Reflecting Boundary Conditions Research Articles

On the interaction between ultralight bosons and quantum-corrected black holes

Both ultralight dark matter and exploring the quantum nature of black holes are all topics of great interest in gravitational wave astronomy at present. The superradiant instability allows an exotic compact object (ECO) to be surrounded by an ultralight boson cloud, which leads to the emission of gravitational waves and further triggers rich dynamical effects. In this paper, we study the gravitational effects of superradiant instabilities by calculating the energy fluxes of gravitational waves emitted from ultralight scalar dark matter fields by solving the Teukolsky equation in the background of a massive ECO phenomenologically described by a Kerr geometry with a reflective boundary condition at its physical boundary. We find that both the amplitude and phase of the reflectivity will either suppress or enhance the energy flux of GWs by several orders of magnitude if Mμ ≳ 0.5 where M and μ are the mass of ECO and boson, respectively. However, the modifications to energy flux are negligible if Mμ ≲ 0.5. Our results suggest that reflectivity will play a significant role in the near-horizon physics of ECO.

Effect of electromagnetic wave reflection from conducting surfaces on blob dynamics in the tokamak scrape-off layer

Electromagnetic dynamics of blobs in hot scrape-off-layer plasmas of the tokamak are affected by excitation of the Alfvén waves and their subsequent propagation to the machine first wall along open magnetic field lines. In this study, the interaction of electromagnetic perturbations with the conducting tokamak wall and the resulting impact of these perturbations on the motion of filaments at the tokamak edge are analyzed. The model describing blob dynamics is presented. To describe the reflection of the Alfvén waves from the tokamak wall, the new form of sheath boundary conditions for the parallel current and electrostatic potential at the plasma–sheath interface is proposed. It is demonstrated that depending on the wall resistivity, the waves can be either absorbed or reflected by the wall, influencing the excitation of electromagnetic fluctuations inside the filament plasma. The theoretical conclusions of the study are supported with the BOUT++ numerical modeling of blob dynamics at the edge of the DIII-D and NSTX tokamaks. It is shown that taking the reflective boundary conditions into account leads to the excitation of the standing Alfvén waves in the filament, periodically canceling the electrostatic currents inside the blob.

Aluminum Nitride Based Film Bulk Acoustic Resonator With Anchor Column Structure

In order to reduce the lateral acoustic energy loss of thin film bulk acoustic resonators (FBARs), the trench structure for FBAR is generally designed to block the leakage of acoustic wave and help improving the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> -factor. One method the designers often used is etching the piezoelectric material around the active area of the FBAR to form the air-wall structure as a perfect reflection boundary condition. In this paper, the FBAR with trench structure is fabricated. The multilayer films in the FBAR with trench structure are easily warped due to excessive compressive stress. The numerical analysis and finite element simulation are used to verify the effects of different stresses on the devices. In order to avoid the degradation of FBAR performance caused by film warpage, the FBAR with anchor columns is proposed. The anchor columns are located on both sides of the FBAR, and they are designed to reduce film bending and the compressive stress of active area of the resonator. The measured results show that the Qs and Qp of the FBAR with anchor columns are increased by 55.8% and 21.1%, respectively, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k_{eff}{}^{2}$ </tex-math></inline-formula> improved from 5.6% to 6.7% compared with the FBAR without the anchor columns. [2022-0179]

Research and Application of the Rehomogenization Method for PWR Core Neutron Physics Simulation

The “two-step” scheme based on assembly homogenization is widely applied in simulations for pressurized water reactor (PWR) cores in which the few-group constants of the fuel assembly are generated with the single-assembly simulation. However, the reflective boundary condition adopted in the single-assembly simulation can’t characterize the real environment in the core, especially the strong heterogeneity between the neighboring assemblies. In order to consider the environmental effects on the homogenized few-group constants, a rehomogenization method is proposed. In this method, the heterogeneous neutron spectral of single-assembly model of the reflective boundary condition is corrected with the homogeneous neutron spectral of the real core environment. Through definition and precalculation of the rehomogenization factors for few-group constants during the fuel assembly simulation, corresponding corrected constants can be recomputed during the core simulation to consider the environmental effects. This method has been implemented in our home-developed code Bamboo-C. For method verification, both the heavy reflector PWR EPR1750 and the baffle reflector PWR HPR1000 have been simulated. It can be observed that the biases of the eigenvalues can be notably reduced with the proposed rehomogenization method. The assembly-averaged powers of the peripheral fuel assemblies were also notably reduced, especially for the EPR1750, which indicates that the environmental effects can be appropriately solved with the rehomogenization method.

