Opposite Boundary Research Articles

Steady state stability features of the electron–positron plasma diode in a mode with particle reflection from potential extrema

Steady state stability features of a diode with electrons and positrons entering from opposite boundaries and moving without collisions in plasma are numerically studied. The most complex regime when charged particles are reflected from potential barriers is considered. This problem arises, in particular, when modeling pulsar diodes. A small perturbation evolution is studied. It has been established that at the initial stage of the process the perturbation amplitude changes in time according to an exponential law. It is shown that stationary solutions with a potential barrier for electrons located near the electron-emitting electrode and a potential barrier for positrons located near the opposite electrode are stable when the inter-electrode distance is below a certain threshold. As the inter-electrode distance increases, the solutions become unstable. Solutions of another type when barriers reflecting particles are located in the opposite to the emitting electrode parts of the gap are also studied. However, these solutions turned out to be unstable.

Quantum wetting transition in the cluster Ising model

The wetting transition in the one-dimensional cluster Ising model with opposite boundary fields is studied. Tuning one boundary field while fixing another leads to the occurrence of phase transitions, where the transition points depend on the cluster coupling. Furthermore, the phase diagram is divided into three regions with different phase transition. For weak and strong cluster coupling, the phase transition is continuous and belongs to the same universality of transverse Ising model with boundary fields. For intermediate cluster coupling, the phase transition is first order. In the strong cluster coupling region, the critical region becomes exponentially small and the asymptotic behavior is absent even for lattice size up to 104. A numerical method to solve the energy gap and the correlation length is proposed on an infinite long spin chain. With this method, one can get the critical behavior as close to the critical point as possible provided that the numerical accuracy is high enough. In the light of this method, we clearly show that there is a preasymptotic regime in which the apparent critical exponents depend on the cluster coupling. Moreover, we obtain the accurate energy gap exponent zν and the correlation length exponent ν in the asymptotic critical region.

Witnessing edge modes in trimerized circuit quantum electrodynamic lattice

We propose a scheme to investigate and witness edge modes of general one-dimensional photonic trimers in a circuit quantum electrodynamic lattice. These in-gap edge modes are strictly and analytically solved and the criteria for their emergence are indicated respectively. Moreover, the energy spectrum of the system shows two different regimes characterized by a discrepancy in the number of edge modes. Specifically, while there are always a couple of edge modes only present at one single boundary in both the regimes, one of the regimes also shows another pair of edge modes localized on the opposite boundary. Furthermore, these edge modes are witnessed with the aid of continuous-time quantum walks and average photon number measurements. Our scheme provides a comprehensive method for studying the edge modes of matter.

Термическое воздействие на приземный слой тропосферы как способ управления рисками природных чрезвычайных ситуаций

Purpose. Natural emergencies that occur in mountainous regions annually damage ecosystems, the country's economy and lead to the death of people. On leeward mountain slopes, where precipitation is insufficient, there is an increased fire hazard of territories, complicating water supply of the population and ecosystems. On windward slopes excessive precipitation leads to the risk of avalanches, floods, and mudflows. The search for ways to redistribute the volume of precipitation between the windward and leeward slopes to control the risks of natural emergencies is relevant. The intensity of precipitation is significantly affected by the dew point height (DPH), which determines the position of the lower cloud boundary (the lower the dew point height, the greater the probability of precipitation). The article discusses the possibility of local thermal impact on the ground layer of the troposphere by heating a section of the mountain windward slope in order to increase the dew point height for the subsequent natural transfer of the precipitation zone to its leeward slope. The purpose of the study is to determine the values intervals of the difference in average temperatures of the tropospheric ground layer at its opposite boundaries and values intervals of average wind speed over the relief, where the thermal interaction of the tropospheric ground layer with a local area of the earth's surface can be used to effectively control the dew point height over the entire windward slope of the mountain. Methods. Three-dimensional field modeling is applied using the Fire Dinamic Simulator software product, which provides a numerical solution of the complete nonlinear Navier-Stokes thermohydrodynamic equations for low-speed temperature-dependent flows. Findings. It has been established that the thermal effect on the ground layer of the troposphere above the foot of the mountain windward slope under forced convection conditions can be used to control the distribution of the dew point height over this entire slope. Research application field. The conducted numerical study is the initial stage of a new scientific direction related to natural emergencies risks control caused by excess or lack of mountain slopes moisture (floods, droughts, forest and steppe fires). The obtained results indicate the fundamental possibility of such control by means of local temperature impact from the earth's surface to the ground layer of the troposphere. The practical significance of the results, including financial costs, required for the specified impact on the ground layer of the troposphere, can be revealed in subsequent publications after conducting full-scale experiments. Conclusions. The possibility of reducing the natural emergencies risks caused by excess or lack of moisture in mountain slopes territories by controlling the dew point height value over windward mountain slopes is shown. A solution to this problem is proposed through thermal impact on the ground layer of the troposphere from the earth's surface.

