Perturbation Of Boundary Conditions Research Articles

Probabilistic Forecasts of Atmospheric River events using the HRRR Ensemble

The nine-member High-Resolution Rapid Refresh Ensemble (HRRRE) is evaluated for its ability to forecast five Atmospheric River (AR) events that impacted California in February–March 2019. Two sets of retrospective HRRRE simulations are conducted, a control with the standard set of perturbations (initial and boundary conditions, stochastic parameters, and physics tendency), and an experiment with initial and boundary perturbations only. Reliability plots suggest the HRRRE control represents the observed Stage IV precipitation frequency well at 6-h to 24-h lead times, and rank histograms suggest the ensemble is slightly underdispersive. The HRRRE overpredicts precipitation frequency at the higher (25 mm) threshold. These results suggest the HRRRE is a useful tool to quantify probabilistic forecasts of AR events in this region. Removing stochastic physics perturbations did not substantially impact probabilistic forecasts, suggesting most of the ensemble spread is from initial and boundary condition perturbations. Spatially, ensemble precipitation coefficient of variance is lower (less forecast uncertainty) over the Sierra Nevada range than other regions, suggesting that these ensemble perturbations have a smaller impact on precipitation processes occurring over the Sierra Nevada range. More work should be conducted to understand the impacts of other model perturbations, such as microphysics, on ensemble performance, and to improve Stage IV accuracy with frozen precipitation in mountainous regions.

Exact domain truncation for the Morse-ingard equations

Morse and Ingard [1] give a coupled system of time-harmonic equations for the temperature and pressure of an excited gas. These equations form a critical aspect of modeling trace gas sensors. Like other wave propagation problems, the computational problem must be closed with suitable far-field boundary conditions. Working in a scattered-field formulation, we adapt a nonlocal boundary condition proposed in [2] for the Helmholtz equation to this coupled system. This boundary condition uses a Green's formula for the true solution on the boundary, giving rise to a nonlocal perturbation of standard transmission boundary conditions. However, the boundary condition is exact and so Galerkin discretization of the resulting problem converges to the restriction of the exact solution to the computational domain. Numerical results demonstrate that accuracy can be obtained on relatively coarse meshes on small computational domains, and the resulting algebraic systems may be solved by GMRES using the local part of the operator as an effective preconditioner. These numerical results taken together combine several advanced techniques, including higher-order finite elements, geometric multigrid in curvilinear geometry, native use of complex arithmetic, and incorporation of nonlocal operators. These are tied together in a high-level simulation using the Firedrake library.

Effects of Rotation and Magnetic Field on Rayliegh Benard Convection

In this paper, a numerical method based on the Chebyshev tau method is applied to analyze the effects of rotation and magnetic fields on Rayleigh-Bénard convection. The rotation and magnetic fields are assumed to be parallel to the vertical direction. The perturbation equations and boundary conditions are analyzed using normal mode analysis. The equations are then converted into a non-dimensional form and transformed into a generalized eigenvalue problem of the form AX=RBX, where R represents the eigenvalue corresponding to the Rayleigh number. The MATLAB software package is utilized to determine the relationship between the Rayleigh number and the Taylor number (rate of rotation), as well as the relationship between the Rayleigh number and the magnetic parameter (strength of the magnetic field) for different boundary conditions (free-free, rigid-rigid, or one free and the other rigid). The numerical and graphical results are presented and found to be in full agreement with the results obtained from previous analytical and numerical studies of the problem.

Study of the dynamic process in a nonlinear mathematical model of the transverse oscillations of a moving beam under perturbed boundary conditions

