Arbitrary Profile Research Articles

Wave-packet scattering at a normal-superconductor interface in two-dimensional materials: A generalized theoretical approach

A wave-packet time evolution method, based on the split-operator technique, is developed to investigate the scattering of quasiparticles at a normal-superconductor interface of arbitrary profile and shape. As a practical application, we consider a system where low-energy electrons can be described as Dirac particles, which is the case for most two-dimensional materials, such as graphene and transition-metal dichalcogenides. However, the method is easily adapted for other cases such as electrons in few-layer black phosphorus or any Schr\"odinger quasiparticles within the effective mass approximation in semiconductors. We employ the method to revisit Andreev reflection in mono-, bi-, and trilayer graphene, where specular- and retro-reflection cases are observed for electrons scattered by a steplike superconducting region. The effect of opening a zero-gap channel across the superconducting region on the electron and hole scattering is also addressed, as an example of the versatility of the technique proposed here.

Dynamic behavior and power flow analyses of a cylindrical shell structure embedded with acoustic black holes

Vibrational energy flow model of ABH cylindrical shells with arbitrary profile and general boundary conditions is established using Rayleigh-Ritz method in conjunction with improved Fourier series expansion. Energy equation based on Love’s shell theory is formulated, while the ABH cylindrical shells including any type of indentation profile can be considered uniformly and invariantly expanded into Fourier series accordingly. The vibrational displacements are expanded with the modified version of Fourier series. The proposed model is validated through the comparisons with experimental results and those calculated from finite element method, and excellent agreement can be observed. The power flow analysis illustrates that the vibrational energy flow into ABH indentations is intensified and absorbed by damping materials compared with that of the uniform one for nearly all the frequency ranges. However, the energy absorption loses efficacy in certain low frequencies, which are coincided with its overall mode shapes. This work can shed some new light on the vibration behavior study of ABH cylindrical shell from the viewpoint of energy transmission, and can provide an efficient analysis tool for the vibration characteristics study and its optimal design of such complex structural system embedded with Acoustic Black Holes.

Compliance and precision modeling of general notch flexure hinges using a discrete-beam transfer matrix

Compliance and precision are two key aspects in designing flexure hinges for use in compliant mechanisms. A generalized method with the finite-discrete idea and beam transfer matrix is developed for quickly predicting the kinetostatic behaviors of single and multiple-axis notch flexure hinges. The transfer matrix of Timoshenko beams explicitly including the shear deformation effect is derived in a concise form of Taylor series expansion. The compliance and rotational precision matrices of general notch flexure hinges are then derived targeting for arbitrary cutout profiles with a step-by-step modeling procedure. It is easy to operate for comparing and synthesizing different flexure hinges within a unified modeling framework. All a designer has to do is to prepare the concerned profile function without being caught into the laborious and even unsolvable derivation of mechanics. Several groups of single and multiple-axis notch flexure hinges are adopted to verify the feasibility of the presented approach by comparing with the numerical and experimental results available in literature. The comparative results indicate the high prediction accuracy and easy operation of the proposed approach for a wide applicability of complex notch flexure hinges.

A hybrid boundary element method based model for wave interaction with submerged viscoelastic plates with an arbitrary bottom profile in frequency and time domain

This study investigates the scattering of surface ocean waves by a submerged viscoelastic plate placed over the variable bottom topography under the assumptions of linear theory. The solution is derived using the hybrid boundary element method. The boundary element method is faster and easier to use when compared to the most widely used analytical method, such as the eigenfunction expansion method. Moreover, the application of analytical methods is restricted to structures with regular geometries and flat sea bottom. However, the present solution technique works for the plate at any angle placed over the variable bottom topography. Furthermore, as a particular case, the scattering problem is analyzed when a rigid wall is placed downstream. Energy balance relations are derived to check the accuracy of the computed numerical results. The effect of sinusoidally varying bottom topography, damping parameter, and plate edge conditions on the Bragg resonance phenomenon is analyzed. Initially, the solutions are presented in the frequency domain using the hybrid boundary element method and then extended to the time domain using the Fourier transform. It is observed that when the edges of the submerged plate are fixed, the Bragg resonance occurs at lower values of the frequency parameter. However, the Bragg resonance occurs around the primary Bragg value when the plate has free edges. For certain incident wave frequencies, the viscoelastic plate that completely covers the undulating bed dissipates a greater amount of wave energy than when the plate only partially covers the seabed.