Wind-driven salinity tongue migration in the Gulf of Finland according to NEMO and ERA5 reanalyses

Two hypothesis that can be responsible for the wind-driven migration of the salinity tongue in the bottom layer of the Gulf of Finland (GoF) are tested based on the NEMO and ERA5 reanalyses. The first hypothesis authored by Krauss and Brügge (1991) implies along-channel wind developing upwelling and downwelling jet-like currents in the wind direction at opposite lateral boundaries of the channel, and a compensatory countercurrent in the deep layer (the so-called coastal jet hypothesis). The second hypothesis implies the cross-channel wind developing the along-channel Ekman transport in the upper layer, and a countercurrent in the deep layer (so-called Ekman transport hypothesis). The salinity tongue migration velocity along the GoF thalweg as estimated from the NEMO output is found to be extremely correlated with the along-thalweg projection of the wind stress calculated from the ERA5 output. This is a convincing evidence in favor of the coastal jet hypothesis as opposed to the Ekman transport hypothesis to correctly describe the mechanism of the wind-driven migration of salinity tongue in GoF. Based on a theory of coastal upwelling/downwelling in a two-layer fluid, some analytical considerations and related empirical estimates are presented to explain the prevailing coastal jet mechanism in GoF.

Fundamentally new approaches to solving thermophysical problems in the field of nanoelectronics

Currently, there is a rapid development of thermophysics of solids associated with the need of creating models with a high degree of predictive reliability. This paper presents new approaches to solving relevant issues related to the study of heat transfer in semiconductors and dielectrics, mainly concerning nano-structures. The first of the considered tasks is the creation of a statistical model of the processes of interaction of heat carriers – phonons – with rough surfaces of solids. For the first time authors proposed a method based on the statistics of the slopes of the profile of a random surface. The calculation results are the mean free paths of phonon between the opposite boundaries of the sample, which are necessary for calculating the effective thermal conductivity in ballistic and diffusion-ballistic regime of heat transfer, depending on the roughness parameters. The second task is to develop methods for calculating the processes of heat transfer through the contact surfaces of solids. We were able to show that, taking into account the phonon dispersion and the corresponding restrictions on the frequency values, the modified acoustic mismatch model for calculating Kapitsa resistances can be extended to temperatures above 300 K. Previously, the limit of applicability of this method was considered to be a temperature of 30 K. Moreover, the proposed method is also generalized to the case of rough interfaces. The third task is a new approach to determining the thermal conductivity of solids. The authors have developed a method of direct Monte Carlo simulation of phonon kinetics with strict consideration of their interaction due to the direct use of the laws of conservation of energy and quasi-momentum. The calculations of the thermal conductivity coefficient for pure silicon in the temperature range from 100 to 300 K showed good agreement with the experiment and ab initio calculations of other authors, and also allowed us to consider in detail the kinetics of phonons.

Wetting transition in the transverse-field spin- 12 XY model with boundary fields

The wetting transition in the transverse-field spin-$\frac{1}{2}$ XY model with opposite boundary fields ${h}_{L}^{x}{h}_{R}^{x}<0$ is studied analytically and numerically. We find that the phase diagram is complex and that the wetting transition is of three types: first, second, and fourth order. The energy gap is obtained analytically, and the magnetization profile, correlation functions, and wetting layer thickness are obtained numerically. For $|{h}_{L}^{x}|,|{h}_{R}^{x}|<{h}_{w}$, a first-order phase transition occurs at ${h}_{L}^{x}=\ensuremath{-}{h}_{R}^{x}$, where ${h}_{w}$ is the continuous wetting transition point. For $|{h}_{R}^{x}|$ larger than ${h}_{w}$, the continuous wetting transition occurs at ${h}_{L}^{x}={h}_{w}$, and vice versa. For $g\ensuremath{\ne}1\ensuremath{-}{\ensuremath{\gamma}}^{2}$, the wetting transition is second order, and commensurate and incommensurate phases occur for $g<1\ensuremath{-}{\ensuremath{\gamma}}^{2}$ and $g>1\ensuremath{-}{\ensuremath{\gamma}}^{2}$, respectively. For $g=1\ensuremath{-}{\ensuremath{\gamma}}^{2}$, the wetting transition is fourth order. For this fourth-order phase transition, the third derivative of the surface magnetization oscillates and diverges near the transition point. The correlation length exponent is $\ensuremath{\nu}=2$, and the dynamic exponent is $z=2$. Thus, this fourth-order transition belongs to a new universality class. The wetting behavior is induced by asymmetric boundary fields ${h}_{L}^{x}=\ensuremath{-}{h}_{R}^{x}$ and its finite-size scaling is discussed.

