General Case Research Articles

A model for physical dislocation transmission through grain boundaries and its implementation in a discrete dislocation dynamics tool

The mechanical behavior of most metals in engineering applications is dominated by the grain size. Physics-based models of the interaction between dislocations and the grain boundary are important to correctly predict the plastic deformation behavior of polycrystalline materials. Dislocation-grain boundary interaction is complex and a challenge to model. We present a model for simulating the physical transmission of dislocations through grain boundaries within Discrete Dislocation Dynamics tools. The properties (glide plane, Burgers vector, initial length) of the transmitted dislocation are chosen based on geometric criteria as well as a maximization of the resolved shear stress of the transmitted dislocation. Additionally, stress and displacement transparency as well as the discontinuity are ensured via a grain boundary dislocation – a butterfly-like geometry in the general case – whose properties are selected to minimize the residual Burgers vector at the interface. This additional ‘grain boundary dislocation’ allows a direct comparison as well as a calibration of the model with experiments on the macroscale particularly for neighboring grains with a high dislocation density contrast. Two basic examples illustrate the model and an application to a 40-grain polycrystal demonstrates the scalability of the approach.

Entropy Production of Run-and-Tumble Particles

We analyze the entropy production in run-and-tumble models. After presenting the general formalism in the framework of the Fokker–Planck equations in one space dimension, we derive some known exact results in simple physical situations (free run-and-tumble particles and harmonic confinement). We then extend the calculation to the case of anisotropic motion (different speeds and tumbling rates for right- and left-oriented particles), obtaining exact expressions of the entropy production rate. We conclude by discussing the general case of heterogeneous run-and-tumble motion described by space-dependent parameters and extending the analysis to the case of d-dimensional motions.

Bare mass effects on the reheating process after inflation

We consider the effects of a bare mass term for the inflaton, when the inflationary potential takes the form V(ϕ)=λϕk about its minimum with k≥4. We concentrate on k=4, but discuss general cases as well. Further, we assume λϕend2≫mϕ2, where ϕend is the inflaton field value when the inflationary expansion ends. We show that the presence of a mass term (which may be present due to radiative corrections or supersymmetry breaking) can significantly alter the reheating process, as the equation of state of the inflaton condensate changes from wϕ=13 to wϕ=0 when λϕ2 drops below mϕ2. We show that, for a mass mϕ≳3λ14TRH, the mass term will dominate at reheating. The value of λ is relatively model independent as it is normalized by the cosmic microwave background perturbation spectrum. For T models of inflation, this leads to mϕ≳TRH/250. We compute the effects on the reheating temperature for cases where reheating is due to inflaton decay (to fermions, scalars, or vectors) or to inflaton scattering (to scalars or vectors). For scattering to scalars and in the absence of a decay, there is always a residual inflaton background that acts as cold dark matter. In this case, we derive a strong upper limit to the inflaton bare mass which for T models is mϕ<350 MeV(TRH/1010 GeV)3/5. We also consider the effect of the bare mass term on the fragmentation of the inflaton condensate. Published by the American Physical Society 2024

Quantum-Inspired Classical Algorithm for Graph Problems by Gaussian Boson Sampling

We present a quantum-inspired classical algorithm that can be used for graph-theoretical problems, such as finding the densest k subgraph and finding the maximum weight clique, which are proposed as applications of a Gaussian boson sampler. The main observation from Gaussian boson samplers is that a given graph’s adjacency matrix to be encoded in a Gaussian boson sampler is non-negative and that computing the output probability of Gaussian boson sampling restricted to a non-negative adjacency matrix is thought to be strictly easier than general cases. We first provide how to program a given graph problem into our efficient classical algorithm. We then numerically compare the performance of ideal and lossy Gaussian boson samplers, our quantum-inspired classical sampler, and the uniform sampler for finding the densest k subgraph and finding the maximum weight clique and show that the advantage from Gaussian boson samplers is not significant in general. We finally discuss the potential advantage of a Gaussian boson sampler over the proposed quantum-inspired classical sampler. Published by the American Physical Society 2024

