Spectrum Of System Research Articles

Dynamics of discrete solitons in the fractional discrete nonlinear Schrödinger equationwith the quasi-Riesz derivative.

We elaborate a fractional discrete nonlinear Schrödinger (FDNLS) equationbased on an appropriately modified definition of the Riesz fractional derivative, which is characterized by its Lévy index (LI). This FDNLS equationrepresents a novel discrete system, in which the nearest-neighbor coupling is combined with long-range interactions, that decay as the inverse square of the separation between lattice sites. The system may be realized as an array of parallel quasi-one-dimensional Bose-Einstein condensates composed of atoms or small molecules carrying, respectively, a permanent magnetic or electric dipole moment. The dispersion relation (DR) for lattice waves and the corresponding propagation band in the system's linear spectrum are found in an exact form for all values of LI. The DR is consistent with the continuum limit, differing in the range of wave numbers. Formation of single-site and two-site discrete solitons is explored, starting from the anticontinuum limit and continuing the analysis in the numerical form up to the existence boundary of the discrete solitons. Stability of the solitons is identified in terms of eigenvalues for small perturbations, and verified in direct simulations. Mobility of the discrete solitons is considered too, by means of an estimate of the system's Peierls-Nabarro potential barrier, and with the help of direct simulations. Collisions between persistently moving discrete solitons are also studied.

An Introduction to Processing, Fitting, and Interpreting Transient Absorption Data.

Transient absorption (TA) spectroscopy is a powerful time-resolved spectroscopic method used to track the evolution of excited-state processes through changes in the system's absorption spectrum. Early implementations of TA were confined to specialized laboratories, but the evolution of commercial turn-key systems has made the technique increasingly available to research groups across the world. Modern TA systems are capable of producing large datasets with high energetic and temporal resolution that are rich in photophysical information. However, processing, fitting, and interpreting TA spectra can be challenging due to the large number of excited-state features and instrumental artifacts. Many factors must be carefully considered when collecting, processing, and fitting TA data in order to reduce uncertainty over which model or set of fitting parameters best describes the data. The goal of data preparation and fitting is to reduce as many of these extraneous factors while preserving the data for analysis. In this method, beginners are provided with a protocol for processing and preparing TA data as well as a brief introduction to selected fitting procedures and models, specifically single wavelength fitting and global lifetime analysis. Commentary on a number of commonly encountered data preparation challenges and methods of addressing them is provided, followed by a discussion of the challenges and limitations of these simple fitting methods.

Fault diagnosis of rotor systems with breathing slant cracks based on nonlinear output frequency response functions

When it comes to practical engineering, there is a high likelihood of shafts developing slant cracks due to torque transmission. These cracks exhibit breathing characteristics, repeatedly opening and closing under gravity and radial forces. To diagnose rotor systems with breathing slant cracks, the nonlinear output frequency response functions (NOFRFs) method is introduced. Firstly, a dynamic model of rotor systems with breathing slant cracks is established, and the system's frequency spectra are obtained by solving the model with different crack angles, depths, and positions. Secondly, the NOFRFs values at different orders are derived based on the NOFRFs theory. The simulation results display increased nonlinear characteristics with crack angle and depth. The system's nonlinear characteristics are stronger when cracks are closer to the disk. The G 3 ( j ω F ) ¯ value for the first-order is sensitive to crack angles, the G 4 ( j 2 ω F ) ¯ value for the second-order is sensitive to crack depths, and the G 4 ( j 4 ω F ) ¯ value for the fourth-order is sensitive to crack positions. As a result, the NOFRFs response at different orders can detect variations in angles, depths, and positions of the breathing slant crack. Finally, experiments are conducted on a rotor system with breathing slant cracks, and the results match those of the simulation, indicating that the NOFRFs method is feasible for identifying breathing slant cracks.

