Momentum Variables Research Articles

Numerical storm surge model with higher order finite difference method of lines for the coast of Bangladesh

In this study, the method of lines (MOLs) with higher order central difference approximation method coupled with the classical fourth order Runge-Kutta (RK(4,4)) method is used in solving shallow water equations (SWEs) in Cartesian coordinates to foresee water levels associated with a storm accurately along the coast of Bangladesh. In doing so, the partial derivatives of the SWEs with respect to the space variables were discretized with 5-point central difference, as a test case, to obtain a system of ordinary differential equations with time as an independent variable for every spatial grid point, which with initial conditions were solved by the RK(4,4) method. The complex land-sea interface and bottom topographic details were incorporated closely using nested schemes. The coastal and island boundaries were rectangularized through proper stair step representation, and the storing positions of the scalar and momentum variables were specified according to the rules of structured C-grid. A stable tidal regime was made over the model domain considering the effect of the major tidal constituent, M2 along the southern open boundary of the outermost parent scheme. The Meghna River fresh water discharge was taken into account for the inner most child scheme. To take into account the dynamic interaction of tide and surge, the generated tidal regime was introduced as the initial state of the sea, and the surge was then made to come over it through computer simulation. Numerical experiments were performed with the cyclone April 1991 to simulate water levels due to tide, surge, and their interaction at different stations along the coast of Bangladesh. Our computed results were found to compare reasonable well with the limited observed data obtained from Bangladesh Inland Water Transport Authority (BIWTA) and were found to be better in comparison with the results obtained through the regular finite difference method and the 3-point central difference MOLs coupled with the RK(4,4) method with regard to the root mean square error values.

Variational and viscosity operators for the evolutionary Hamilton–Jacobi equation

We study the Cauchy problem for the first-order evolutionary Hamilton–Jacobi equation with a Lipschitz initial condition. The Hamiltonian is not necessarily convex in the momentum variable and not a priori compactly supported. We build and study an operator giving a variational solution of this problem, and get local Lipschitz estimates on this operator. Iterating this variational operator we obtain the viscosity operator and extend the estimates to the viscosity framework. We also check that the construction of the variational operator gives the Lax–Oleinik semigroup if the Hamiltonian is convex or concave in the momentum variable.

Ensemble in phase space: Statistical formalism of quantum mechanics

We present an alternative formalism of quantum mechanics tailored to statistical ensemble in phase space. The purpose of our work is to show that it is possible to establish an alternative autonomous formalism of quantum mechanics in phase space using statistical methodology. The adopted perspective leads to obtaining within the framework of its theory the master quantum-mechanical equation without recourse to the other formalisms of quantum mechanics, and gives the idea of operators pertaining to dynamical quantities. The derivation of this equation starts with the ensemble in phase space. We have explained with the help of this equation the structure of quantum mechanics in phase space and the approximation to the Schrodinger equation. Furthermore, we have shown that this formalism provides reasonable results of quantization by dealing with some simple cases, which confirm the validity of this formalism. In particular, we have demonstrated that this formalism can easily give the relativistic wave equation without treating the problem of linearizing the Hamiltonian operator by making the most of the point that the master equation is a first-order partial differential equation with respect to time, position and momentum variables, and makes use of the phase velocity. The ultimate outcome this formalism produces is that primary and general matters of quantum mechanics can be studied reasonably within the framework of statistical mechanics.

Application of Heisenberg uncertainty relation for the optimal modeling of surface diffraction.

The modeling of the scattering of a plane wave at a rough aperiodic surface-as well as its diffraction by a microstructured surface-is possible only by limiting the infinite surface to a window of finite width D. We show that the scattering spectrum at infinity in the Fraunhofer zone can be obtained from the diffraction modeling of a grating of period D whose surface profile coincides with the aperiodic surface in this window. This is justified by adopting the corpuscular representation of light and resorting to Heisenberg's uncertainty relation applied to the photon's canonically conjugate variables momentum and position. This approach gives a deep and comprehensive representation of scattering phenomena, and also the limit of what can be meaningfully calculated and measured. Numerical examples of grating profiles demonstrate that results obtained under the widely used Beckmann-Kirchoff approximation are matched. The described approach can solve scattering problems that usual methods cannot, or face difficulties, such as when there is significant roughness with respect to the wavelength.

