Miracle-dz/UniFAR-FTUs huggingface dataset:
Comparison of coupling techniques in a high-order discontinuous Galerkin-based particle-in-cell solver

Highly rarefied plasma flows in technical devices are physically modelled by the Maxwell–Lorentz equations. They combine the solution of the Maxwell equations, where the electric field E and magnetic induction B are determined, with the Lorentz system, accounting for the movement of charged particles due to the electromagnetic forces. To solve these equations for complex-shaped domains, a fully electromagnetic particle-in-cell (PIC) code has been developed using high-order discontinuous Galerkin methods for the Maxwell equations on a computational mesh, coupled with a Lorentz solver on the basis of a second-order leapfrog scheme, acting on the particles at their current positions. Since the particles move freely in space, the mesh-based and the mesh-free values have to be coupled. This coupling includes the deposition of the charge and current densities from the current particle positions onto the mesh as well as the interpolation of the electromagnetic fields from the mesh to the actual particle positions. Both steps have to be computed with appropriate accuracy. Different approaches to particle-grid coupling within the PIC solver have been investigated. In this paper, these concepts are described and corresponding simulation results with respect to accuracy and computational demand are presented.
Initial rates of aggregation for dilute, granular flows of wet particles

Molecular dynamics (MD) simulations are used to determine the agglomeration rates of wet grains (particles coated with a viscous, liquid layer) engaged in simple shear flow under dilute conditions. In this work, a closed-form model derived from the elastohydrodynamic theory describes the normal restitution coefficient for binary collisions. Unlike previous MD studies, the particle deformation is not assumed to depend on a particle “overlap” (penetration), but instead depends on the formal coupling of Hertzian deformation theory with lubrication theory. The initial rate of doublet formation is studied as a function of system properties and the energy input to the system. In addition to the system properties, the distribution of relative velocities in the system is found to be a key factor influencing the initial rates of clustering. A theory based on estimating the collision frequency and the critical velocity below which no rebound is observed—due to viscous dissipation—is found to provide a good approxim.
The non-monotonicity of the KPP speed with respect to diffusion in the presence of a shear flow

In this paper, we prove via counterexamples that adding an advection term of the form Shear flow (whose streamlines are parallel to the direction of propagation) to a reaction-diffusion equation will be an enough heterogeneity to spoil the increasing behavior of the KPP speed of propagation with respect to diffusion. The non-monotonicity of the speed with respect to diffusion will occur even when the reaction term and the diffusion matrices are considered homogeneous (do not depend on space variables). For the sake of completeness, we announce our results in a setting which allows domains with periodic perforations that may or may not be equal to the whole space $\mathbb{R}^N. $
Democracy of shearlet bases with applications to approximation and interpolation

Shearlets on the cone provide Parseval frames for $L^2$. They also provide near-optimal approximation for the class $\mathcal{E}$ of cartoon-like images. Moreover, there are spaces associated to them other than $L^2$ and there exist embeddings between these and classical spaces. We prove approximation properties of the cone-adapted shearlets in a more general context, namely, when the target function belongs to a class or space different to $\mathcal{E}$ and when the error is not necessarily measured in the $L^2$-norm but in a much wider family of smoothness space of high anisotropy.
Iron and Molecular Opacities and the Evolution of Population I Stars

Effects of recent opacity revisions on the evolution of Population I stars are explored over the range 1.5-60 solar masses. Opacity parameters considered include the angular momentum coupling scheme for iron, the relative iron abundance, the total metal abundance, and diatomic and triatomic molecular sources. Only the total metal abundance exerts an important control over the evolutionary tracks. Blue loops on the H-R diagram during core helium burning can be very sensitive to opacity, but only insofar as the simple formation or suppression of a blue loop is concerned. The blue loops are most robust for stellar masses around 10 solar masses. We confirm, from a comparison of stellar models with observational data, that the total metal abundance is close to solar and that convective core overshooting is likely to be very slight. The new models predict the existence of an iron convection zone in the envelope and a great widening of the main-sequence band in the H-R diagram at luminosities brighter than 100,000 solar luminosities.
A Characterization of Radial Herz-Schur Multipliers on Free Products of Discrete Groups