Mortensen observer for a class of variational inequalities – lost equivalence with stochastic filtering approaches

We address the problem of deterministic sequential estimation for a nonsmooth dynamics governed by a variational inequality. An example of such dynamics is the Skorokhod problem with a reflective boundary condition. For smooth dynamics, Mortensen introduced in 1968 a nonlinear estimator based on likelihood maximisation. Then, starting with Hijab in 1980, several authors established a connection between Mortensen’s approach and the vanishing noise limit of the robust form of the so-called Zakai equation. In this paper, we investigate to what extent these methods can be developed for dynamics governed by a variational inequality. On the one hand, we address this problem by relaxing the inequality constraint by penalization: this yields an approximate Mortensen estimator relying on an approximating smooth dynamics. We verify that the equivalence between the deterministic and stochastic approaches holds through a vanishing noise limit. On the other hand, inspired by the smooth dynamics approach, we study the vanishing viscosity limit of the Hamilton-Jacobi equation satisfied by the Hopf-Cole transform of the solution of the robust Zakai equation. In contrast to the case of smooth dynamics, the zero-noise limit of the robust form of the Zakai equation cannot be understood in our case from the Bellman equation on the value function arising in Mortensen’s procedure. This unveils a violation of equivalence for dynamics governed by a variational inequality between the Mortensen approach and the low noise stochastic approach for nonsmooth dynamics.

About Lanford's theorem in the half-space with specular reflection

&lt;p style='text-indent:20px;'&gt;The present article proposes a rigorous derivation of the Boltzmann equation in the half-space. We show an analog of the Lanford's theorem in this domain, with specular reflection boundary condition, stating the convergence in the low density limit of the first marginal of the density function of a system of N hard spheres towards the solution of the Boltzmann equation associated to the initial data corresponding to the initial state of the one-particle-density function. The original contributions of this work consist in two main points: the rigorous definition of the collision operator and of the functional space in which the BBGKY hierarchy is solved in a strong sense; and the adaptation to the case of the half-space of the control of the recollisions performed by Gallagher, Saint- Raymond and Texier, which is a crucial step to obtain a quantitative version of the Lanford's theorem.&lt;/p&gt;

Neutronics Modeling and Nuclear Analysis Based on the Full CAD Geometry of CFETR

Radiation field analyses of the fusion reactor are vital to machine design and personal/environmental irradiation protection. Owing to the complicated and toroidal symmetry of fusion reactors, these nuclear analyses have been performed based on a sector model with reflecting boundary conditions. However, not all sections of a fusion reactor are symmetrical in the toroidal direction, particularly the neutron flow channels introduced by auxiliary systems from which particles can leak directly from the plasma. Hence, the reflecting boundary conditions cannot accurately describe the particle transport. Consequently, radiation field analyses based on a full-sector model must be performed to verify the results obtained. In this regard, the neutronics model of CFETR has been built in 360 deg. Meanwhile, the development of the automatic geometry conversion platform cosVMPT has enabled an entire 360-deg model of the CFETR to be established. The model contains all primary components and the outer house building. Sixteen upper/lower ports and six equatorial ports are included, in which two of them are slanted for neutral beam injection, whereas the other ports are filled with a shielding block. The on-the-fly (OTF) global variance reduction method is utilized to accelerate neutron/photon coupling transport. The results show that cosVMPT and the OTF method are reliable, and that the obtained neutron/photon flux is asymmetric outside the main machine. The computational results of the 360-deg model are compared with those of the sector model such that the application scope of simplifying the modeling and calculation using the sector model can be further confirmed.

Investigation of effects of lateral boundary conditions on current filament movements in Trench-Gate IGBTs

When designing the reliability of high voltage power devices, it is very useful to confirm the behavior of current filaments in various structures and situations by Technology CAD simulation. Current filaments are caused by the electrical instability inherent in the device when a large voltage is applied to the device or a large current flows through the device, which is the current concentration phenomenon into only a few cells and moves around mainly in the plane of the cell region of the device. The ease of movement of the current filament is determined by the design of the device structure and has a great impact on device reliability. This design is difficult to examine by actual measurement, so simulations are often used. Since device simulations with a large three-dimensional (3D) structure take a huge amount of calculation time, it is common to cut out a part of the chip as small as possible and set boundary conditions on each cut surface to build a simulation setup that fits the purpose of the simulation. In 2D current filament simulations, it is known that when the reflective boundary condition (ideal Neumann) are imposed on the sidewalls, the boundary condition can significantly affect the results. In this work, to the best of my knowledge, I clearly show for the first time the relationship between the current filament movements and lateral boundary conditions in a large-scale three-dimensional trench-gate IGBT structure under conditions especially in which the current filament is highly mobile. In this case, the convergence is very poor and the calculation is difficult, so I also describe how to calculate it well by mathematical settings.