Robust Boundary Controller Design with Proportional Integral Observer for a Linear 1D Heat Equation*

The problem of state estimation with boundary disturbance reconstruction and output regulation for linear 1D parabolic systems with a boundary measurement and unknown constant disturbance input on the opposite boundary is addressed. As the disturbance is unmatched it cannot be directly compensated by the measurement. The problem is addressed with an approach that consists of a backstepping observer for the nominal part with an asymptotic compensation term for the disturbance reconstruction and control offset compensation. The main difference to similar studies relies in the fact that the state space does not need to be extended, leading to a reduced-order observer setup. The effectiveness of the approach is illustrated using numerical simulations.

Radio-frequency sheath excitation at the extremities of scrape-off layer plasma filaments, mediated by resonant high harmonic fast wave scattering

Resonant filament-assisted mode conversion (FAMC) scattering of high harmonic fast waves (HHFW) by cylindrical field-aligned density inhomogeneities can efficiently redirect a fraction of the launched HHFW power flux into the parallel direction. Within a simplified analytic approach, this contribution compares the parallel propagation, reflection and dissipation of nearly resonant FAMC modes for three magnetic field line geometries in the scrape-off layer, in the presence of radio-frequency (RF) sheaths at field line extremities and phenomenological wave damping in the plasma volume. When a FAMC mode, excited at the HHFW antenna parallel location and guided along the open magnetic field lines, impinges onto a boundary at normal incidence, we show that it can excite sheath RF oscillations, even toroidally far away from the HHFW launcher. The RF sheaths then dissipate part of the power flux carried by the incident mode, while another part reflects into the FAMC mode with the opposite wave vector parallel to the magnetic field. The reflected FAMC mode in turn propagates and can possibly interact with the sheath at the opposite field line boundary. The two counter-propagating modes then form in the bounded magnetic flux tube a lossy cavity excited by the HHFW scattering. We investigate how the presence of field line boundaries affects the total HHFW power redirected into the filament, and its splitting between sheath and volume losses, as a function of relevant parameters in the model.

Solution of Inverse Problem of Non-Stationary Heat Conduction Using a Laplace Transform

This paper presents some solutions to the one-dimensional Cauchy-type transient inverse heat conduction problem. Based on known courses of temperature and the heat flux on one of the boundaries of the region, courses of temperature and heat flux on the opposite boundary of the region were determined with the use of the Laplace’s transform. Solution of the inverse problem does not require determination of temperature distribution on subsequent time moments inside the region. Stability of the solution to the inverse problem of the Cauchy type was investigated by means of determining the minimal time step ensuring the stability of the solution. Two examples of one-dimensional transient inverse problems were solved. The first one is related to the reconstruction of shock temperature change on the boundary of the region based on known courses of temperature and heat flux on the opposite boundary. The second one concerned the reconstruction of the heat flux acting on one of the boundaries through a period of time. In both considered problems the reconstructed boundary conditions were discontinuous. Stable results were obtained for both investigated examples, however, the stability of the inverse problem depended on the length of time step.

Double bubbles with high constant mean curvatures in Riemannian manifolds

We obtain existence of double bubbles of large and constant mean curvatures in Riemannian manifolds. These arise as perturbations of geodesic standard double bubbles centered at critical points of the ambient scalar curvature and aligned along eigen-vectors of the ambient Ricci tensor. We also obtain general multiplicity results via Lusternik–Schnirelman theory, and extra ones in case of double bubbles whose opposite boundaries have the same mean curvature.