A characterization of radial Herz-Schur multipliers on groups which are free products G = ∗Ni=1Gi of subgroups of the same order (finite or infinite) is given. The multiplier norm is computed in terms of trace norms of appropriate trace operators. This applies in particular to free groups FN = ∗Ni=1 Z with block length. This method also applies to characterizing radial multipliers of free product groups of distinct orders, all greater than 2, but in this case we can compute only the multiplier norm up to some constant.
Around Sperner's lemma

We consider a generalization of the classic Sperner lemma. This lemma states that every Sperner coloring of a triangulation of a simplex contains a fully colored simplex. We found a weaker assumption than Sperner's coloring. It is also shown that the main theorem implies Tucker's lemma and some other theorems.
On the monoidal center of Deligne's category Re̲p(St)

We explicitly compute a monoidal subcategory of the monoidal center of Deligne's interpolation category Re̲p(St) , for t not necessarily a natural number, and we show that this subcategory is a ribbon category. For t=n , a natural number, there exists a functor onto the braided monoidal category of modules over the Drinfeld double of Sn which is essentially surjective and full. Hence the new ribbon categories interpolate the categories of crossed modules over the symmetric groups. As an application, we obtain invariants of framed ribbon links which are polynomials in the interpolating variable t . These polynomials interpolate untwisted Dijkgraaf–Witten invariants of the symmetric groups.
Linear modeling of elongated bending EAP actuator at large deformations

This paper describes a linear dynamic model of an elongated bending Electroactive Polymer (EAP) actuator applicable with deformations of any magnitude. The model formulates relation of a) voltage applied to the EAP sheet, b) current passing through the EAP sheet, c) force applied by the actuator and d) deformation of the actuator. In this model only the geometry of EAP piece and four empirical parameters of the EAP material: a) bending stiffness, b) electromechanical coupling term, c) electrical impedance and d) initial curvature are considered. The contribution of this paper is introducing a model that can be used to characterize the properties of different EAP materials and compare them. The advantage of the model is its simplicity and ability to provide insights in to the behavior of bending EAPs. Additionally, due to linearity of the model, the real-time control is feasible. Experiments, using Ionomeric Polymer-Metal Composite (IPMC) sheet from Environmental Robotics Inc., where carried out to verify the model. The experimental results confirm the model is valid.
Control of Body Motion in an Ideal Fluid Using the Internal Mass and the Rotor in the Presence of Circulation Around the Body

In this paper, we study the controlled motion of an arbitrary two-dimensional body in an ideal fluid with a moving internal mass and an internal rotor in the presence of constant circulation around the body. We show that by changing the position of the internal mass and by rotating the rotor, the body can be made to move to a given point and discuss the influence of nonzero circulation on the motion control. We have found that in the presence of circulation around the body the system cannot be completely stabilized at an arbitrary point of space, but fairly simple controls can be constructed to ensure that the body moves near the given point.
On a conjecture of Hefetz and Keevash on Lagrangians of intersecting hypergraphs and Turán numbers

Let $S^r(n)$ be the $r$-graph on $n$ vertices with parts $A$ and $B$, where the edges consist of all $r$-tuples with $1$ vertex in $A$ and $r-1$ vertices in $B$, and the sizes of $A$ and $B$ are chosen to maximise the number of edges. Let $M_t^r$ be the $r$-graph with $t$ pairwise disjoint edges. Given an $r$-graph $F$ and a positive integer $p\geq |V(F)|$, we define the {\em extension} of $F$, denoted by $H_{p}^{F}$ as follows: Label the vertices of $F$ as $v_1,\dots,v_{|V(F)|}$. Add new vertices $v_{|V(F)|+1},\dots,v_{p}$. For each pair of vertices $v_i,v_j, 1\le i<j \le p$ not contained in an edge of $F$, we add a set $B_{ij}$ of $r-2$ new vertices and the edge $\{v_i,v_j\} \cup B_{ij}$, where the $B_{ij}$ 's are pairwise disjoint over all such pairs $\{i,j\}$. Hefetz and Keevash conjectured that the Turan number of the extension of $M_2^r$ is ${1 \over r}n\cdot{{r-1\over r}n \choose r-1}$ for $r \ge 4$ and sufficiently large $n$. Moreover, if $n$ is sufficiently large and $G$ is an $H_{2r}^{M_2^r}$-free $r$-graph with $n$ vertices and ${1 \over r}n\cdot{{r-1\over r}n \choose r-1}$ edges, then $G$ is isomorphic to $S^r(n)$. In this paper, we confirm the above conjecture for $r=4$.
A mathematical proof for the existence of a possible source for dark energy

