Energy Phase Shifts Research Articles

Scale transformations in model exchange potentials in low energy electron-atom scattering

Model exchange potentials are particularly interesting to account for the indistinguishability between the projectile and target electrons in electron-atom scattering in vacuo and plasma environments. It is well known that their performance is pretty satisfactory in the high energies but also that discrepancies from the results obtained with exact exchange are found toward the zero energy limit. In this article, we examine how well established model exchange potentials based on the free electron gas approach compare to phase shifts calculated considering exchange in exact form. In particular, we show that the Hara and the semiclassical exchange potentials are able to reproduce reference low energy phase shifts through a simple scale transformation, in opposition to the previous approaches where energy dependent corrections to the local momentum were adopted. We provide the scale factors and phase shifts for electron scattering by He, Ne and Ar atoms for k< 1,0 a0−1. Such scaling factors can be determined reproducing the scattering length and the number of s-wave bound states from exact exchange calculations. We also show that the scaling procedure works for electronic densities that present the physically correct asymptotic behavior. The present results are important to the research field, since they form the basis to construction of scattering models based on optical potential approaches.

Stackelberg Game-Based Multiple Access Design for Intelligent Reflecting Surface Assisted Wireless Powered IoT Networks

This paper integrates an intelligent reflecting surface (IRS) into a wireless powered Internet-of-Things (IoT) network, where IoT devices need to harvest energy from an energy station (ES) before transmitting their monitoring data to an access point. An IRS is invoked to improve energy and spectral efficiency by changing propagation environment. Considering that the ES and IoT devices come from different operators, IoT devices need to provide monetary payment in exchange for the ES’s charging before implementing nonlinear energy harvesting. We build this energy interaction via Stackelberg game under three multiple access schemes, i.e., IRS-assisted time division multiple access (IRS-TDMA), IRS-assisted non-orthogonal multiple access (IRS-NOMA), and IRS-assisted frequency division multiple access (IRS-FDMA). To solve the common follower game among the three schemes, we first employ an alternating optimization (AO) algorithm with Majorization-Minimization (MM) to alternately optimize the energy beamforming and energy phase shifts, and then derive the optimal ES transmit power. For the leader game of IRS-TDMA, the optimal time allocation and optimal information phase shifts are first derived in closed form through Lagrange dual method and triangular inequality, respectively. On this basis, an AO algorithm is developed to optimize energy price and energy transfer time alternately. Similar procedures are also used to solve the leader games for IRS-NOMA and IRS-FDMA. Simulation results show that IRS-NOMA and IRS-FDMA achieve the same utilities for the ES and IoT devices. Due to IRS time selectivity, IRS-TDMA is more energy and spectral efficient than IRS-NOMA and IRS-FDMA, and this advantage is more pronounced in higher numbers of IRS elements and IoT devices.

Mechanical responses and acoustic emission behaviors of coal under compressive differential cyclic loading (DCL): a numerical study via 3D heterogeneous particle model

The stability of coal walls (pillars) can be seriously undermined by diverse in-situ dynamic disturbances. Based on a 3D particle model, this work strives to numerically replicate the major mechanical responses and acoustic emission (AE) behaviors of coal samples under multi-stage compressive cyclic loading with different loading and unloading rates, which is termed differential cyclic loading (DCL). A Weibull-distribution-based model with heterogeneous bond strengths is constructed by both considering the stress–strain relations and AE parameters. Six previously loaded samples were respectively grouped to indicate two DCL regimes, the damage mechanisms for the two groups are explicitly characterized via the time-stress-dependent variation of bond size multiplier, and it is found the two regimes correlate with distinct damage patterns, which involves the competition between stiffness hardening and softening. The numerical b-value is calculated based on the magnitudes of AE energy, the results show that both stress level and bond radius multiplier can impact the numerical b-value. The proposed numerical model succeeds in replicating the stress–strain relations of lab data as well as the elastic-after effect in DCL tests. The effect of damping on energy dissipation and phase shift in numerical model is summarized.

Tensile energy dissipation and mechanical properties of the knee meniscus: relationship with fiber orientation, tissue layer, and water content.