Complete Solutions for the Approximate Synthesis of Spherical Four-Bar Function Generators

Abstract Kinematic synthesis to meet an approximate motion specification naturally forms a constrained optimization problem. Instead of using local methods, we conduct global design searches by direct computation of all critical points. The idea is not new, but performed at scale is only possible through modern polynomial homotopy continuation solvers. Such a complete computation finds all minima, including the global, which allows for a full exploration of the design space, whereas local solvers can only find the minimum nearest to an initial guess. We form equality-constrained objective functions that pertain to the synthesis of spherical four-bar linkages for approximate function generation. We consider the general case where all mechanism dimensions may vary and a more specific case that enables the placement of ground pivots. The former optimization problem is shown to permit 268 sets of critical points, and the latter permits 61 sets. Critical points are classified as saddles or minima through a post-process eigenanalysis of the projected Hessian. The discretization points are contained within the coefficients of the stationarity polynomials, so the algebraic structure of the synthesis equations remains invariant to the number of points. The results of our computational work were used to design a mechanism that coordinates the folding wings. We also use this method to parameterize mechanism dimensions for a family of hyperbolic curves.

Sampling the user controls in neural modeling of audio devices

This work studies neural modeling of nonlinear parametric audio circuits, focusing on how the diversity of settings of the target device user controls seen during training affects network generalization. To study the problem, a large corpus of training datasets is synthetically generated using SPICE simulations of two distinct devices, an analog equalizer and an analog distortion pedal. A proven recurrent neural network architecture is trained using each dataset. The difference in the datasets is in the sampling resolution of the device user controls and in their overall size. Based on objective and subjective evaluation of the trained models, a sampling resolution of five for the device parameters is found to be sufficient to capture the behavior of the target systems for the types of devices considered during the study. This result is desirable, since a dense sampling grid can be impractical to realize in the general case when no automated way of setting the device parameters is available, while collecting large amounts of data using a sparse grid only incurs small additional costs. Thus, the result provides guidance for efficient collection of training data for neural modeling of other similar audio devices.

Fractional particle and sigma model

We introduce a classical fractional particle model in ℝn, extending the Newtonian particle concept with the incorporation of the fractional Laplacian. A comprehensive discussion on kinetic properties, including linear momentum and kinetic energy, is provided. We further derive the equations of motion and discuss the symmetries of the system. The Green’s function method is employed to solve the equations of motion in a general case. We illustrate the theory with three important examples: the free fractional particle, the fractional harmonic oscillator, and the charged fractional particle that interacts locally with the electromagnetic field. We use the results of the extension problem by Caffarelli and Silvestre, to construct the associated classical local sigma model for the fractional particle. The sigma model is then quantized using the canonical quantization method, and we compute the vacuum energy at the boundary.

Tunable spin splitting of reflected Laguerre-Gaussian beams on controllable metamaterials with anti-PT symmetry

The intriguing photonic spin Hall effect (PSHE) of reflected Laguerre-Gaussian (LG) beams can be exhibited on the systems with optical anti-parity-time (Anti-PT) symmetry. During the reflection, the left/right circularly polarized (LCP/RCP) components of reflected LG beams are considered. By controlling parameters of the Anti-PT systems, the PSHE of reflected LCP/RCP can be identical and symmetrical with respect to incident-reflected plane (IRP). Due to gain/non-Hermitian effects of designed Anti-PT systems, special PSHE near the strong gain points (SGP) and exceptional points (EPs) can be obtained simulatively. Through analyses in PSHE of reflected LCP on four similar Anti-PT systems, specific conclusions that can even be extended to more general cases. Moreover, simulations of PSHE by simultaneously varying the incident angles * and imaginary/real dielectric constants Im/Re[ε] of the Anti-PT systems, specal PSHE and other novel optical phenomena with real applications can be revealed. So Anti-PT systems not only provide novel ways to regulate the PSHE of reflected LG beams, but also offer possibilities for new optical characteristics of devices.