Semi-inverse variational approach to solve the Klein-Gordon equation for harmonic- and perturbed Coulomb potentials

The events observable at the atomic scale cannot be adequately explained by classical physics, hence a new conceptual framework for physics must be developed. "Quantum mechanics" is the name given to this new theory of the physical cosmos. The basic formula of relativistic quantum mechanics is the problem of Klein-Gordon. In relativistic quantum physics, the wave function is crucial since it contains all the data describing a quantum system, in relativity quantum physics, they are crucial. How to solve Klein Gordon's equation has been the topic of intense debate in recent years. To determine the system's spectrum using numerous potentials and methodologies. To obtain the Klein-Gordon issues solution Through determining the harmonic and perturbed Coulomb potentials' energies, The recent study employed an entirely distinct methodology. using the Semi-Inverse Variational Technique to aid in the process, we were able to identify the eigen energies for Harmonic- and Perturbed Coulomb Potentials for a variety of quantum numbers. A further benefit of the technique was that it enabled us to obtain the wave eigenfunctions for various potentials, demonstrating the viability of this approach. We are excited to deal with additional challenges in our upcoming works, the first being the use of nonlinear potentials to solve the Dirac equation due to the effectiveness of this approach.

Design of a graphene-based multi-band metamaterial perfect absorber in THz frequency region for refractive index sensing

In this paper, a multi-band metamaterial perfect absorber, formed by an array of combined H and U-shaped graphene stripes, is proposed. The structure is numerically simulated using the finite element method . The simulation results show that if the graphene layer's chemical potential is equal to 0.9eV, three absorption peaks are found in the proposed system's transmission spectrum at frequencies of 5.29, 6.76, and 9.1 THz with absorption coefficients of 99%, 99.8%, and 86%, respectively. Using an external DC-bias voltage which changes the chemical potential of the graphene layer, the absorption spectra of the combined absorber can be adjusted. It is also shown that the proposed absorber can act as a good refractive index sensor, with a maximum sensitivity of 1783 GHz /RIU , where RIU stands for the refractive index unit. Based on the simulation results, the proposed absorber appears to be a good candidate for applications such as biochemical sensing. • A graphene multi-band metamaterial perfect absorber formed by array of H-shapes and double U-shaped ribbons is proposed. • The finite element method is used for the simulation of the proposed device. • A maximum sensitivity of 1783 (GHz/RIU) has been achieved. • When μ c = 0.9 eV and τ = 1 ps, the proposed structure has three absorption peaks. • The absorption efficiency of the peaks are 99%, 99.8% and 86%, respectively.

Hybrid quantum-classical approach for coupled-cluster Green's function theory

The three key elements of a quantum simulation are state preparation, time evolution, and measurement. While the complexity scaling of time evolution and measurements are well known, many state preparation methods are strongly system-dependent and require prior knowledge of the system's eigenvalue spectrum. Here, we report on a quantum-classical implementation of the coupled-cluster Green's function (CCGF) method, which replaces explicit ground state preparation with the task of applying unitary operators to a simple product state. While our approach is broadly applicable to many models, we demonstrate it here for the Anderson impurity model (AIM). The method requires a number ofTgates that grows asO(N5)per time step to calculate the impurity Green's function in the time domain, whereNis the total number of energy levels in the AIM. Since the number ofTgates is analogous to the computational time complexity of a classical simulation, we achieve an order of magnitude improvement over a classical CCGF calculation of the same order, which requiresO(N6)computational resources per time step.

Synthesis and characterization of Cu–doped Cs2KBiBr6 double perovskite phosphors for photoluminescent applications

In the present study, we report on the synthesis and photo-luminescent applications of hexagonal double perovskite Cs2BIBiBr6 (where BI = K, Li) doped with Cu 2+ ions. Powder XRD patterns were used to confirm the formation of single-phase compounds. Near-UV light was significantly assimilated by localized excitations focused on Bi 3+ ions in the host lattice. Only very faint photoluminescence was detected in the undoped host lattice, while energy transfer from Bi 3+ to Cu 2+ causes immense green photoluminescence in copper-doped materials. A photoluminescence emission peak was obtained at 415 nm for Cs2KBiBr6. PL peaks were gradually red-shifted to higher wavelengths of 417 nm and 419 nm for Cu-doped Cs2 Li0.5K0.5BiBr4Cl2 and Cu-doped Cs2KBiBr4Cl2, respectively. Their capacity to modify a phosphor system's excitation and emission spectrum has enhanced these novel classes of material.