The expansion of the universe has been accepted by scientists for more than a century. However, since the 1990s, observations have suggested that the universe is expanding at an accelerating rate. Although the source of this acceleration is still unknown, cosmologists call it dark energy; a type mysterious energy which exerts a negative pressure on the universe. In this paper, applying different approach from those of classical mathematical physics based mainly on functional analysis, we propose an answer to this question. In fact, we first establish a theorem for multivalued mappings; and as result we apply this theorem to show the existence of a remnant field of high energy in a continuously expanding system of energy. The results may also be applied to the early universe to show the existence of a possible source for dark energy. The answer is partially confirmed by a paper published in Nature Asronomy.
Composition of Fractals

This work is an analytical and numerical study of the composition of several fractals into one and of the relation between the composite dimension and the dimensions of the component fractals. In the case of composition of standard IFS with segments of equal size, the composite dimension can be expressed as a function of the component dimensions. But in the case of the compositions including component multifractals, the composite dimension cannot be expressed as explicit function of component dimensions and can only be solved numerically. An application of fractal composition to a physics problem within the incomplete statistics is discussed.
Modal Analysis of Rubbing Acoustic Emission for Rotor-Bearing System Based on Reassigned Wavelet Scalogram

Rubbing between the rotor and the stator is the frequent and harmful malfunction in the rotating machinery, which will cause a very serious accident, even catastrophe, to the machine. Thus, such fault needs timely detection to avoid severe consequences. Vibration based methods are the traditional ones for the detection and diagnosis of the rubbing fault, which are effective when the rubbing has been severe, but always do not work in early detection of such fault. Rubbing between the rotor and the stator will cause elastic strain in the rubbing location and thus can produce acoustic emission (AE). Apparently, such AE contains direct and abundant information about the rubbing and thus can be used to detect and diagnose such fault effectively. In this paper, the AE based method is proposed for detecting and identifying the rubbing of the rotor-bearing system. Using the modal acoustic emission (MAE) theory and reassigned wavelet scalogram, the present study emphasizes on modal analysis and time-frequency characteristics analysis for further understanding the characteristics, phenomenon, and features of the rubbing AE. The results show that the rubbing AE is the elastic wave with multiple modals, which has an impact characteristic and mainly consists of the flexural wave and extensional wave. The transmission of the rubbing AE has some directivity. Moreover, different modals have different transmission characteristics: The flexural wave has lower frequency and its attenuation is influenced mainly by the sectional area of the transmission passage. The extensional wave has higher frequency and its attenuation is mainly sensitive to the interface transmission between the two surfaces. The results also reveal that the reassigned wavelet scalogram is more effective than its original scalogram for the characteristic analysis of the rubbing AE. DOI: 10.1115/1.2981091
On the Thomas–Fermi Approximation of the Ground State in a PT ‐Symmetric Confining Potential

For the stationary Gross–Pitaevskii equation with harmonic real and linear imaginary potentials in the space of one dimension, we study the ground state in the limit of large densities (large chemical potentials), where the solution degenerates into a compact Thomas–Fermi approximation. We prove that the Thomas–Fermi approximation can be constructed by using the unstable manifold theorem for a planar dynamical system. To justify the Thomas–Fermi approximation, the existence problem can be reduced to the Painlevé‐II equation, which admits a unique global Hastings–McLeod solution. We illustrate numerically that an iterative approach to solving the existence problem converges but give no analytical proof of this result. Generalizations are discussed for the stationary Gross–Pitaevskii equation with harmonic real and localized imaginary potentials.
Resonant bands, Aomoto complex, and real 4-nets