Twisted Whittaker category on affine flags and the category of representations of the mixed quantum group

Let $G$ be a reductive group, and let $\check {G}$ be its Langlands dual group. Arkhipov and Bezrukavnikov proved that the Whittaker category on the affine flags ${\operatorname {Fl}}_G$ is equivalent to the category of $\check {G}$ -equivariant quasi-coherent sheaves on the Springer resolution of the nilpotent cone. This paper proves this theorem in the quantum case. We show that the twisted Whittaker category on ${\operatorname {Fl}}_G$ and the category of representations of the mixed quantum group are equivalent. In particular, we prove that the quantum category $\mathsf {O}$ is equivalent to the twisted Whittaker category on ${\operatorname {Fl}}_G$ in the generic case. The strong version of our main theorem claims a motivic equivalence between the Whittaker category on ${\operatorname {Fl}}_G$ and a factorization module category, which holds in the de Rham setting, the Betti setting, and the $\ell$ -adic setting.

Forming off-center massive black hole binaries in dwarf galaxies through Jacobi capture

It is well established that black holes reside in the central regions of virtually all types of known galaxies. Recent observational and numerical studies however challenge this picture, suggesting that intermediate-mass black holes in dwarf galaxies may be found on orbits far from the center. In particular, constant-density cores minimize orbital energy losses due to dynamical friction, and allow black holes to settle on stable off-center orbits. Using controlled simulations, we study the dynamics of off-center black holes in dwarf galaxies with such cores. We propose a new scenario to describe off-center mergers of massive black holes, starting with a Jacobi capture. We focus on initially circular and co-planar black hole orbits and explore a large parameter space of black hole masses and orbital parameters. We find that Jacobi captures are a complex and chaotic phenomenon that occurs in about $13<!PCT!>$ of cases in this simplified setup, and we quantify how the likelihood of capture depends on the simulation parameters. We note that this percentage is likely an upper limit of the general case. Nevertheless, we show that Jacobi captures in cored dwarf galaxies can facilitate the formation of off-center black hole binaries, and that this process is sufficiently common to have a substantial effect on black hole growth. While our setup only allows for temporary captures, we expect dissipative forces from baryons and post-Newtonian corrections to maintain the captures over time and to lead to the formation of stable binary systems. This motivates future studies of the effectiveness of such dissipative forces, within stripped nuclei or globular clusters, in forming stable bound systems.

Magnetotelluric sampling theorem

We consider a general case of a magnetotelluric (MT) study to reveal three-dimensional (3D) distribution of the electrical conductivity within the Earth based on measurements of electromagnetic (EM) fields by a two-dimensional (2D) array. Such an MT array observation can be regarded as a spatially discrete sampling of the MT responses (impedances), and each observation site can be regarded as a sampling point. This means that MT array measurements must follow the Nyquist–Shannon sampling theorem. This paper discusses how the sampling theorem is applied to MT array studies and what kind of consideration is required in the application on the basis of synthetic model calculations, with special attention to spatial resolutions. With an aid of the EM scattering theory and the sampling theorem, we can show that an observation array resolves some features of the MT impedance but does not others. We call the resolvable and unresolvable features the MT signal and noise, respectively. This study introduces the spatial Fourier transform of array MT data (impedances) which helps us investigating sampling effects of lateral heterogeneity from a different angle (in the wavenumber domain). Shallow heterogeneities cause a sharp spatial change of impedance elements near structural boundaries. High wavenumber Fourier components are required to describe such a feature, which means the site spacing must be sufficiently short to be able to resolve such features. Otherwise, a set of array MT data will suffer from aliasing, which is one of the typical causes of MT distortion (MT geologic noise). Conversely, a signal due to a deep-seated conductivity anomaly will have more reduced amplitude at higher wavenumbers, which means focused imaging of such an anomaly is generally difficult. Finally, it is suggested to properly consider the sampling theorem in an observation array design, so as to have best performance in resolving MT signals.Graphical abstract

Møller-Plesset Adiabatic Connection at Large Coupling Strengths for Open-Shell Systems.