A data-based reduced-order model for dynamic simulation and control of district-heating networks

This study concerns the development of a data-based compact model for the prediction of the fluid temperature evolution in district heating (DH) pipeline networks. This so-called “reduced-order model” (ROM) is obtained from reduction of the conservation law for energy for each pipe segment to a semi-analytical input–output relation between the pipe outlet temperature and the pipe inlet and ground temperatures that can be identified from training data. The ROM basically is valid for generic pipe configurations involving 3D unsteady heat transfer and 3D steady flow as long as heat-transfer mechanisms are linearly dependent on the temperature field. Moreover, the training data can be generated by physics-based computational “full-order” models (FOMs) yet also by (calibration) experiments or field measurements. Performance tests using computational training data for a single-pipe configuration demonstrate that the ROM (i) can be successfully identified and (ii) can accurately describe the response of the outlet temperature to arbitrary input profiles for inlet and ground temperatures. Application of the ROM to two case studies, i.e. fast simulation of a small DH network and design of a controller for user-defined temperature regulation of a DH system, demonstrate its predictive ability and efficiency also for realistic systems. Dedicated cost analyses further reveal that the ROM may significantly reduce the computational costs compared to FOMs by (up to) orders of magnitude for higher-dimensional pipe configurations. These findings advance the proposed ROM as a robust and efficient simulation tool for practical DH systems with a far greater predictive ability than existing compact models.

ITER Toroidal Interferometer and Polarimeter (TIP) beam refraction in 3D density profiles

Calculations of the expected refraction of the five ITER Toroidal Interferometer and Polarimeter (TIP) chords are presented for a range of conditions including high-density axisymmetric, ELMing H-mode cases and shattered pellet disruption mitigation cases. The calculations are carried out with a newly developed ray tracing code capable of following TIP’s 10.59μm laser beams through arbitrary 3D electron density profiles. Using JOREK simulations of ELM density perturbations in a 15MA ITER baseline plasma, it is shown that refraction from ELMs is expected to be negligible. It is found, however, that TIP interferometers will be able to clearly resolve the line-integrated density perturbation from ELMs and contribute to the ITER measurement requirement “14. H-mode, ELMs and L-H mode transition indicator”. Calculations of the expected refraction in a NIMROD simulated shattered pellet disruption mitigation scenario with peak local electron densities of ne=3.7×1021 m−3 (max line-averaged densities of navg=1.3×1021 m−3) also show tolerable refraction and it is likely that most, if not all chords, would avoid signal loss. For both axisymmetric and structured plasmas with line-averaged densities in the mid to upper 1021 m−3 range, values likely present only during disruption mitigation, refraction becomes significant and could limit the ability of TIP to make reliable density measurements.

Elastic and thermoelastic response of multilayer inhomogeneous hollow cylinders

An approach is presented for solving plane axisymmetric problems of elasticity and thermoelasticity for multilayer hollow cylinders with per-layer properties having arbitrary distribution profiles within the radial coordinate. The approach is based on the representation of material profiles within the entire assembly in the form of stepwise-variable functions with the implication of the direct integration method toward the compatibility equation in terms of strains. The approach avoids using the generalized derivative apparatus. The original problems are reduced to a governing integral equation with an integral condition implying a solution through explicit dependence on the force and thermal loadings.

Simulating the Action Principle in Optics

Light has a fascinating property: it always travels the path that takes the least time between any two points. This is the motivating property behind optical phenomena such as reflection and refraction. The unreasonable economic efficiency of light is captured by a single proposition: the principle of least action (PLA) in optics. Unlike reflection and refraction, which emerge from optimizing a one-dimensional function, the PLA emerges from optimizing an infinite-dimensional functional. The PLA can be difficult for students to comprehend, as the formulation of the Lagrangian is often left unexplained. To this end, this paper presents various simulations to demonstrate the action principle, including a numerical solution to a generalization of the brachistochrone problem to an arbitrary refractive profile. The interactive simulations discussed in the paper are available at Ref. 1.