Classification of noncommutative monoid structures on normal affine surfaces

In 2021, Dzhunusov and Zaitseva classified two-dimensional normal affine commutative algebraic monoids. In this work, we extend this classification to noncommutative monoid structures on normal affine surfaces. We prove that two-dimensional algebraic monoids are toric. We also show how to find all monoid structures on a normal toric surface. Every such structure is induced by a comultiplication formula involving Demazure roots. We also give descriptions of opposite monoids, quotient monoids, and boundary divisors.

Symmetric Mass Generation in the 1+1 Dimensional Chiral Fermion 3-4-5-0 Model.

Lattice regularization of chiral fermions has been a long-standing problem in physics. In this Letter, we present the density matrix renormalization group simulation of the 3-4-5-0 model of (1+1)D chiral fermions with an anomaly-free chiral U(1) symmetry, which contains two left-moving and two right-moving fermions carrying U(1) charges 3,4 and 5,0, respectively. Following the Wang-Wen chiral fermion model, we realize the chiral fermions and their mirror partners on the opposite boundaries of a thin strip of (2+1)D lattice model of multilayer Chern insulator, whose finite width implies the quantum system is effectively (1+1)D. By introducing two sets of carefully designed six-fermion local interactions to the mirror sector only, we demonstrate that the mirror fermions can be gapped out by the interaction beyond a critical strength without breaking the chiral U(1) symmetry, via the symmetric mass generation mechanism. We show that the interaction-driven gapping transition is in the Berezinskii-Kosterlitz-Thouless universality class. We determine the evolution of Luttinger parameters before the transition, which confirms that the transition happens exactly at the point when the interaction term becomes marginal. As the mirror sector is gapped after the transition, we check that the fermions in the light chiral fermion sector remain gapless, which provides the desired lattice regularization of chiral fermions.

Boundary Modes from Periodic Magnetic and Pseudomagnetic Fields in Graphene.

Single-layer graphene subject to periodic lateral strains is an artificial crystal that can support boundary spectra with an intrinsic polarity. This is analyzed by comparing the effects of periodic magnetic fields and strain-induced pseudomagnetic fields that, respectively, break and preserve time-reversal symmetry. In the former case, a Chern classification of the superlattice minibands with zero total magnetic flux enforces single counterpropagating modes traversing each bulk gap on opposite boundaries of a nanoribbon. For the pseudomagnetic field, pairs of counterpropagating modes migrate to the same boundary where they provide well-developed valley-helical transport channels on a single zigzag edge. We discuss possible schemes for implementing this situation and their experimental signatures.

Effective Thermal Conductivity of Typical Composite Plate with Inner Heat Source and Temperature Difference

Composite materials are essential in various energy fields owing to their improved heat transfer characteristics. Due to their inhomogeneous structure, it is difficult to obtain the heat transfer details. Effective thermal conductivity (ETC) is an important lumped thermal parameter used to analyze the heat transfer process in composite materials. Existing ETC models are derived by applying a temperature difference (TD) on two opposite boundaries of the composite material to induce heat flow. However, for some composite materials, such as nuclear fuels, the effect of the inner heat source (IHS) is typically ignored. Thus, the suitability of using ETC models based on a TD scheme for composite materials with IHS still requires further investigation. In this study, first the conserved quantities of ETC of the TD and IHS schemes were determined. For normal materials of the TD scheme, the conserved quantity of ETC can be selected as heat flow, whereas for nuclear fuels of the IHS scheme, the average temperatures are recommended as the conserved quantity. Then the general ETC models for composite plate were derived considering both the TD and IHS schemes and special cases with either TD or IHS were also analyzed. Finally, based on the results of this study, the idea of studying the ETC of tristructural-isotropic or TRISO particle-based nuclear fuels is proposed.

Frequency Comb Free Vibration Behavior of a Single-Span Plate Pumped by Low-Speed Moving Inertial Loads

Structures carrying moving loads present rich vibration phenomena and colorful spectrum characteristics. This study analytically investigates the moving-inertial-load-pumped frequency comb free vibration behavior of a single-span rectangular linear elastic Kirchhoff thin plate in the low-speed region. Multiple-time-scales expansion is made and the asymptotic solution describing the non-resonance modal oscillation is derived. Case studies on a single-span rectangular isotropic plate with the clamped opposite boundaries dominated by the first two transverse flexural modes are presented. Numerical computation based on finite element method structure modeling and response numerical integration verifies the modal frequency comb characteristics as predicted by the proposed theoretical model. The results also present the weak modal interaction for the studied single-span structure in the observed light-mass low moving speed region. The outcomes of this study will benefit the related structural dynamic system design and intervention.