Stability of the microcanonical ensemble in Euclidean Quantum Gravity

This work resolves a longstanding tension between the physically-expected stability of the microcanonical ensemble for gravitating systems and the fact that the known negative mode of the asymptotically flat Schwarzschild black hole decays too rapidly at infinity to affect the ADM energy boundary term at infinity. The key to our study is that we fix an appropriate off-shell notion of energy, which we obtain by constructing the microcanonical partition function as an integral transform of the canonical partition function. After applying the rule-of-thumb for Wick rotations from our recent companion paper to deal with the conformal mode problem of Euclidean gravity, we find a positive definite action for linear perturbations about any Euclidean Schwarzchild (-AdS) black hole. Most of our work is done in a cavity with reflecting boundary conditions, but the cavity wall can be removed by taking an appropriate limit.

Stochastic delay differential equations: Analysis and simulation studies

Stochastic delay differential equations play an important role in modelling scientific and engineering systems. In this paper the partial differential equation satisfying the time evolution of the probability density function of the state variable governed by the stochastic delay differential equation (SDDE) with additive white noise and coloured noise perturbation is obtained under small time delay and small correlation time approximation using path integral formalism. This partial differential equation reduces to a Fokker–Planck equation for particular linear and non-linear SDDE. Fokker–Planck equation is then solved with reflecting boundary conditions to get the analytical solutions for Stationary Probability Density Function (SPDF). The analytical solutions for SPDF is compared with the SPDF obtained using simulation. Further the Mean First Passage Time (MFPT) of the bistable system is calculated for various values of time delay and noise strength and compared with that of the simulation. The MFPT for the time delayed system for the case of cubic potential driven by Gaussian and Levy noise as well as asymmetric bistable potential driven by a noise and periodic driving force has been investigated.

Ion kinetic effects and instabilities in the plasma flow in the magnetic mirror

Kinetic effects in plasma flow due to a finite ion temperature and ion reflections in a converging–diverging magnetic nozzle are investigated with collisionless quasineutral hybrid simulations with kinetic ions and isothermal Boltzmann electrons. It is shown that in the cold ions limit, the velocity profile of the particles agrees well with the analytical theory, predicting the formation of the global accelerating potential due to the magnetic mirror with the maximum of the magnetic field and resulting in the transonic ion velocity profile. The global transonic ion velocity profile is also obtained for warm ions with isotropic and anisotropic distributions. Partial ion reflections are observed due to a combined effect of the magnetic mirror and time-dependent fluctuations of the potential as a result of the wave breaking and instabilities in the regions when the fluid solutions become multi-valued. Despite partial reflections, the flow of the passing ions still follows the global accelerating profile defined by the magnetic field profile. In simulations with reflecting boundary condition imitating the plasma source and allowing the transitions between trapped and passing ions, the global nature of the transonic accelerating solution is revealed as a constrain on the plasma exhaust velocity that ultimately defines plasma density in the source region.

Brane dynamics of holographic BCFTs

In this paper we study various dynamical aspects of the AdS/BCFT correspondence in higher dimensions. We study properties of holographic stress energy tensor by analyzing the metric perturbation in the gravity dual. We also calculate the stress energy tensor for a locally excited state on a half plane in a free scalar CFT. Both of them satisfy a reflective boundary condition that is expected for any BCFTs. We also study the behavior of the scalar field perturbation in the AdS/BCFT setup and show that they also show complete reflections. Moreover, we find that the entanglement entropy of a BCFT computed from the AdS/BCFT matched with that calculated from the Island formula, which supports the Island/BCFT correspondence in higher dimensions. Finally we show how we can calculate one point functions in a BCFT in our gravity dual.

Effects of a global monopole on the thermodynamic phase transition of a charged AdS black hole* *Supported by the National Natural Science Foundation of China (11873001, 12047564), the Fundamental Research Funds for the Central Universities (2021CDJZYJH-003) and the Postdoctoral Science Foundation of Chongqing (cstc2021jcyj-bsh0124)

We study the dynamical properties of the thermodynamic phase transition (PT) of a charged AdS black hole (BH) with a global monopole via the Gibbs free energy landscape and reveal the effects of the global monopole on the kinetics of thermodynamic PTs. First, we briefly review the thermodynamics of a charged AdS BH with a global monopole. Then, we introduce the Gibbs free energy landscape to investigate the thermodynamic stability of the BH states. Because of thermal fluctuations, the small black hole (SBH) state can transit to a large black hole (LBH) state, and vice versa. Further, we use the Fokker-Planck equation with the reflecting boundary condition to study the probability evolution of the BH state with and without a global monopole separately. It is found that for both the SBH and LBH states, the global monopole could slow down the evolution of the BH state. In addition, we obtain the relationship between the first passage time and the monopole parameter η. The result shows that as the monopole parameter η increases, the mean first passage time becomes longer for both the SBH and LBH states.