The study of transverse oscillations of systems moving along their axis is a very difficult, but at the same time a very important task. Mathematical models of nonlinear transverse oscillations of a beam moving along its axis are analyzed in this paper work, both for non-resonant and resonant cases. The task becomes even more complicated if we additionally take into account the method of fastening the ends of the beam or the perturbation at its ends. We have obtained dependencies that can be used in construction, transport, industry, mechanical engineering and other domains of technology, ensuring the stability and safety of the operation of such mechanical systems. Mathematical models have been obtained for structural engineers to determine the amplitude–frequency response of relevant structures. These mathematical models are key to researching the dynamics of moving media. The obtained results allow considering not only the influence of kinematic and physical-mechanical parameters on the amplitude–amplitude frequency response of the medium, but also the fastening method. In addition, the correlations obtained in the paper make it possible to study not only the influence of the moving medium parameters on the nature of changes in the frequency and amplitude of oscillations, but also to consider the movement at the points of support of the medium. Namely, even at the stage of designing a pipeline for a liquid flowing at a certain speed, it is possible to consider the influence of the oscillation of the supports or their fastening method on the dynamics of the oscillatory process. The resulting dependencies allow designers to consider the influence of the characteristics given in the paper with a high level of accuracy and predict dynamic phenomena in them. In engineering calculations of various mechanical systems, the resulting dependencies can be used to optimize parameters to avoid negative destructive phenomena during operation.

Analysis of a hybrid fractional coupled system of differential equations in $ n $-dimensional space with linear perturbation and nonlinear boundary conditions

<abstract><p>In this paper, we investigated $ n $-dimensional fractional hybrid differential equations (FHDEs) with nonlinear boundary conditions in a nonlinear coupled system. For this purpose, we used Dhage's fixed point theory, and applied the Krasnoselskii-type coupled fixed point theorem to construct existence conditions of the solution of the FHDEs. To illustrated this idea, suitable examples are presented in $ 3 $-dimensional space at the end of the paper.</p></abstract>

A New Solution to the Strong CP Problem

We suggest a new solution to the strong CP problem. The solution is based on the proper use of the boundary conditions for the QCD-generating functional integral. We expand the perturbative boundary conditions to both perturbative and nonperturbative fields integrated into the QCD-generating functional integral. It allows us to nullify the CP odd term in the QCD Lagrangian and, thus, to solve the strong CP problem. The presently popular solution to the strong CP problem of introducing axions violates the principle of renormalizability of the Quantum Field Theory, which is very successful phenomenologically. Our solution obeys the principle of renormalizability of the Quantum Field Theory and does not involve new exotic particles like axions.

On System of Root Vectors of Perturbed Regular Second-Order Differential Operator Not Possessing Basis Property

This article delves into the spectral problem associated with a multiple differentiation operator that features an integral perturbation of boundary conditions of one specific type, namely, regular but not strengthened regular. The integral perturbation is characterized by the function px, which belongs to the space L20,1. The concept of problems involving integral perturbations of boundary conditions has been the subject of previous studies, and the spectral properties of such problems have been examined in various early papers. What sets the problem under consideration apart is that the system of eigenfunctions for the unperturbed problem (when px≡0) lacks the property of forming a basis. To address this, a characteristic determinant for the spectral problem has been constructed. It has been established that the set of functions px, for which the system of eigenfunctions of the perturbed problem does not constitute an unconditional basis in L20,1, is dense within the space L20,1. Furthermore, it has been demonstrated that the adjoint operator shares a similar structure.

Reconstruction of a time-dependent wave source and the initial condition in a hyperbolic equation

This article is concerned with determination of a time-dependent wave source together with the initial condition in a hyperbolic equation. Based on the given data including the flux tensions of a string at end points and a nonlocal integral observation along with the wave displacement at two distinct instants of time, we prove the unique solvability of the inverse problem. Moreover, we estimate the modulus of continuity of the inverse problem under special conditions. The numerical solution of the problem is also presented by means of Bernstein spectral method, which converts the problem to a linear system of algebraic equations and then Tikhonov regularization technique is employed to derive reliable solutions. Regarding the perturbed boundary conditions, we use a regularized numerical technique to obtain stable derivatives. Numerical simulations are provided to show the effectiveness of the proposed scheme.

Supersonic Euler-Poisson flows in divergent nozzles

This paper concerns the steady Euler-Poisson system in a two-dimensional divergent nozzle of finite length. The structural stability of supersonic potential flows for the Euler-Poisson system is transformed into the well-posedness of a second order quasilinear hyperbolic-elliptic coupled system with nonlinear boundary conditions. The well-posedness and the nonlinear structural stability of such supersonic flows under perturbations of boundary conditions are established by combining the iteration method with the estimates for hyperbolic-elliptic system.