Integrated Convex Speed Planning and Energy Management for Autonomous Fuel Cell Hybrid Electric Vehicles

Fuel cell hybrid electric vehicles (FCHEVs) have zero harmful emissions, fast refueling times, and long driving ranges. Autonomous FCHEVs add benefits such as collision avoidance and driver convenience yet increase vehicle energy usage due to sensors and computation. Thus, it is important to optimize vehicle speed trajectories and the energy management strategy (EMS) of autonomous FCHEVs to minimize energy use. This article uniquely proposes to achieve this goal using convex optimization, with detailed vehicle loss calculations that can be run in real time. The two novel approaches proposed are: 1) the successive method, which solves the speed problem then the EMS problem, and 2) the integrated method, which uniquely feeds back the fuel cell efficiency to the speed algorithm to solve the problem in an iterative integrated manner. The simulation results show that the integrated method uses 0.19% to 2.37% less hydrogen than the successive method on short drive cycles with varying accessory loads, and 10.12%–21.62% less hydrogen than an arbitrary constant speed profile. On longer real-world drive cycles, the integrated method reduces hydrogen use by 1.43% to 2.82% just through speed optimization. Compared to a dynamic programming benchmark, which is not implementable in real time, the integrated method uses less than 1% more hydrogen.

An Ab Initio, Fully Coherent, Semi-Analytical Model of Surface-Roughness-Induced Scattering

Integrated optics and silicon photonics is a rapidly maturing technology and is progressing in telecom, computation, and sensing. Surface-roughness-induced scattering is the primary source of optical loss in most photonic integrated circuits, and as such, ultimately limits the performance of their applications. However, a closed-form description for arbitrary refractive index profiles remains lacking, even though such a one is essential to enable an objective-oriented design of the waveguide platform. We present an ab initio, fully coherent, analytical model based on the volume current method that uses the surface roughness' autocorrelation function and the unperturbed mode's electromagnetic fields to predict the loss coefficient in closed form. An improved expression for the perturbation facilitates the application also to high-index-contrast systems. Hence, it is flexible concerning wavelength, materials, fabrication process, geometry and mode. Consequently, our model may be seamlessly integrated into electromagnetic simulation software suites, once the surface roughness is known for the utilized fabrication process. To verify our model, we compare the calculated scattering losses to measured propagation losses and established models for a wide range of waveguide systems in literature. We find that the previously neglected correlation along the waveguide height significantly impacts the scattering, which necessitates the holistic statistical analysis of the surface roughness. We believe these comprehensive prediction capabilities to be a useful tool for the optimization of silicon photonics design and fabrication, especially for low-confinement applications like sensors.

Free Long-Wave Transformation in the Nearshore Zone through Partial Reflections

Abstract Long waves play an important role in coastal inundation and shoreline and dune erosion, requiring a detailed understanding of their evolution in nearshore regions and interaction with shorelines. While their generation and dissipation mechanisms are relatively well understood, there are fewer studies describing how reflection processes govern their propagation in the nearshore. We propose a new approach, accounting for partial reflections, which leads to an analytical solution to the free wave linear shallow-water equations at the wave-group scale over general varying bathymetry. The approach, supported by numerical modeling, agrees with the classic Bessel standing solution for a plane sloping beach but extends the solution to arbitrary alongshore uniform bathymetry profiles and decomposes it into incoming and outgoing wave components, which are a combination of successively partially reflected waves lagging each other. The phase lags introduced by partial reflections modify the wave amplitude and explain why Green’s law, which describes the wave growth of free waves with decreasing depth, breaks down in very shallow water. This reveals that the wave amplitude at the shoreline is highly dependent on partial reflections. Consistent with laboratory and field observations, our analytical model predicts a reflection coefficient that increases and is highly correlated with the normalized bed slope (bed slope relative to wave frequency). Our approach shows that partial reflections occurring due to depth variations in the nearshore are responsible for the relationship between the normalized bed slope and the amplitude of long waves in the nearshore, with direct implications for determining long-wave amplitudes at the shoreline and wave runup.