Planar Multi-Link Swimmers: Experiments and Theoretical Investigation using “Perfect Fluid” Model

SummaryRobotic swimmers are currently a subject of extensive research and development for several underwater applications. Clever design and planning must rely on simple theoretical models that account for the swimmer’s hydrodynamics in order to optimize its structure and control inputs. In this work, we study a planar snake-like multi-link swimmer by using the “perfect fluid” model that accounts for inertial hydrodynamic forces while neglecting viscous drag effects. The swimmer’s dynamic equations of motion are formulated and reduced into a first-order system due to symmetries and conservation of generalized momentum variables. Focusing on oscillatory inputs of joint angles, we study optimal gaits for 3-link and 5-link swimmers via numerical integration. For the 3-link swimmer, we also provide a small-amplitude asymptotic solution which enables obtaining closed-form approximations for optimal gaits. The theoretical results are then corroborated by experiments and motion measurement of untethered robotic prototypes with three and five links floating in a water pool, showing a reasonable agreement between the experiments and the theoretical model.

The 2D Kramers–Dirac oscillator

The Dirac oscillator was initially introduced as a Dirac operator which is linear in momentum and coordinate variables. In contrast to the usual 2D Dirac oscillator, the 2D Kramers–Dirac oscillator admits the time-reversal symmetry, which is a reason for the present nomenclature. It is shown that there exists a family of eigenstates associated with an eigenvalue linear in the control parameter, and the eigenvalue in question goes down from positive values to negative values as the parameter varies in the positive direction. The other eigenvalues are broken up into two bands, positive and negative. The 2D Dirac and the 2D Kramers–Dirac oscillators are compared in their physical grounds and in their spectral structure from the viewpoint of the time-reversal symmetry.

D-dimensional Klein-Gordon equation with spatially q-deformed of radial momentum for Kratzer potential analyzed by using hypergeometric method

Hypergeometric method can be used to solve D-dimensional Klein-Gordon equation with q-deformed of radial momentum for Kratzer potential. By substituting q-deformed of radial momentum variable, the D-dimensional and the potential parameters to obtain the second order of D-dimensional Klein-Gordon equation which is used to determine the energy and wave function equations. The analytical result of energy can be founded with D-dimension and q-deformed of radial momentum variations. As a result, the rise of D-dimension values cause the rise of energy values, while the rice of q deformation values causes the decline of energy values.

Structure preserving feedback of port-thermodynamic systems

Recently a class of Hamiltonian control systems was defined for open irreversible thermodynamic systems. These systems are Hamiltonian control systems defined on a symplectic manifold, however departing from standard Hamiltonian control systems, due to the property that the Hamiltonian function is homogeneous in the generalized momentum variables. In this paper we study the class of state feedbacks preserving the geometric structure of such Homogeneous Hamiltonian control systems and rendering the closed-loop system again a Homogeneous Hamiltonian control system. It is shown that only a constant control preserves the canonical Liouville form. Hence a non-trivial state feedback necessarily changes the geometric structure in closed-loop defined by a modified Pfaffian form. Finally we derive a matching equation on the nonlinear feedback and the closed-loop Pfaffian form.