Quantum Theory of Longitudinal-Transverse Polaritons in Nonlocal Thin Films

When midinfrared light interacts with nanoscale polar dielectric structures, optical phonon propagation cannot be ignored, leading to a rich nonlocal phenomenology that we have only recently started to uncover. In properly crafted nanodevices this includes the creation of polaritonic excitations with hybrid longitudinal-transverse nature, which are predicted to allow energy funneling from longitudinal electrical currents to far-field transverse radiation. In this work we study the physics of these longitudinal-transverse polaritons in a dielectric nanolayer in which the nonlocality strongly couples epsilon-near-zero modes to longitudinal phonons. After having calculated the system's spectrum solving Maxwell's equations, we develop an analytical polaritonic theory able to transparently quantify the nonlocality-mediated coupling as a function of the system parameters. Such a theory provides a powerful tool for the study of longitudinal-transverse polariton interactions and we use it to determine the conditions required for the hybrid modes to appear.

Non-reciprocal energy transfer through the Casimir effect.

One of the fundamental predictions of quantum mechanics is the occurrence of random fluctuations in a vacuum caused by the zero-point energy. Remarkably, quantum electromagnetic fluctuations can induce a measurable force between neutral objects, known as the Casimir effect1, and it has been studied both theoretically2,3 and experimentally4-9. The Casimir effect can dominate the interaction between microstructures at small separations and is essential for micro- and nanotechnologies10,11. It has been utilized to realize nonlinear oscillation12, quantum trapping13, phonon transfer14,15 and dissipation dilution16. However, a non-reciprocal device based on quantum vacuum fluctuations remains an unexplored frontier. Here we report quantum-vacuum-mediated non-reciprocal energy transfer between two micromechanical oscillators. We parametrically modulate the Casimir interaction to realize a strong coupling between the two oscillators with different resonant frequencies. We engineer the system's spectrum such that it possesses an exceptional point17-20 in the parameter space and explore the asymmetric topological structure in its vicinity. By dynamically changing the parameters near the exceptional point and utilizing the non-adiabaticity of the process, we achieve non-reciprocal energy transfer between the two oscillators with high contrast. Our work demonstrates a scheme that employs quantum vacuum fluctuations to regulate energy transfer at the nanoscale and may enable functional Casimir devices in the future.

Space–frequency‐mode multi‐dimensional hybrid modulation for vortex wave MIMO‐OFDM systems

By exploiting a dimension called orbital angular momentum (OAM) modes, a new modulation scheme referred to as multi-dimensional space–frequency-mode hybrid modulation (SFMHM) is proposed in this paper, which aims to further improve the MIMO-OFDM system's spectrum efficiency and meet the demand of the future wireless communication networks. The key idea of SFMHM is to map a block of information bits to two information-carrying units: (1) symbols chosen from a constellation diagram, (2) the indices of a subset chosen from all combinations of antennas, OAM modes, and subcarriers. A mapping method with low complexity for SFMHM is presented in this paper, which can reduce the computational complexity of the transmitter significantly. Simulation results show that, in LOS channels, SFMHM systems can achieve better performance compared with traditional MIMO-OFDM systems.

Thermal properties of magnetopolaron in a GaAs delta potential under Rashba effect

Abstract This work treats the polaron's magnetic and thermal properties with delta confinement and interacting with external magnetic and electric areas have been investigated under Rashba effect. We used the Schrodinger equation to find the wave function and the quantified energies of the system. We found that the corresponding wave function can be separated into the product of the longitudinal and transverse gaussian wave function. Moreover, we have obtained an almost exact expression of the system's power spectrum in terms of Rashba spin orbit coupling, delta parameters and electromagnetic field. We have calculated the most common magnetic and thermal elements namely the free energy, entropy, the magnetization, heat capacity and the magnetic susceptibility with the help of the partition function. We found that the results for magnetic and thermal features are strongly affected by external fields, delta length and temperature. Moreover, the results show that the system can cross from ferromagnetic to paramagnetic phase by adjusting magnetic properties.

Solitons in a chain of charge-parity-symmetric dimers

We consider an array of dual-core waveguides, which represent an optical realization of a chain of dimers, with an active (gain-loss) coupling between the cores, opposite signs of discrete diffraction in the parallel arrays, and a phase-velocity mismatch between them (which is necessary for the stability of the system). The array provides an optical emulation of the charge-parity ($\mathcal{CP}$) symmetry. The addition of the intracore cubic nonlinearity gives rise to several species of fundamental discrete solitons, which exist in continuous families, although the system is non-Hermitian. The existence and stability of the soliton families are explored by means of analytical and numerical methods. An asymptotic analysis is presented for the case of weak intersite coupling (i.e., near the anticontinuum limit), as well as weak coupling between cores in each dimer. Several families of fundamental discrete solitons are found in the semi-infinite gap of the system's spectrum, that have no counterparts in the continuum limit, as well as a branch which belongs to the finite band gap and carries over into a family of stable gap solitons in that limit. One branch develops an oscillatory instability above a critical strength of the intersite coupling, others being stable in their entire existence regions. Unlike solitons in conservative lattices, which are controlled solely by the strength of the intersite coupling, here fundamental-soliton families have several control parameters, one of which, viz., the coefficient of the intercore coupling in the active host medium, may be readily adjusted in the experiment by varying the gain applied to the medium.