The resonant band is a useful notion for the computation of the nontrivial monodromy eigenspaces of the Milnor fiber of a real line arrangement. In this article, we develop the resonant band description for the cohomology of the Aomoto complex. As an application, we prove that real 4-nets do not exist.
Derivation and Analysis of the Primal-Dual Method of Multipliers Based on Monotone Operator Theory

In this paper, we present a novel derivation of an existing algorithm for distributed optimization termed the primal-dual method of multipliers (PDMM). In contrast to its initial derivation, monotone operator theory is used to connect PDMM with other first-order methods such as Douglas–Rachford splitting and the alternating direction method of multipliers, thus, providing insight into its operation. In particular, we show how PDMM combines a lifted dual form in conjunction with Peaceman–Rachford splitting to facilitate distributed optimization in undirected networks. We additionally demonstrate sufficient conditions for primal convergence for strongly convex differentiable functions and strengthen this result for strongly convex functions with Lipschitz continuous gradients by introducing a primal geometric convergence bound.
Quotients and subgroups of Baumslag–Solitar groups

Abstract We determine all generalized Baumslag–Solitar groups (finitely generated groups acting on a tree with all stabilizers infinite cyclic) which are quotients of a given Baumslag–Solitar group BS(m,n), and (when BS(m,n) is not Hopfian) which of them also admit BS(m,n) as a quotient. We determine for which values of r, s one may embed BS(r,s) into a given BS(m,n), and we characterize finitely generated groups which embed into some BS(n,n).
Convexity of momentum map, Morse index, and quantum entanglement

We analyze from the topological perspective the space of all SLOCC (Stochastic Local Operations with Classical Communication) classes of pure states for composite quantum systems. We do it for both distinguishable and indistinguishable particles. In general, the topology of this space is rather complicated as it is a non-Hausdorff space. Using geometric invariant theory (GIT) and momentum map geometry, we propose a way to divide the space of all SLOCC classes into mathematically and physically meaningful families. Each family consists of possibly many "asymptotically" equivalent SLOCC classes. Moreover, each contains exactly one distinguished SLOCC class on which the total variance (a well-defined measure of entanglement) of the state Var[v] attains maximum. We provide an algorithm for finding critical sets of Var[v], which makes use of the convexity of the momentum map and allows classification of such defined families of SLOCC classes. The number of families is in general infinite. We introduce an additional refinement into finitely many groups of families using some developments in the momentum map geometry known as the Kirwan–Ness stratification. We also discuss how to define it equivalently using the convexity of the momentum map applied to SLOCC classes. Moreover, we note that the Morse index at the critical set of the total variance of state has an interpretation of number of non-SLOCC directions in which entanglement increases and calculate it for several exemplary systems. Finally, we introduce the SLOCC-invariant measure of entanglement as a square root of the total variance of state at the critical point and explain its geometric meaning.
Understanding internetwork magnetic fields as determined from visible and infrared spectral lines

We present numerical experiments aimed at understanding why near-infrared observations systematically deliver weak magnetic fields in the internetwork, whereas analyses based on visible lines indicate that kG fields are ubiquitous. Synthetic noisy Stokes V profiles of the iron lines at 6302 A and 1.565 µm have been produced under varying conditions in an effort to simulate polarized spectra coming from the internetwork. An inversion technique has been applied to the profiles, as it is usually done with real observations, in order to derive the distribution of magnetic fields in the simulated region. Our results show that infrared lines yield distributions which are very similar to those used as input for the simulation, while visible lines are to a large extent affected by noise. Analyses based on the Fe I lines at 6302 A may lead to an overabundance of kG fields if the signal-to-noise ratio in Stokes V is poorer than about 10. A particular example is shown where strong fields are retrieved in nearly 30% of the pixels of a simulated internetwork region in which only fields of 200 G exist.
On the degree of ultrametricity