Metasurface-stabilized optical microcavities

Cavities concentrate light and enhance its interaction with matter. Confining to microscopic volumes is necessary for many applications but space constraints in such cavities limit the design freedom. Here we demonstrate stable optical microcavities by counteracting the phase evolution of the cavity modes using an amorphous Silicon metasurface as cavity end mirror. Careful design allows us to limit the metasurface scattering losses at telecom wavelengths to less than 2% and using a distributed Bragg reflector as metasurface substrate ensures high reflectivity. Our demonstration experimentally achieves telecom-wavelength microcavities with quality factors of up to 4600, spectral resonance linewidths below 0.4 nm, and mode volumes below 2.7{lambda }^{3}. The method introduces freedom to stabilize modes with arbitrary transverse intensity profiles and to design cavity-enhanced hologram modes. Our approach introduces the nanoscopic light control capabilities of dielectric metasurfaces to cavity electrodynamics and is industrially scalable using semiconductor manufacturing processes.

Elements of spin Hurwitz theory: closed algebraic formulas, blobbed topological recursion, and a proof of the Giacchetto–Kramer–Lewański conjecture

In this paper, we discuss the properties of the generating functions of spin Hurwitz numbers. In particular, for spin Hurwitz numbers with arbitrary ramification profiles, we construct the weighed sums which are given by Orlov’s hypergeometric solutions of the 2-component BKP hierarchy. We derive the closed algebraic formulas for the correlation functions associated with these tau-functions, and under reasonable analytical assumptions we prove the loop equations (the blobbed topological recursion). Finally, we prove a version of topological recursion for the spin Hurwitz numbers with the spin completed cycles (a generalized version of the Giacchetto–Kramer–Lewański conjecture).

Deep‐Learning Assisted Polarization Holograms

AbstractMultiplexing holography with metasurfaces using different degrees of freedom of light has enabled recent applications in display and information processing. In terms of polarization‐multiplexed holograms, the most general form is an arbitrary Jones matrix profile in storing the maximum amount of information. It requires a relaxation to bianisotropic metasurfaces from a conventional single‐layer implementation of nanostructures, but it will also complicate both the inverse design of the nanostructures and the hologram generation algorithm. Here, an integrated neural network approach, being extended from the recent DeepCGH algorithm, is developed to obtain metasurface structural profiles directly from independent holograms from an arbitrary set of polarizations to another, with maximally four different co‐ and cross‐polarization conversion channels. Such an information‐driven approach enables designing complex polarization holograms directly from an existing metamaterial library without detailed physical knowledge on the constraints, and can be extended to other multiplexing holograms to further facilitate an efficient usage of the information stored on a metasurface.

Flexible Cold Atmospheric Plasma Jet Sources

The properties of non-thermal atmospheric pressure plasma jets (APPJs) make them suitable for industrial and biomedical applications. They show many advantages when it comes to local and precise surface treatments, and there is interest in upgrading their performance for irradiation on large areas and uneven surfaces. The generation of charged species (electrons and ions) and reactive species (radicals), together with emitted UV photons, enables a rich plasma chemistry that should be uniform on arbitrary sample profiles. Lateral gradients in plasma parameters from multi-jets should, therefore, be minimized and addressed by means of plasma monitoring techniques, such as electrical diagnostics and optical emission spectroscopy analysis (OES). This article briefly reviews the main strategies adopted to build morphing APPJ arrays and ultra-flexible and long tubes to project cold plasma jets. Basic aspects, such as inter-jet interactions and nozzle shape, have also been discussed, as well as potential applications in the fields of polymer processing and plasma medicine.

A method for non-destructive microwave focusing for deep brain and tissue stimulation.