The Vlasov–Poisson–Landau System with the Specular-Reflection Boundary Condition

We consider the Vlasov–Poisson–Landau system, a classical model for a dilute collisional plasma interacting through Coulombic collisions and with its self-consistent electrostatic field. We establish global stability and well-posedness near the Maxwellian equilibrium state with decay in time and some regularity results for small initial perturbations, in any general bounded domain (including a torus as in a tokamak device), in the presence of specular reflection boundary condition. We provide a new improved \(L^{2}\rightarrow L^{\infty }\) framework: \(L^{2}\) energy estimate combines only with \(S_{ }^{p}\) estimate for the ultra-parabolic equation.

On the Diffusive Limits of Radiative Heat Transfer System I: Well-Prepared Initial and Boundary Conditions

We study the diffusive limit approximation for a nonlinear radiative heat transfer system that arises in the modeling of glass cooling and greenhouse effects and in astrophysics. The model is considered with the reflective radiative boundary conditions for the radiative intensity and with periodic, Dirichlet and Robin boundary conditions for the temperature. The global existence of weak solutions for this system is given by using a Galerkin method with a careful treatment of the boundary conditions. Using the compactness method, averaging lemma and Young measure theory, we prove our main result that the weak solution converges to a nonlinear diffusion model in the diffusive limit. Moreover, under more regularity conditions on the limit system, the diffusive limit is also analyzed by using a relative entropy method. In particular, we get a rate of convergence. The initial and boundary conditions are assumed to be well-prepared in the sense that no initial or boundary layer exists.

The initial boundary value problem for the Vlasov–Poisson–Fokker–Planck system

This paper is devoted to the initial boundary value problem of the Vlasov–Poisson–Fokker–Planck system in a bounded domain. The global existence of a unique strong solution and its exponential convergence rate to the equilibrium state are proved under the specular reflection boundary condition. The proof is based on an elementary energy method and the SLp theory developed by Guo et al. [Arch. Ration. Mech. Anal. 236(3), 1389–1454 (2020)] for kinetic models.

Transition Gas Flow Between Two Parallel Plates with a Slit-Type Obstacle of Various Geometry by Event Driven Molecular Dynamics Simulation

In this study, pressure-driven flow through a slit-type obstacle with various length (L) and height (H) placed in between two parallel plates was investigated by Event Driven Molecular Dynamics (EDMD) simulation. Mach number, temperature and pressure distributions were obtained along the channel in the transition regime. The change in these macroscopic properties and flow rate were examined for different cases created by changing Knudsen number (Kn) of the gas, the geometry of the slit and the outlet/inlet pressure ratio of the flow. Collision of gas molecules with plates and the obstacle were modeled with diffuse reflection boundary condition. The flow rate showed a sudden change in the transition regime and significant differences in the molecular regime depending on the pressure ratio. Except for the Kn, H and L dimensions were found to be effective in Mach disc formation. Pressure drops at the exit of the slit were shaped differently in normalized pressure profiles depending on Kn, H and L dimensions. In addition, the structure of the vortices formed at the entrance and exit of the slit varies depending on Kn. Some of the results obtained were confirmed to be consistent with the similar studies in the literature.

Implications of the quantum nature of the black hole horizon on the gravitational-wave ringdown

Motivated by capturing putative quantum effects at the horizon scale, we model the black hole horizon as a membrane with fluctuations following a Gaussian profile. By extending the membrane paradigm at the semiclassical level, we show that the quantum nature of the black hole horizon implies partially reflective boundary conditions and a frequency-dependent reflectivity. This generically results into a modified quasi-normal mode spectrum and the existence of echoes in the postmerger signal. On a similar note, we derive the horizon boundary condition for a braneworld black hole that could originate from quantum corrections on the brane. This scenario also leads to a modified gravitational-wave ringdown. We discuss general implications of these findings for scenarios predicting quantum corrections at the horizon scale.

On a Vlasov–Poisson system in a bounded set with direct reflection boundary conditions

Existence (resp. uniqueness) of global (resp. local) in time continuous solutions to the Vlasov-Poisson system is proven in a one-dimensional bounded domain, with direct reflection boundary conditions. Generalized characteristics are used. Electroneutrality is obtained in the limit.

Hypocoercivity for kinetic linear equations in bounded domains with general Maxwell boundary condition

We establish the convergence to the equilibrium for various linear collisional kinetic equations (including linearized Boltzmann and Landau equations) with physical local conservation laws in bounded domains with general Maxwell boundary condition. Our proof consists in establishing an hypocoercivity result for the associated operator; in other words, we exhibit a convenient Hilbert norm for which the associated operator is coercive in the orthogonal of the global conservation laws. Our approach allows us to treat general domains with all types of boundary conditions in a unified framework. In particular, our result includes the case of vanishing accommodation coefficient and thus the specific case of the specular reflection boundary condition.