Introduction: The knee meniscus distributes and dampens mechanical loads. It is composed of water (∼70%) and a porous fibrous matrix (∼30%) with a central core that is reinforced by circumferential collagen fibers enclosed by mesh-like superficial tibial and femoral layers. Daily loading activities produce mechanical tensile loads which are transferred through and dissipated by the meniscus. Therefore, the objective of this study was to measure how tensile mechanical properties and extent of energy dissipation vary by tension direction, meniscal layer, and water content. Methods: The central regions of porcine meniscal pairs (n = 8) were cut into tensile samples (4.7mm length, 2.1mm width, and 0.356mm thickness) from core, femoral and tibial components. Core samples were prepared parallel (circumferential) and perpendicular (radial) to the fibers. Tensile testing consisted of frequency sweeps (0.01-1Hz) followed by quasi-static loading to failure. Dynamic testing yielded energy dissipation (ED), complex modulus (E*), and phase shift (δ) while quasi-static tests yielded Young's Modulus (E), ultimate tensile strength (UTS), and strain at UTS (εUTS). To investigate how ED is influenced by the specific mechanical parameters, linear regressions were performed. Correlations between sample water content (φw) and mechanical properties were investigated. A total of 64 samples were evaluated. Results: Dynamic tests showed that increasing loading frequency significantly reduced ED (p < 0.05). Circumferential samples had higher ED, E*, E, and UTS than radial ones (p < 0.001). Stiffness was highly correlated with ED (R2 > 0.75, p < 0.01). No differences were found between superficial and circumferential core layers. ED, E*, E, and UTS trended negatively with φw (p < 0.05). Discussion: Energy dissipation, stiffness, and strength are highly dependent on loading direction. A significant amount of energy dissipation may be associated with time-dependent reorganization of matrix fibers. This is the first study to analyze the tensile dynamic properties and energy dissipation of the meniscus surface layers. Results provide new insights on the mechanics and function of meniscal tissue.

Improving Physical Layer Security in IRS-Aided WPCN Multicast Systems via Stackelberg Game

This paper investigates an intelligent reflecting surface (IRS) aided secure wireless powered communication network (WPCN), where a transmitter first harvests energy from a power station (PS), and then uses the collected energy to transmit information to multiple internet of things (IoT) devices in the form of multicast in the presence of multiple eavesdroppers. An IRS is deployed to enhance the efficiency of wireless energy transfer (WET) and secure wireless information transfer (WIT). Considering that the PS and transmitter belong to different service providers, we model this energy interaction through a Stackelberg game and propose an IRS-aided energy trading and secure communication (IRS-ETSC) scheme, in which the transmitter needs to pay an energy price as an incentive for the PS energy service. Specifically, the transmitter as the leader can control the energy price, WET time, two-stage phase shifts, and beamforming vector, while the PS as the follower can adjust the transmit power. To solve the non-convex leader game problem, we propose a two-step approach to decompose the original problem into two subproblems. The first subproblem can be solved independently by an efficient alternating optimization (AO) based algorithm, in which the closed-form optimal beamforming vector and energy phase shifts are alternately optimized. Then, the second subproblem is relaxed by semidefinite relaxation (SDR) and solved by an iterative algorithm based on block coordinate descent (BCD), where the optimal energy price, optimal WET time, and suboptimal information phase shifts can be obtained by golden section method and successive convex approximation (SCA) respectively. Both subproblems can converge to a stationary point. Numerical results show that compared with the traditional non-IRS scheme, the proposed IRS-ETSC scheme achieves utility improvement for both the PS and transmitter.

Alpha-alpha scattering in the Multiverse

We investigate the phase shifts of low-energy α-α scattering under variations of the fundamental parameters of the Standard Model, namely the light quark mass, the electromagnetic fine-structure constant as well as the QCD θ-angle. As a first step, we recalculate α-α scattering in our Universe utilizing various improvements in the adiabatic projection method, which leads to an improved, parameter-free prediction of the S- and D-wave phase shifts for laboratory energies below 10 MeV. We find that positive shifts in the pion mass have a small effect on the S-wave phase shift, whereas lowering the pion mass adds some repulsion in the two-alpha system. The effect on the D-wave phase shift turns out to be more pronounced as signaled by the D-wave resonance parameters. Variations of the fine-structure constant have almost no effect on the low-energy α-α phase shifts. We further show that up-to-and-including next-to-leading order in the chiral expansion, variations of these phase shifts with respect to the QCD θ-angle can be expressed in terms of the θ-dependent pion mass.

Numerical study of large cross-phase modulation with stationary light pulses

We report a systematic investigation of cross-phase modulation using techniques of light storage (LS) and stationary light pulse (SLP) based on the effect of electromagnetically induced transparency. Two light fields are stopped in the medium to prolong the interaction time, which enhances the efficiency of optical nonlinearity. We numerically study the properties of the signal SLP field such as lifetime, light pulse storage efficiency, and stored peak intensity as functions of optical density (OD) and coupling field intensity. The strong nonlinearity between LS and SLP photons leads to a phase shift of up to π at the single-photon level. Meanwhile, both the LS and SLP photons maintain energy transmission higher than 20%, as the OD of the SLP subsystem is larger than 700. The energy transmission and phase shift can be further improved by increasing the OD of the medium. The performance of the quantum phase gate between two single photons is expected by applying such strong photon interaction.