Experimental demonstration of a method to actively stabilize satellite structures against random perturbations of thermal boundary conditions using a closed-loop filter and controller approach

Modern space travel requires increasingly stable support structures for optical instruments or antennas, which can hardly be realized with the traditional approaches. Therefore, an approach for active structural stabilization of thermal-induced distortions was developed, simulated, and patented within the framework of the Infrared Astronomy Satellite Swarm Interferometry (IRASSI) project. Based on this approach, the thermomechanical transfer functions between the change in heat flux and the change in displacement of the finite-element (FE) model of a structure have already been validated in their basic functionality. In an experimental setup, the FE model was extended to include a closed-loop filter and controller approach consisting of a Kalman filter processing the temperature measurements in conjunction with a Linear Quadratic Regulator (LQR). It was shown that this setup can compensate for predefined sinusoidally oscillating disturbance heat flows, with an improvement of 4 dB compared to the uncontrolled case. In this paper, an experimental setup revised with respect to the positioning of the sensors and control heating elements, in conjunction with an extension of the filter and controller approach, will demonstrate that the system can respond to reproducible, random fluctuations in the disturbance heat flux, as well as stepped changes, and that performance has improved due to the revision.

Rate-dependency of residual shear strength of soils: implications for landslide evolution

Shear-rate weakening or strengthening behaviours can effectively control landslide runouts, defining sudden runaway sliding or years-long slow-creep phases. These behaviours are partly controlled by the properties of the basal material. Understanding its stress–strain–time response is crucial in physically-based assessments of landslide dynamics and the associated risk. We investigate the frictional resistance of a calcium bentonite, a kaolin and a quartz sand by means of a conventional ring-shear apparatus under normal stresses representative of landslide shear zones. Results for the fine-grained soils, in line with literature on pure clays, indicate important velocity strengthening, whereas small shear-rate effects were observed in sand. As long as effective stresses remain constant, a velocity strengthening response can exert a feedback that, under certain conditions, counteracts perturbations in boundary conditions and prevents fast runouts on pre-existing shear zones. Accordingly, we argue that specifically testing for shear-rate-dependency and incorporating observed behaviours in model formulations can be beneficial for better predicting landslide fates.

DeWitt Boundary Condition in One-Loop Quantum Cosmology

DeWitt’s suggestion that the wave function of the universe should vanish at the classical Big Bang singularity is considered here within the framework of one-loop quantum cosmology. For pure gravity at one loop about a flat four-dimensional background bounded by a 3-sphere, three choices of boundary conditions are considered: vanishing of the linearized magnetic curvature when only transverse-traceless gravitational modes are quantized; a one-parameter family of mixed boundary conditions for gravitational and ghost modes; and diffeomorphism-invariant boundary conditions for metric perturbations and ghost modes. A positive ζ(0) value in these cases ensures that, when the three-sphere boundary approaches zero, the resulting one-loop wave function approaches zero. This property may be interpreted by saying that, in the limit of small three-geometry, the resulting one-loop wave function describes a singularity-free universe. This property holds for one-loop functional integrals, which are not necessarily equivalent to solutions of the quantum constraint equations.

Perturbation of Boundary Conditions to Create Appropriate Ensembles for Regional Data Assimilation in Coastal Estuary Modeling

AbstractRegional data assimilation is conducted for a coastal estuary using the ensemble Kalman filter, real observation data from Ise Bay, Japan, and a simulation model called the Ise Bay Simulator. The applicability and robustness of the method are then examined. We also analyze the relationship between the boundary conditions, which add perturbations and the data assimilation results of water temperature and salinity. A method of creating an ensemble by perturbing three boundary conditions (atmospheric forcing, lateral boundary conditions [open boundary conditions], and river discharge forcing) is then proposed. In situ water temperature and salinity profiles observed at fixed points are assimilated daily. The proposed assimilation method provides stable data assimilation without unnatural values for water temperature and salinity throughout the year. Further, applying a perturbation to the three boundary conditions does not lead to filter divergence, thus indicating good applicability and robustness, that is, applying a perturbation to the three boundary conditions does not degenerate the ensemble spread. According to a sensitivity experiment, perturbing the atmospheric boundary conditions of both air temperature and wind speed increases the ensemble spread of water temperature, especially near the surface layer. Wind speed has the greatest influence on the magnitude of the salinity ensemble spread, and its dominance depends on location. Perturbation of lateral boundary conditions increases the ensemble spread of water temperature and salinity at all water depths near the bay mouth, and the observations are effectively assimilated. Perturbation of river discharge forcing successfully assimilates water temperature and salinity near the estuary.