Uncertainty product of the spherical Abel–Poisson wavelet

The space and momentum variances of the spherical Abel–Poisson wavelet, as well as the limit of the uncertainty product as $\rho \to 0$, where $\rho $ is a scale parameter, are computed. The values of these quantities coincide with a certain accuracy with

Low-Dissipation Simulation Methods and Models for Turbulent Subsonic Flow

The simulation of turbulent flows by means of computational fluid dynamics is highly challenging. The costs of an accurate direct numerical simulation (DNS) are usually too high, and engineers typically resort to cheaper coarse-grained models of the flow, such as large-eddy simulation (LES). To be suitable for the computation of turbulence, methods should not numerically dissipate the turbulent flow structures. Therefore, energy-conserving discretizations are investigated, which do not dissipate energy and are inherently stable because the discrete convective terms cannot spuriously generate kinetic energy. They have been known for incompressible flow, but the development of such methods for compressible flow is more recent. This paper will focus on the latter: LES and DNS for turbulent subsonic flow. A new theoretical framework for the analysis of energy conservation in compressible flow is proposed, in a mathematical notation of square-root variables, inner products, and differential operator symmetries. As a result, the discrete equations exactly conserve not only the primary variables (mass, momentum and energy), but also the convective terms preserve (secondary) discrete kinetic and internal energy. Numerical experiments confirm that simulations are stable without the addition of artificial dissipation. Next, minimum-dissipation eddy-viscosity models are reviewed, which try to minimize the dissipation needed for preventing sub-grid scales from polluting the numerical solution. A new model suitable for anisotropic grids is proposed: the anisotropic minimum-dissipation model. This model appropriately switches off for laminar and transitional flow, and is consistent with the exact sub-filter tensor on anisotropic grids. The methods and models are first assessed on several academic test cases: channel flow, homogeneous decaying turbulence and the temporal mixing layer. As a practical application, accurate simulations of the transitional flow over a delta wing have been performed.

Text-Based Industry Momentum

We test the hypothesis that low-visibility shocks to text-based network industry peers can explain industry momentum. We consider industry peer firms identified through 10-K product text and focus on economic peer links that do not share common Standard Industrial Classification (SIC) codes. Shocks to less visible peers generate economically large momentum profits and are stronger than own-firm momentum variables. More visible traditional SIC-based peers generate only small, short-lived momentum profits. Our findings are consistent with momentum profits arising partially from inattention to economic links of less visible industry peers.

The Density‐Driven Winter Intensification of the Ross Sea Circulation

AbstractThe circulation over the Ross Sea continental shelf facilitates the exchange between the Southern Ocean and the Ross Ice Shelf cavity. Here transport and mixing processes control the access of oceanic heat from the Southern Ocean to the ice shelf base, the formation of sea ice, and the production of High Salinity Shelf Water (HSSW) in polynyas and hence the subsequent formation of Antarctic Bottom Water. A climatological ocean‐ice shelf coupled model of the Ross Sea Sector including the cavity, with prescribed sea ice fluxes, was used to examine the details of currents and their seasonal variability over the continental shelf. A system of two cyclonic and three anticyclonic persistent circulation features has been identified. Transports steadily increase throughout winter, with individual currents carrying up to 2 Sv, nearly doubling their minimum. The seasonal modulation is driven by lateral differences in density and subsequent baroclinic pressure gradients, induced through dense shelf water formation in the Ross Sea and the Terra Nova Bay Polynas. Wind plays a minor role in ocean momentum variability. Sensitivity experiments suggest a weakening of transports with increasing wind stress. Horizontal density variations at the ocean surface are smoothed by the wind. The source of momentum in the cavity is the gravity‐driven bottom flow of HSSW, produced in the Ross Sea Polynya as part of the thermohaline overturning circulation. Tracer experiments suggest that HSSW forming in the Terra Nova Bay Polynya has no cavity access, but instead is the main contributor to Antarctic Bottom Water formed in the northwest slope.