Non-invasive stimulation of biological tissue is highly desirable for several biomedical applications. Of specific interest are methods for tumor treatment, endometrial ablation, and neuro-modulation. In traditional neuro-modulation, single- and multi-coil transcranial stimulation techniques in low oscillation frequencies are utilized to non-invasively penetrate the skull and elicit action potentials in cortical neurons. Although these methods have been proven effective, tightly focusing these signals to localized regions is difficult. In recent years, microwave (MW) methods have seen an increase usage as a minimally invasive treatment modality for ablation and neuro-stimulation. Unlike low frequency signals, MW signals can be focused to localized sub-centimeter regions. In this work we demonstrate that a three-dimensional array of MW antennas can be used to tightly focus signals to a localized region in space within the human body with MW frequencies. Assuming an array of small MW loop antennas are placed around the body, the optimal amplitude and phase of each array element can be accurately determined to match an arbitrary desired field profile. The major innovation of the presented method is that the fields that penetrate the biological region are determined via computing numerical Green's functions (NGF) that are then used to drive an optimization algorithm. Using simplified models of regions in the human body, it is shown that the MW fields at 1 GHz can be focused to sub-centimeter sized "hot spots" at depths of several centimeters. The algorithm can be easily extended to more realistic models of the human body or for non-biological applications.

Unsteady thermal transport in an instantly heated semi-infinite free end Hooke chain

We consider unsteady ballistic heat transport in a semi-infinite Hooke chain with free end and arbitrary initial temperature profile. An analytical description of the evolution of the kinetic temperature is proposed in both discrete (exact) and continuum (approximate) formulations. By comparison of the discrete and continuum descriptions of kinetic temperature field, we reveal some restrictions to the latter. Specifically, the far-field kinetic temperature is well described by the continuum solution, which, however, deviates near and at the free end (boundary). We show analytically that, after thermal wave reflects from the boundary, the discrete solution for the kinetic temperature undergoes a jump near the free end. A comparison of the descriptions of heat propagation in the semi-infinite and infinite Hooke chains is presented. Results of the current paper are expected to provide insight into non-stationary heat transport in the semi-infinite lattices.

Sequential Detection of an Arbitrary Transient Change Profile by the FMA Test

This article addresses the sequential detection of transient changes by using the finite moving average (FMA) test. It is assumed that a change occurs at an unknown (but nonrandom) change point and the duration of postchange period is finite and known. We relax the assumption that the profile of a transient change is chosen so that the log-likelihood ratios of the observations are associated random variables (r.v.s) in the prechange mode. Hence, the profile of the transient change is arbitrary and it is not necessarily of constant sign for a distribution with monotone likelihood ratio. A new upper bound for the worst-case probability of false alarm is proposed. It is shown that the optimization of the window-limited cumulative sum (CUSUM) test again leads to the FMA test. Three particular transient changes are considered: in the Gaussian mean, in the Gaussian variance, and in the parameter of exponential distribution. In the first case, a comparison between the bounds for the FMA test operating characteristics and the exact operating characteristics calculated by numerical integration is used to estimate the sharpness of the bounds. In the second and third cases, special attention is paid to the calculation of the FMA distribution in the case of arbitrary profile. The method of convolution is used to solve the problem.

Generalized Tevelev degrees of [formula omitted

Let (C,p1,…,pn) be a general curve. We consider the problem of enumerating covers of the projective line by C subject to incidence conditions at the marked points. These counts have been obtained by the first named author with Pandharipande and Schmitt via intersection theory on Hurwitz spaces and by the second named author with Farkas via limit linear series. In this paper, we build on these two approaches to generalize these counts to the situation where the covers are constrained to have arbitrary ramification profiles: that is, additional ramification conditions are imposed at the marked points, and some collections of marked points are constrained to have equal image.

Using an acousto-optic modulator as a fast spatial light modulator.

High-speed spatial light modulators (SLM) are crucial components for free-space communication and structured illumination imaging. Current approaches for dynamical spatial mode generation, such as liquid crystal SLMs or digital micromirror devices, are limited to a maximum pattern refresh rate of 10 kHz and have a low damage threshold. We demonstrate that arbitrary spatial profiles in a laser pulse can be generated by mapping the temporal radio-frequency (RF) waveform sent to an acousto-optic modulator (AOM) onto the optical field. We find that the fidelity of the SLM performance can be improved through numerical optimization of the RF waveform to overcome the nonlinear effect of AOM. An AOM can thus be used as a 1-dimensional SLM, a technique we call acousto-optic spatial light modulator (AO-SLM), which has 50 µm pixel pitch, over 1 MHz update rate, and high damage threshold. We simulate the application of AO-SLM to single-pixel imaging, which can reconstruct a 32×32 pixel complex object at a rate of 11.6 kHz with 98% fidelity.