The propagation of several well-known nonlinear waves in fluid-filled elastic tube

By using the reductive perturbation method, the nonlinear Schrödinger equation in fluid-filled elastic tube is obtained. We study several different kinds of the nonlinear wave solutions for the nonlinear Schrödinger equation. It is noted that the kinds of the nonlinear waves are determined by a parameter of ab (a is the amplitude of the background plane wave, while b is a controllable parameter which depend on the initial condition, boundary condition and other external perturbations). As the decreases of parameter ab, the number of the waves frequency increases, while their amplitude decreases. It is also found that all the waves amplitude increases as the wave number k and the radius of elastic tube increases, however, they are independent of the fluid density, the thickness of elastic tube and the Young’s modulus of the elastic tube. The amplitudes are different among different kinds of waves. However, the wave velocities of different waves are the same under the same parameters. They decrease as the wave number k, fluid density and the radius of elastic tube increase, while they increase as the thickness of elastic tube and the Young’s modulus of elastic tube increase.

A world without pythons would be so simple

We show that bulk operators lying between the outermost extremal surface and the asymptotic boundary admit a simple boundary reconstruction in the classical limit. This is the converse of the Python’s lunch conjecture, which proposes that operators with support between the minimal and outermost (quantum) extremal surfaces—e.g. the interior Hawking partners—are highly complex. Our procedure for reconstructing this ‘simple wedge’ is based on the HKLL construction, but uses causal bulk propagation of perturbed boundary conditions on Lorentzian timefolds to expand the causal wedge as far as the outermost extremal surface. As a corollary, we establish the Simple Entropy proposal for the holographic dual of the area of a marginally trapped surface as well as a similar holographic dual for the outermost extremal surface. We find that the simple wedge is dual to a particular coarse-grained CFT state, obtained via averaging over all possible Python’s lunches. An efficient quantum circuit converts this coarse-grained state into a ‘simple state’ that is indistinguishable in finite time from a state with a local modular Hamiltonian. Under certain circumstances, the simple state modular Hamiltonian generates an exactly local flow; we interpret this result as a holographic dual of black hole uniqueness.

Chaotic vibrations of 3D linear hyperbolic PDEs with linear perturbations of superlinear boundary conditions

This article studies the chaotic vibrations of the infinite-dimensional dynamical systems governed by linear hyperbolic partial differential equations (PDEs) in three-dimensional (3D) space, where the boundary conditions include two linear perturbations of superlinear types. A rigorous mathematical theorem that guarantees the occurrence of chaos of such systems is obtained. The main theme of this article is the advancement of existing chaos to 3D hyperbolic PDEs. As applications, two examples are provided for showing the effectiveness of the theoretical chaotic results.

Nonlocal Problem with Multipoint Perturbations of Sturm-Type Boundary Conditions for an Ordinary Differential Equation of Even Order

Nonlocal Problem with Multipoint Perturbations of Sturm-Type Boundary Conditions for an Ordinary Differential Equation of Even Order

Tidal response and near-horizon boundary conditions for spinning exotic compact objects