We study the adiabatic connection that has as weak-coupling expansion the Møller-Plesset perturbation series, generalizing to the open-shell case previous closed-shell results for the large-coupling limit. We first focus on the hydrogen atom with fractional spins, providing results along the adiabatic connection from small to large coupling strengths. We reveal an intriguing phase diagram and an equation for the large-coupling leading order that has closed-form solutions for specific choices of its relevant quantum numbers. We then show that the hydrogen atom results provide variational estimates for the large-coupling leading terms for the general many-electron open-shell case in terms of functionals of the Hartree-Fock α-spin and β-spin densities.

A mechanism design approach for multi-party machine learning

In a multi-party machine learning system, different parties cooperate on optimizing towards better models by sharing data in a privacy-preserving way. A major challenge in learning is the incentive issue. For example, if there is competition among the parties, one may strategically hide their data to prevent other parties from getting better models.In this paper, we study the problem through the lens of mechanism design and incorporate the features of multi-party learning in our setting. First, each agent's valuation has externalities that depend on others' types and actions. Second, each agent can only misreport a type lower than his true type, but not the other way round. We provide the optimal truthful mechanism in the separable utility setting, as well as necessary and sufficient conditions for truthful mechanisms in general cases. Finally, we propose an algorithm to find the desirable mechanism that is truthful, individually rational, efficient and weakly budget-balanced, and analyze the computational complexity of the algorithm.

Simplified Beam Hardening Correction for Ultrafast X-ray CT Imaging of Binary Granular Mixtures.

Ultrafast X-ray computed tomography is an advanced imaging technique for multiphase flows. It has been used with great success for studying gas-liquid as well as gas-solid flows. Here, we apply this technique to analyze density-driven particle segregation in a rotating drum as an exemplary use case for analyzing industrial particle mixing systems. As glass particles are used as the denser of two granular species to be mixed, beam hardening artefacts occur and hamper the data analysis. In the general case of a distribution of arbitrary materials, the inverse problem of image reconstruction with energy-dependent attenuation is often ill-posed. Consequently, commonly known beam hardening correction algorithms are often quite complex. In our case, however, the number of materials is limited. We therefore propose a correction algorithm simplified by taking advantage of the known material properties, and demonstrate its ability to improve image quality and subsequent analyses significantly.

On Optimal Point Sets Determining Distinct Triangles

Erdős and Fishburn studied the maximum number of points in the plane that span $k$ distances (i.e. the set of pairwise distances between points has cardinality $k$) and classified these configurations, as an inverse problem of the Erdős distinct distances problem. We consider the analogous problem for triangles. Past work has obtained the optimal sets for one and two distinct triangles in the plane. In this paper, we resolve a conjecture that at most six points in the plane can span three distinct triangles, and obtain the hexagon as the unique configuration that achieves this. We also provide evidence that optimal sets cannot be on the square lattice in the general case.

On the limitations of non-geometric fluxes to realize dS vacua

In this paper, we perform a systematic and analytical exploration of de Sitter conditions in type IIA compactifications with (non-)geometric fluxes along with the standard NS-NS and RR p-form fluxes. Exploiting the fact that the F-term scalar potential can be written as a bilinear form, we start by studying the most generic case. We find four conditions that the scalar fields and fluxes must satisfy to achieve de Sitter vacua. Particularizing to different configurations, we recover and extend previous results in the literature. We then impose an Ansatz in which the F-terms are proportional to the respective Kähler derivatives. In this set-up we are able to derive additional constraints and to classify the possible dS no-go scenarios in terms of eight axionic fluxes. Individually considering that any of these fluxes can be vanishing or non-vanishing leads to a total of 256 flux configurations. We find that 227 of these 256 possibilities result in a dS no-go scenario. The remaining 29 flux configurations, a priori, do not lead to dS no-go cases and would deserve further investigation.