The mott based double turn method for the MEG II spectrometer characterisation

The MEG experiment has set the latest limit of 4.2 × 10 −13 at 90 % Confidence Level (C.L.) to the branching ratio of the charged Lepton Flavour Violating (cLFV) decay μ + → e + γ . The MEG II experiment will be more sensitive by an order of magnitude. High resolutions in terms of the kinematic variables used to identify a μ + → e + γ event are mandatory among other aspects to achieve this sensitivity. Thus careful calibration and monitoring of the experimental apparatus are required. One of the dedicated calibration methods involves the Mott scattering process of a mono-energetic positron beam on the MEG II target. As a result positrons with energies around the MEG II signal energy get scattered into the drift chamber. The calibration and extraction of resolution can then be done by the double turn method presented in this article. • Simulation of Mott events provides similar results as the expected MEG II signal. • Beam quality and details of scattering process hardly affect the outcome. • The Double Turn Method provides the detector resolution up to an expected factor. • Resolution in momentum and angular variables can be estimated.

Pentagon functions for massless planar scattering amplitudes

Loop amplitudes for massless five particle scattering processes contain Feynman integrals depending on the external momentum invariants: pentagon functions. We perform a detailed study of the analyticity properties and cut structure of these functions up to two loops in the planar case, where we classify and identify the minimal set of basis functions. They are computed from the canonical form of their differential equations and expressed in terms of generalized polylogarithms, or alternatively as one-dimensional integrals. We present analytical expressions and numerical evaluation routines for these pentagon functions, in all kinematical configurations relevant to five-particle scattering processes.

Attractive Bose-Einstein condensates in anharmonic traps: Accurate numerical treatment and the intriguing physics of the variance

The dynamics of attractive bosons trapped in one dimensional anharmonic potentials is investigated. Particular emphasis is put on the variance of the position and momentum many-particle operators. Coupling of the center-of-mass and relative-motion degrees-of-freedom necessitates an accurate numerical treatment. The multiconfigurational time-dependent Hartree for bosons (MCTDHB) method is used, and high convergence of the energy, depletion and occupation numbers, and position and momentum variances is proven numerically. We demonstrate for the ground state and out-of-equilibrium dynamics, for condensed and fragmented condensates, for small systems and en route to the infinite-particle limit, that intriguing differences between the density and variance of an attractive Bose-Einstein condensate emerge. Implications are briefly discussed.

Forecasting Commodity Futures Returns: An Economic Value Analysis of Macroeconomic vs. Specific Factors

We test whether three well-known commodity-specific variables (basis, hedging pressure, and momentum) may improve the predictive power for commodity futures returns of models otherwise based on macroeconomic factors. We compute recursive, out-of-sample forecasts for fifteen monthly commodity futures return series, when estimation is based on a stepwise model selection approach under a probability-weighted regime-switching regression that identifies different volatility regimes. Comparisons with an AR(1) benchmark show that the inclusion of commodity-specific factors does not improve the forecasting power. We perform a back-testing exercise of a mean-variance investment strategy that exploits any predictability of the conditional risk premium of commodities, stocks, and bond returns, also taking into account transaction costs caused by portfolio rebalancing. The risk-adjusted performance of this strategy does not allow us to conclude that any forecasting approach outperforms the others. However, there is evidence that investment strategies based on commodity-specific predictors outperform the remaining strategies in the high-volatility state.

Probing microscopic models for system-bath interactions via parametric driving

We show that strong parametric driving of a quantum harmonic oscillator coupled to a thermal bath allows one to distinguish between different microscopic models for the oscillator-bath coupling. We consider a bath with an Ohmic spectral density and a model where the system-bath interaction can be tuned continuously between position and momentum coupling via the coupling angle $\alpha$. We derive a master equation for the reduced density operator of the oscillator in Born-Markov approximation and investigate its quasi-steady state as a function of the driving parameters, the temperature of the bath and the coupling angle $\alpha$. We find that the time-averaged variance of position and momentum exhibits a strong dependence on these parameters. In particular, we identify parameter regimes that maximise the $\alpha$-dependence and provide an intuitive explanation of our results.