Using the notion of the subdominant ultrametric, the degree of ultrametricity of a given metric space (e.g. phase space) is introduced. A simple and efficient method for the calculation of is outlined. is shown to provide a simple quantitative measure of the deviation from exact ultrametricity. Explicit examples are used to illustrate this notion which is argued to be of some interest in statistical-mechanical models and combinatorial optimization problems La notion de degre d'ultrametricite d'un espace metrique donne est introduite a partir de l'ultrametrique sous-dominante. On decrit une procedure simple et efficace pour le calcul de . On montre que fournit une mesure quantitative simple de la deviation par rapport a l'ultrametricite exacte. Cette notion est illustree pour des exemples explicites et nous suggerons son interet dans les modeles de mecanique statistique ainsi que les problemes d'optimisation combinatoire
Distributed Finite-time Least Squares Solver for Network Linear Equations

In this paper, we study the problem of finding the least square solutions of over-determined linear algebraic equations over networks in a distributed manner. Each node has access to one of the linear equations and holds a dynamic state. We first propose a distributed least square solver over undirected interaction graphs, for which we establish the conditions on the interaction graphs and the step-size under which the proposed algorithm exponentially converges to the least square solution. Next, we develop a finite-time least square solver by equipping the proposed algorithm with a finite-time decentralized computation mechanism. The proposed finite-time computation mechanism enables an arbitrarily chosen node to compute the least square solution in a finite number of time steps, by using its own local successive state values obtained from the underlying algorithm. Finally, we discuss how to extend the proposed algorithm to directed interaction graphs and how the finite-time computation mechanism computes the least square solution even when the underlying algorithms diverge. The theoretical findings are validated and illustrated by numerical simulation examples.
Zero-Point Drift in Low-Frequency Mechanical Spectroscopy

The concept of the ‘zero-point drift’, ZPD, is introduced and analyzed on the basis of mechanical loss measurements carried out in a low-frequency mechanical spectrometer – inverted torsion pendulum. It is demonstrated that the ZPD, which modifies damped harmonic oscillations leads to false values of the logarithmic decrement computed from several widely accepted algorithms.
Long-Time Oscillatory Energy Conservation of Total Energy-Preserving Methods for Highly Oscillatory Hamiltonian Systems

For an integrator when applied to a highly oscillatory system, the near conservation of the oscillatory energy over long times is an important aspect. In this paper, we study the long-time near conservation of oscillatory energy for the adopted average vector field (AAVF) method when applied to highly oscillatory Hamiltonian systems. This AAVF method is an extension of the average vector field method and preserves the total energy of highly oscillatory Hamiltonian systems exactly. This paper is devoted to analysinganother important property of AAVF method, i.e., the near conservation of its oscillatory energy in a long term. The long-time oscillatory energy conservation is obtained via constructing a modulated Fourier expansion of the AAVF method and deriving an almost invariant of the expansion. A similar result of the method in the multi-frequency case is also presented in this paper.
Actions of amenable groups and crossed products of Z-absorbing C*-algebras

We study actions of countable discrete amenable groups on unital separable simple nuclear Z-absorbing C*-algebras. Under a certain assumption on tracial states, which is automatically satisfied in the case of a unique tracial state, the crossed product is shown to absorb the Jiang-Su algebra Z tensorially.
Convergence of an adaptive mixed finite element method for general second order linear elliptic problems

The convergence of an adaptive mixed finite element method for general second order linear elliptic problems defined on simply connected bounded polygonal domains is analyzed in this paper. The main difficulties in the analysis are posed by the non-symmetric and indefinite form of the problem along with the lack of the orthogonality property in mixed finite element methods. The important tools in the analysis are a posteriori error estimators, quasi-orthogonality property and quasi-discrete reliability established using representation formula for the lowest-order Raviart-Thomas solution in terms of the Crouzeix-Raviart solution of the problem. An adaptive marking in each step for the local refinement is based on the edge residual and volume residual terms of the a posteriori estimator. Numerical experiments confirm the theoretical analysis.