Teukolsky equations for $|s|=2$ provide efficient ways to solve for curvature perturbations around Kerr black holes. Imposing regularity conditions on these perturbations on the future (past) horizon corresponds to imposing an ingoing (outgoing) wave boundary condition. For exotic compact objects (ECOs) with external Kerr spacetime, however, it is not yet clear how to physically impose boundary conditions for curvature perturbations on their boundaries. We address this problem using the membrane paradigm, by considering a family of zero-angular-momentum fiducial observers (FIDOs) that float right above the horizon of a linearly perturbed Kerr black hole. From the reference frame of these observers, the ECO will experience tidal perturbations due to ingoing gravitational waves, respond to these waves, and generate outgoing waves. As it also turns out, if both ingoing and outgoing waves exist near the horizon, the Newman-Penrose (NP) quantity ${\ensuremath{\psi}}_{0}$ will be numerically dominated by the ingoing wave, while the NP quantity ${\ensuremath{\psi}}_{4}$ will be dominated by the outgoing wave---even though both quantities contain full information regarding the wave field. In this way, we obtain the ECO boundary condition in the form of a relation between ${\ensuremath{\psi}}_{0}$ and the complex conjugate of ${\ensuremath{\psi}}_{4}$, in a way that is determined by the ECO's tidal response in the FIDO frame. We explore several ways to modify gravitational-wave dispersion in the FIDO frame and deduce the corresponding ECO boundary condition for Teukolsky functions. Using the Starobinsky-Teukolsky identity, we subsequently obtain the boundary condition for ${\ensuremath{\psi}}_{4}$ alone, as well as for the Sasaki-Nakamura and Detweiler functions. As it also turns out, the reflection of spinning ECOs will generically mix between different $\ensuremath{\ell}$ components of the perturbation fields, and it will be different for perturbations with different parities. It is straightforward to apply our boundary condition to computing gravitational-wave echoes from spinning ECOs, and to solve for the spinning ECOs' quasinormal modes.

The Naval Research Laboratory’s Coupled Ocean–Atmosphere Mesoscale Prediction System-Tropical Cyclone Ensemble (COAMPS-TC Ensemble)

AbstractThe 11-member Coupled Ocean–Atmosphere Mesoscale Prediction System-Tropical Cyclones (COAMPS-TC) ensemble has been developed by the Naval Research Laboratory (NRL) to produce probabilistic forecasts of tropical cyclone (TC) track, intensity and structure. All members run with a storm-following inner grid at convection-permitting 4-km horizontal resolution. The COAMPS-TC ensemble is constructed via a combination of perturbations to initial and boundary conditions, the initial vortex, and model physics to account for a variety of different sources of uncertainty that affect track and intensity forecasts. Unlike global model ensembles, which do a reasonable job capturing track uncertainty but not intensity, mesoscale ensembles such as the COAMPS-TC ensemble are necessary to provide a realistic intensity forecast spectrum. The initial and boundary condition perturbations are responsible for generating the majority of track spread at all lead times, as well as the intensity spread from 36 to 120 h. The vortex and physics perturbations are necessary to produce meaningful spread in the intensity prediction from 0 to 36 h. In a large sample of forecasts from 2014 to 2017, the ensemble-mean track and intensity forecast is superior to the unperturbed control forecast at all lead times, demonstrating a clear advantage to running an ensemble versus a deterministic forecast. The spread–skill relationship of the ensemble is also examined, and is found to be very well calibrated for track, but is underdispersive for intensity. Using a mixture of lateral boundary conditions derived from different global models is found to improve upon the spread–skill score for intensity, but it is hypothesized that additional physics perturbations will be necessary to achieve realistic ensemble spread.

A Physically Based Stochastic Boundary Layer Perturbation Scheme. Part II: Perturbation Growth within a Superensemble Framework

AbstractConvection-permitting forecasts have improved the forecasts of flooding from intense rainfall. However, probabilistic forecasts, generally based upon ensemble methods, are essential to quantify forecast uncertainty. This leads to a need to understand how different aspects of the model system affect forecast behavior. We compare the uncertainty due to initial and boundary condition (IBC) perturbations and boundary layer turbulence using a superensemble (SE) created to determine the influence of 12 IBC perturbations versus 12 stochastic boundary layer (SBL) perturbations constructed using a physically based SBL scheme. We consider two mesoscale extreme precipitation events. For each, we run a 144-member SE. The SEs are analyzed to consider the growth of differences between the simulations, and the spatial structure and scales of those differences. The SBL perturbations rapidly spin up, typically within 12 h of precipitation commencing. The SBL perturbations eventually produce spread that is not statistically different from the spread produced by the IBC perturbations, though in one case there is initially increased spread from the IBC perturbations. Spatially, the growth from IBC occurs on larger scales than that produced by the SBL perturbations (typically by an order of magnitude). However, analysis across multiple scales shows that the SBL scheme produces a random relocation of precipitation up to the scale at which the ensemble members agree with each other. This implies that statistical postprocessing can be used instead of running larger ensembles. Use of these statistical postprocessing techniques could lead to more reliable probabilistic forecasts of convective events and their associated hazards.