Ciliary propulsion through non-uniform flows

The classical paper by Lighthill (Commun. Pure Appl. Maths, vol. 109, 1952, p. 118) on the propulsion of ciliated microorganisms has become the reference against which many modern studies on swimming in low Reynolds number are compared. However, Lighthill's study was limited to propulsion in a uniform flow, whereas several biologically relevant microorganisms experience non-uniform flows. Here we propose a benchmark for ciliary propulsion in paraboloidal flows. We first consider the axisymmetric problem, with the microorganisms on the centreline of the background flow, and derive exact analytical solutions for the flow field. Our results reveal flow features, swimming characteristics and performance metrics markedly different from those generated in a uniform flow. In particular, the background paraboloidal flow introduces a Stokes quadrupole singularity at the leading-order flow field, generating vortices. Moreover, we determine the necessary conditions on the strength of the background flow for optimal power dissipation and swimming efficiency. We then consider the more general case of a microorganism off the centreline of the background flow. In this case, the squirmer experiences a paraboloidal, linear shear and uniform flows due to its position relative to the flow's centreline. Our findings show that while the linear shear flow does not affect the translational and rotational velocities of the squirmer, it does influence the velocity field and, therefore, the power dissipation.

A generic quantum Wielandt's inequality

Quantum Wielandt's inequality gives an optimal upper bound on the minimal length k such that length-k products of elements in a generating system span Mn(C). It is conjectured that k should be of order O(n2) in general. In this paper, we give an overview of how the question has been studied in the literature so far and its relation to a classical question in linear algebra, namely the length of the algebra Mn(C). We provide a generic version of quantum Wielandt's inequality, which gives the optimal length with probability one. More specifically, we prove based on [KS16] that k generically is of order Θ(log⁡n), as opposed to the general case, in which the best bound to date is O(n2log⁡n). Our result implies a new bound on the primitivity index of a random quantum channel. Furthermore, we shed new light on a long-standing open problem for Projected Entangled Pair State, by concluding that almost any translation-invariant PEPS (in particular, Matrix Product State) with periodic boundary conditions on a grid with side length of order Ω(log⁡n) is the unique ground state of a local Hamiltonian. We observe similar characteristics for matrix Lie algebras and provide numerical results for random Lie-generating systems.

Mass generation via nonlinear massive solution in Higgs potential and particle creations

The nonlinear massive plane wave solution of the classical scalar field in the Higgs potential is revisited to study the mass generation and particle creation. In particular, by assuming that the Higgs system is in the slightly excited state in early universe and it is described by the nonlinear solution, we study the mass generation mechanism for massive vector bosons and a heavy fermion in the quantum field theory around the nonlinear massive classical field. The nonlinear massive classical solution gives the transition from the vacuum to a pair of vector bosons and fermions. We present the new formulae of the probability density of the production process for particles in the standard model of elementary particle physics. The probability densities of the particle productions vanish when the nonlinear massive solution reduces to the constant solution (the classical vacuum expectation value); while the probability densities are expressed as the function of the free parameter in the classical solution in general case. We discuss the behavior of the probability densities for the three oscillating modes in the classical solution.

Supermassive black holes triggered by QCD axion bubbles

Supermassive black holes (SMBHs) are ubiquitous in the center of galaxies, although the origin of their massive seeds is still unknown. In this paper, we investigate the formation of SMBHs from the quantum chromodynamics (QCD) axion bubbles. In this case, primordial black holes (PBHs) are considered as the seeds of SMBHs, which are generated from the QCD axion bubbles due to an explicit Peccei–Quinn (PQ) symmetry breaking after inflation. The QCD axion bubbles are formed when the QCD axion starts to oscillate during the QCD phase transition. We consider a general case in which the axion bubbles are formed with the bubble effective angle θ eff ∈ (0, π], leading to the minimum PBH mass ∼O(104−107)M⊙ for the axion decay constant fa∼O(1016)GeV . The PBHs at this mass region may account for the seeds of SMBHs.