High-fidelity numerical simulation of solitary wave propagation

As a classic problem in oceanographic and coastal engineering hydrodynamics, solitary wave propagation is used to benchmark a novel high-fidelity numerical model based on the Navier–Stokes equations. The model combines the Finite Volume method based on Merged Stencil with 3rd-order reconstruction (FVMS3) and Tangent of Hyperbola for INterface Capturing method with Quadratic surface representation and Gaussian Quadrature (THINC/QQ) schemes. Accurate predictions are made of inviscid and viscous solitary waves propagating on plane and sloping beaches. Model performance is assessed by comparing the predictions with analytical solutions, alternative numerical results obtained using interFoam solver in OpenFOAM and commercial flow software ANSYS Fluent, as well as experimental data. It is demonstrated that the present model significantly reduces undesirable numerical effects, including energy loss, wave decay, phase shift, and overestimation of the velocity profile of propagating waves even after long duration computations, by suppressing numerical dissipation and dispersion.

A Current-Sharing Method for Interleaved High-Frequency LLC Converter With Partial Energy Phase Shift Regulation

In this article, a current-sharing method for interleaved high-frequency LLC converter with partial energy phase shift regulation is presented. An auxiliary low-power converter is added in each phase, which is able to achieve natural current sharing and the zero-voltage switching (ZVS) operation for the auxiliary circuit. Meanwhile, the perfect current sharing between phases is achieved by controlling the phase shift angle between the LLC bridge and the auxiliary bridge. Only partial energy is processed by the auxiliary converter; hence, the power losses of the added auxiliary converters are minimized, and the overall high efficiency is maintained. By transforming the current sharing of the resonant converter into phase shift control between the LLC bridge and the auxiliary bridge, the proposed method is simple to implement and easy to extend to multiple phases. The frequency of the auxiliary converter is the same as that of of the main LLC converter, so it is suitable to operate the auxiliary circuit at a high switching frequency to improve the power density. The operating principle, design considerations, and the control schemes are presented, and a 400-kHz two-phase interleaved LLC prototype was built to verify the theoretical analysis.

Using an Electromechanical Analogy to Describe the Damping Characteristics of an MFC Actuator

In this article, a mathematical model was formulated that describes the dynamic behavior of MFC actuators. The model was developed on the basis of numerical-analytical methods for solving coupled boundary value problems of electromagnetoelasticity for inhomogeneous media equipped with piezoactive structural elements and loaded with coherent electromechanical disturbances. Within the framework of the performed numerical experiments, stationary harmonic axisymmetric oscillations of an elementary composite two-phase MFC actuator cell loaded with coherent electromechanical disturbances were considered. The calculation of the MFC actuators complex impedance and conductivity values, taking into account the energy losses and phase shift at different levels of the control electric voltage, was carried out.

Rydberg electron-atom scattering in forbidden regions of negative kinetic energy

Scattering of a Rydberg electron by ground-state atoms (scatterers) located in its classically forbidden region can be viewed as electron-atom scattering with negative incident energy. We propose a treatment of this unusual case of scattering in the context of long-range molecular potentials arising from the interaction of a Rydberg electron with ground state atoms. We describe a treatment leading to proper equivalents of scattering lengths and phase shifts for negative incident energies, which becomes advantageous when a Rydberg atom is penetrated by more than one scatterer and the Rydberg electron scatters back and forth between the atoms in the classically allowed and forbidden regions. We apply this approach to Cs and Rb samples, and find evidence for a resonance-like feature for their 3S1 states.

Inequalities between fixed energy phase shifts II

In this note we continue the study of the properties of phase shifts arising in the 3D inverse scattering with spherically symmetrical potential. Themain result of our paper improves Regge’s inequality for a class of potentials with compact support.

Organization in complex brain networks: Energy distributions and phase shift

The Hamiltonian function of a network, derived from the intrinsic distributions of nodes and edges, magnified by resolution parameter has information on the distribution of energy in the network. In brain networks, the Hamiltonian function follows hierarchical features reflecting a power-law behavior which can be a signature of self-organization. Further, the transition of three distinct phases driven by resolution parameter is observed which could correspond to various important brain states. This resolution parameter could thus reflect a key parameter that controls and balances the energy distribution in the brain network.

Correlation between Nucleon-Nucleon Interaction, Pairing Energy Gap and Phase Shift for Identical Nucleons in Nuclear Systems

Assuming some known nucleon-nucleon interactions, and using the relations between phase shift δ and nucleon-nucleon interaction potential V (r) ; the relation between nucleon-nucleon interaction and scattering length a; the relation between energy gap Δ, and scattering length a; an equation is obtained between energy gap Δ and Fermi momentum kF via the phase shift δ (kF). Assuming 1s0 (singlet) pairing between the nucleons, the energy gap Δ has been calculated and it is found that Δ = 3.0 MeV at Fermi momentum kF = 0.8 fm-1.