Nodal points of Weyl semimetals survive the presence of moderate disorder

In this work we address the physics of individual three dimensional Weyl nodes subject to a moderate concentration of disorder. Previous analysis indicates the presence of a quantum phase transition below which disorder becomes irrelevant and the integrity of sharp nodal points of vanishing spectral density is preserved in this system. This statement appears to be at variance with the inevitable presence of statistically rare fluctuations which cannot be considered as weak and must have strong influence on the system's spectrum, no matter how small the average concentration. We here reconcile the two pictures by demonstrating that rare fluctuation potentials in the Weyl system generate a peculiar type of resonances which carry spectral density in any neighborhood of zero energy, but never at zero. In this way, the vanishing of the DoS for weak disorder survives the inclusion of rare events. We demonstrate this feature by considering three different models of disorder, each emphasizing specific aspects of the problem: a simplistic box potential model, a model with Gaussian distributed disorder, and one with a finite number of $s$-wave scatterers. Our analysis also explains why the protection of the nodal DoS may be difficult to see in simulations of finite size lattices.

Utilization of multiple spinal cord stimulation (SCS) waveforms in chronic pain patients

ABSTRACTBackground: Advances in spinal cord stimulation (SCS) have improved patient outcomes, leading to its increased utilization for chronic pain. Chronic pain is dynamic showing exacerbations, variable severity, and evolving pain patterns. Given this complexity, SCS systems that provide a broad range of stimulation waveforms may be valuable.Methods: The aim of this research was to characterize the usage pattern of stimulation waveforms and field shapes in chronic pain patients implanted with the Spectra System. A review of daily device usage in a cohort of 250 patients implanted for a minimum duration of one month was conducted.Results: With follow-ups ranging between 1 month and 1 year post-implant, 72.8% of patients used Standard Rate, 34.8% Anode Intensification, 23.2% Higher Rate, and 8.4% Burst stimulation waveforms. Collectively, 60% used 1 or more advanced waveforms, either exclusively or along with Standard Rate. A trend showed patients continuing to use up to 3 programs one year post-implant.Conclusion: When given a choice, SCS patients often utilize a variety of waveforms, suggesting that patients may benefit from a single system that provides multiple waveforms and field shapes to customize therapy and improve efficacy.

Single and double linear and nonlinear flatband chains: Spectra and modes.

We report results of systematic analysis of various modes in the flatband lattice, based on the diamond-chain model with the on-site cubic nonlinearity, and its double version with the linear on-site mixing between the two lattice fields. In the single-chain system, a full analysis is presented, first, for the single nonlinear cell, making it possible to find all stationary states, viz., antisymmetric, symmetric, and asymmetric ones, including an exactly investigated symmetry-breaking bifurcation of the subcritical type. In the nonlinear infinite single-component chain, compact localized states (CLSs) are found in an exact form too, as an extension of known compact eigenstates of the linear diamond chain. Their stability is studied by means of analytical and numerical methods, revealing a nontrivial stability boundary. In addition to the CLSs, various species of extended states and exponentially localized lattice solitons of symmetric and asymmetric types are also studied, by means of numerical calculations and variational approximation. As a result, existence and stability areas are identified for these modes. Finally, the linear version of the double diamond chain is solved in an exact form, producing two split flatbands in the system's spectrum.

