect (ADCE). Here, we investigate the necessary conditions and general structure of the ADCE through both a waves-based and a particles-based perspective. We review the current state of the ADCE literature and expand upon previous studies to generate new asymmetric solutions. The physical consequences of the ADCE are examined, as the imbalance of particles produced must be balanced with the subsequent motion of the mirror. The transfer of momentum from the vacuum to macroscopic objects is discussed.