Effect of Low Temperature on a 4 W/60 K Pulse-Tube Cryocooler for Cooling HgCdTe Detector

Temperature is an extremely important parameter for the material of the space-borne infrared detector. To cool an HgCdTe-infrared detector, a Stirling-type pulse-tube cryocooler (PTC) has been developed based on a great deal of numerical simulations, which are performed to investigate the thermodynamic behaviors of the PTC. The effects of different low temperatures are presented to analyze different energy flows, losses, phase shifts, and impedance matching of the PTC at a temperature range of 40–120 K, where woven wire screens are used. Finally, a high-efficiency coaxial PTC has been designed, built, and tested, operating around 60 K after a number of theoretical and experimental studies. The PTC can offer a no-load refrigeration temperature of 40 K with an input electric power of 150 W, and a cooling power of 4 W at 60 K is obtained with Carnot efficiency of 12%. In addition, a comparative study of simulation and experiment has been carried out, and some studies on reject temperatures have been presented for a thorough understanding of the PTC system.

Solution of Spin and Pseudo-Spin Symmetric Dirac Equation in (1+1) Space-Time Using Tridiagonal Representation Approach

The aim of this work is to find exact solutions of the Dirac equation in (1+1) space-time beyond the already known class. We consider exact spin (and pseudo-spin) symmetric Dirac equations where the scalar potential is equal to plus (and minus) the vector potential. We also include pseudo-scalar potentials in the interaction. The spinor wavefunction is written as a bounded sum in a complete set of square integrable basis, which is chosen such that the matrix representation of the Dirac wave operator is tridiagonal and symmetric. This makes the matrix wave equation a symmetric three-term recursion relation for the expansion coefficients of the wavefunction. We solve the recursion relation exactly in terms of orthogonal polynomials and obtain the state functions and corresponding relativistic energy spectrum and phase shift.

Approximate bound and scattering solutions of Dirac equation for the modified deformed Hylleraas potential with a Yukawa-type tensor interaction

Analytical bound and scattering state solutions of Dirac equation are investigated for the modified deformed Hylleraas potential with a Yukawa-type tensor interaction. The energy equation, phase shifts and normalization constants of the pseudospin and spin symmetry limits are represented. Since the modified deformed Hylleraas potential reduces to the Poschl–Teller, Hulthen and deformed Hylleraas potential, we have obtained energy equation and scattering properties of the Dirac equation for these potentials within a Yukawa-type tensor interaction. We have also reported some numerical results to show the effect of tensor interaction.

Bound and scattering states in harmonic waveguides in the vicinity of free space Feshbach resonances

The two-body bound and scattering properties in an one-dimensional harmonic waveguide close to free space magnetic Feshbach resonances are investigated based on the local frame transformation approach within a single partial wave approximation. An energy and magnetic field dependent free space phase shift is adopted in the current theoretical framework. For both s- and p-wave interaction, the least bound state in the waveguide dissociates into the continuum at the resonant magnetic field where the effective one-dimensional scattering length diverges. Consequently, the association of atoms into molecules in the waveguide occurs when the magnetic field is swept adiabatically across the pole of . In the vicinity of broad s-wave resonances, the resonant magnetic field is nearly independent on the transverse confining frequency of the waveguide. Close to p-wave and narrow s-wave resonances, the resonant magnetic field changes as varies.

Effective-range approximations for resonant scattering of cold atoms

Studies of cold atom collisions and few-body interactions often require the energy dependence of the scattering phase shift, which is usually expressed in terms of an effective-range expansion. We use accurate coupled-channel calculations on $^{6}$Li, $^{39}$K and $^{133}$Cs to explore the behavior of the effective range in the vicinity of both broad and narrow Feshbach resonances. We show that commonly used expressions for the effective range break down dramatically for narrow resonances and near the zero-crossings of broad resonances. We present an alternative parametrization of the effective range that is accurate through both the pole and the zero-crossing for both broad and narrow resonances. However, the effective range expansion can still fail at quite low collision energies, particularly around narrow resonances. We demonstrate that an analytical form of an energy and magnetic field-dependent phase shift, based on multichannel quantum defect theory, gives accurate results for the energy-dependent scattering length.

The inverse scattering problem at fixed energy based on the Marchenko equation for an auxiliary Sturm–Liouville operator

A new approach is proposed to the solution of the quantum mechanical inverse scattering problem at a fixed energy. The method relates the fixed energy phase shifts to those arising in an auxiliary Sturm–Liouville problem via the interpolation theory of the Weyl–Titchmarsh m-function. Then a Marchenko equation is solved to obtain the potential. As an illustration test results are shown including the reconstructions of the piecewise constant and Coulomb-type potentials. A byproduct of the new framework is a demonstration of the connection found between the Gelfand–Levitan and Marchenko formalisms.