Two-dimensional dipolar gap solitons in free space with spin-orbit coupling

We present gap solitons (GSs) that can be created in free nearly two-dimensional (2D) space in dipolar spinor Bose-Einstein condensates with the spin-orbit coupling (SOC), subject to tight confinement, with size $a_{\perp }$, in the third direction. For quasi-2D patterns, with lateral sizes $l\gg a_{\perp }$, the kinetic-energy terms in the respective spinor Gross-Pitaevskii equations may be neglected in comparison with SOC. This gives rise to a bandgap in the system's spectrum, in the presence of the Zeeman splitting between the spinor components. While the present system with contact interactions does not produce 2D solitons, stable gap solitons(GSs), with vorticities $0$ and $1$ in the two components, are found, in quasi-analytical and numerical forms, under the action of dipole-dipole interaction (DDI). Namely, isotropic and anisotropic 2D GSs are obtained when the dipoles are polarized, respectively, perpendicular or parallel to the 2D plane. The GS families extend, as \textit{embedded solitons} (ESs), into spectral bands, a part of the ES branch being stable for isotropic solitons. The GSs remain stable if the competing contact interaction, with the sign opposite to that of the DDI, is included, while the addition of the contact term with the same sign destabilizes the GSs, at first replacing them by breathers, and eventually leading to destruction of the solitons. Mobility and collision of the GSs are studied too, revealing negative and positive effective masses of the isotropic and anisotropic solitons, respectively.

Keplerobservations of the asteroseismic binary HD 176465

Binary star systems are important for understanding stellar structure and evolution, and are especially useful when oscillations can be detected and analysed with asteroseismology. However, only four systems are known in which solar-like oscillations are detected in both components. Here, we analyse the fifth such system, HD 176465, which was observed by Kepler. We carefully analysed the system's power spectrum to measure individual mode frequencies, adapting our methods where necessary to accommodate the fact that both stars oscillate in a similar frequency range. We also modelled the two stars independently by fitting stellar models to the frequencies and complementary parameters. We are able to cleanly separate the oscillation modes in both systems. The stellar models produce compatible ages and initial compositions for the stars, as is expected from their common and contemporaneous origin. Combining the individual ages, the system is about 3.0$\pm$0.5 Gyr old. The two components of HD 176465 are young physically-similar oscillating solar analogues, the first such system to be found, and provide important constraints for stellar evolution and asteroseismology.

On the Irregular Part of V -Statistics Multifractal Spectra for Systems with Non-Uniform Specification

Let (X, f) be a dynamical system with X a compact metric space. Let Xr be the product of r-copies of X, r≥ 1, and Φ: Xr → R. The multifractal decomposition for V –statistics for Φ, f is defined as .The set of points x ∊ X, for which the limit does not exist is called the irregular part, or historic set, of the spectrum. In this article we analyze the irregular part of the V -statistics for systems satisfying a weak form of the known Bowen specification property, called the non-uniform specification property. This concept was introduced by P. Varandas and allows to work in a nonuniformly hyperbolic context.

Traffic Pattern Prediction and Spectrum Allocation with Multiple Channel Width in Cognitive Cellular Networks

This paper investigates the traffic pattern prediction based on seasonal deviation and spectrum reallocation with multiple channel width in cognitive cellular networks. Compared to the existing approaches based on time series or classical statistic method, the binary exponential deviation offset prediction proposed in this paper focuses on the increment or decrement on every sampling point during an exponential offset period. Then the deviations will be revised at different levels in the next prediction process. The proposed approach is validated with some real end-user data from a WiFi network and simulation experiments. Based on such a precise prediction, we allocate the channels with different bandwidth to end-users according to diverse quality-of-service (QoS), which increases both the system's profits and actual spectrum utilization. The multidimensional bounded knapsack problem is introduced to divide channels, to which the proposed balance between value density and request probability strategy gets the approximate solution. The simulation experiment results show its good performance in not only utility but also spectrum utilization of the base-stations, especially when the resources are deficient.

Flexible all-optical frequency allocation of OFDM subcarriers

We investigate the underlying mechanism that allows OFDM subcarriers in an all-optical OFDM system to be assigned to any optical frequency using an optical filter, even if that frequency is not generated by the comb-line source feeding the filters. We confirm our analysis using simulations, and present experimental results from a 252-subcarrier system that uses a mode-locked laser (MLL) as the comb source and a wavelength selective switch. The experimental results show that there is no correlation between the programmed frequency offset between a subcarrier and nearest comb line, and the received signal quality. Thus, subcarriers could be inserted into unused portions of an optical transmission system's spectrum without restriction on their particular center frequencies. Any percentage of cyclic prefix can be added to the OFDM symbol simply by reprogramming the optical filter to give wider subcarrier frequency spacing than the comb line spacing, which is useful for tailoring the CP to the dispersion of various optical transmission paths, to maximize the spectral efficiency. Finally, the MLL's center frequency need not be locked to a system reference.