Observation of the spin-Hall effect in Pt/GaAs by circular polarized photoconductivity

Electrically generated spin accumulation due to the spin Hall effect of Pt/GaAs is detected by circular polarized photoconductivity (CPPC), which shows electron spins with different polarizations accumulated around opposite sample boundaries. An optical absorption model incorporating spin is used to explain these features. The detailed analysis of the observed degree of circular polarization of the photocurrent strongly suggests that Pt and GaAs have the same spin accumulation length in the Pt/GaAs heterostructure.

Flatness-based analysis and control design for 2 × 2 hyperbolic PDEs with nonlinear boundary dynamics

Distributed-parameter systems represented by linear one-dimensional 2 × 2 hyperbolic PDEs with nonlinear finite-dimensional differentially flat dynamics at one boundary and control acting linearly via the opposite boundary are considered. Flatness of the overall system, deduced from the flatness of the boundary system, allows for the parametrization of the systems solutions by the trajectory of a flat output. The state associated with this parametrization corresponds to the restriction of the flat-output trajectory to a compact interval. This state is intrinsically linked to a nonlinear hyperbolic controller form and associated with the original system variables by an invertible transformation. Moreover, it allows for immediate and constructive reachability analysis. State feedback for tracking a desired reference trajectory is achieved by choosing arbitrary stable closed-loop dynamics. A numerical example illustrates the control performance for different choices of the closed-loop dynamics.

Nanograin size effects on deformation mechanisms and mechanical properties of nickel: A molecular dynamics study

The grain size refinement of metallic materials to the nanometer scale produces interesting properties compared to the coarse-grained counterparts. Their mechanical behavior, however, cannot be explained by the classical deformation mechanisms. Using molecular dynamics simulations, the present work examines the influence of grain size on the deformation mechanisms and mechanical properties of nanocrystalline nickel. Samples with grain sizes from 3.2 to 24.1 nm were created using the Voronoi tessellation method and simulated in tensile and relaxation tests. The yield and ultimate tensile stresses follow an inverse Hall-Petch relationship for grain sizes below ca. 20 nm. For samples within the conventional Hall-Petch regime, no perfect dislocations were observed. Nonetheless, a few extended dislocations were nucleated from triple junctions, suggesting that the suppression of conventional slip mechanism is not uniquely responsible for the inverse Hall-Petch behavior. For samples respecting the inverse Hall-Petch regime, the high number of triple junctions and grain boundaries allowed grain rotation, grain boundary sliding, and diffusion-like behavior that act as competitive deformation mechanisms. For all samples, the atomic configuration analysis showed that Shockley partial dislocations are nucleated at grain boundaries, crossing the grain before being absorbed in opposite grain boundaries, leaving behind stacking faults. Interestingly, the stress relaxation tests showed that the strain rate sensitivity decreases with grain size for a specific grain size range, whereas for grains below approximately 10 nm, the strain rate sensitivity increases as observed experimentally. Repeated stress relaxation tests were also performed to obtain the effective activation volume parameter. However, the expected linear trend in pertinent plots required to obtain this parameter was not found.

Quantum wetting transition in the one-dimensional transverse-field Ising model with random bonds

The quantum wetting transition in the one-dimensional transverse-field Ising model with random bonds is studied. Opposite boundary fields are applied at the two ends of the Ising chain. The interface between two domains with oppositely oriented magnetization is localized near the boundary or in the middle of the chain. The wetting transition refers to the phase transition of localization and delocalization of the interface. The tuning parameter ${h}_{L}$ is the boundary field at one end, e.g., the left end. At the transition point ${h}_{L}={h}_{w}$, the wetting transition occurs. First, we study the wetting transition with one defect bond. It is a first-order transition, and the interface jumps from the left end of the chain to the defect bond at the transition point. Second, we study the wetting transition with two defect bonds and find that the weaker defect bond dominates the phase transition. The wetting transition is still first order, and the interface is localized at the left end of the chain or at the weaker defect bond. Lastly, the random bond case is studied. The random bonds have a rectangular distribution. The wetting transition is still first order. The finite-size effects are studied. The statistics of the transition points and the energy gaps are obtained. We study lattices with sizes $N=100$, 150, 200, 250, 300, and 350. The deviation of the phase transition points ${h}_{w}$ does not decrease as the lattice size increases. It is argued that the transition point is sample dependent, i.e., the variation in the transition point ${h}_{w}$ does not approach zero, even at the thermodynamic limit.