Multiyear Observations of Gravity Wave Momentum Fluxes in the Midlatitude Mesosphere and Lower Thermosphere Region by Meteor Radar

AbstractMultiyear high‐frequency gravity wave (GW) momentum fluxes and variances in the mesosphere and lower thermosphere region are revealed using four meteor radars along 120°E longitude at Northern Hemisphere midlatitudes for the first time, which are located at Mohe (53.5°N, 122.3°E), Beijing (40.3°N, 116.2°E), Mengcheng (33.3°N, 116.5°E), and Wuhan (30.5°N, 114.2°E), respectively. The seasonal and latitudinal variations of GW momentum fluxes in the midlatitude are discussed. The directions of the monthly mean zonal momentum fluxes are mostly against the background mean zonal winds, which agree well with the selective filtering mechanism. The seasonal variations of meridional momentum fluxes have similar trends over all four stations. The latitudinal variations in the seasonal variation of GW momentum fluxes are mainly due to the latitudinal variations of background winds and GW sources. The unexpected eastward momentum fluxes in winter over Beijing are likely caused by the secondary GWs propagating eastward from the source region over the Tibetan Plateau (25°–40°N, 70–100°E). The GW variances show a V‐shaped structure indicating annual and semiannual variations over four stations in zonal component. A quasi‐4‐month oscillation was observed over Mohe, Mengcheng, and Wuhan in meridional component. The background winds play decisive roles in these GW variance structures.

Open spin chains and complexity in the high energy limit

In the high energy limit of scattering amplitudes in Quantum Chromodynamics and supersymmetric theories the dominant Feynman diagrams are characterized by a hidden integrability in the planar limit. A well-known example is that of Odderon exchange, which can be described as a composite state of three reggeized gluons and corresponds to a closed spin chain with periodic boundary conditions. In the N=4 supersymmetric Yang–Mills theory a similar spin chain arises in the multi-Regge asymptotics of the eight-point amplitude in the planar limit. We investigate the associated open spin chain in transverse momentum and rapidity variables solving the corresponding effective Feynman diagrams. We introduce the concept of complexity in the high energy effective field theory and study its emerging scaling laws.

The tunneling effect for a class of difference operators

We analyze a general class of self-adjoint difference operators [Formula: see text] on [Formula: see text], where [Formula: see text] is a multi-well potential and [Formula: see text] is a small parameter. We give a coherent review of our results on tunneling up to new sharp results on the level of complete asymptotic expansions (see [30–35]).Our emphasis is on general ideas and strategy, possibly of interest for a broader range of readers, and less on detailed mathematical proofs.The wells are decoupled by introducing certain Dirichlet operators on regions containing only one potential well. Then the eigenvalue problem for the Hamiltonian [Formula: see text] is treated as a small perturbation of these comparison problems. After constructing a Finslerian distance [Formula: see text] induced by [Formula: see text], we show that Dirichlet eigenfunctions decay exponentially with a rate controlled by this distance to the well. It follows with microlocal techniques that the first [Formula: see text] eigenvalues of [Formula: see text] converge to the first [Formula: see text] eigenvalues of the direct sum of harmonic oscillators on [Formula: see text] located at several wells. In a neighborhood of one well, we construct formal asymptotic expansions of WKB-type for eigenfunctions associated with the low-lying eigenvalues of [Formula: see text]. These are obtained from eigenfunctions or quasimodes for the operator [Formula: see text], acting on [Formula: see text], via restriction to the lattice [Formula: see text].Tunneling is then described by a certain interaction matrix, similar to the analysis for the Schrödinger operator (see [22]), the remainder is exponentially small and roughly quadratic compared with the interaction matrix. We give weighted [Formula: see text]-estimates for the difference of eigenfunctions of Dirichlet-operators in neighborhoods of the different wells and the associated WKB-expansions at the wells. In the last step, we derive full asymptotic expansions for interactions between two “wells” (minima) of the potential energy, in particular for the discrete tunneling effect. Here we essentially use analysis on phase space, complexified in the momentum variable. These results are as sharp as the classical results for the Schrödinger operator in [22].