IA Scholar Query: Existence of solutions to a doubly degenerate fourth-order parabolic equation.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgWed, 28 Sep 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Turbulence as Clebsch Confinement
https://scholar.archive.org/work/qrlmjshh65cfddfvw4x3lbhb44
We argue that in the strong turbulence phase, as opposed to the weak one, the Clebsch variables compactify to the sphere S_2 and are not observable as wave excitations like weak turbulence. Various topologically nontrivial configurations of this confined Clebsch field are responsible for vortex sheets. Stability equations (CVS) for closed vortex surfaces (bubbles of Clebsch field) are derived and investigated. The exact non-compact solution for the stable vortex sheet family is presented. Compact solutions are proven not to exist by De Lellis and Brué. Asymptotic conservation of anomalous dissipation on stable vortex surfaces in the turbulent limit is discovered. We derive an exact formula for this anomalous dissipation as a surface integral of the square of velocity gap times the square root of minus local normal strain. Topologically stable time-dependent solutions, which we call Kelvinons, are introduced. They have a conserved velocity circulation around static loop; this makes them responsible for asymptotic PDF tails of velocity circulation, perfectly matching numerical simulations. The loop equation for fluid dynamics is derived and studied. This equation is exactly equivalent to the Schrödinger equation in loop space, with viscosity ν playing the role of Planck's constant. Area law and the asymptotic scaling law for mean circulation at a large area are derived. The exact representation of the solution of the loop equation in terms of a singular stochastic equation for momentum loop trajectory is presented. Kelvinons are fixed points of the loop equation at turbulent limit ν→ 0. The Loop equation's linearity makes the PDF's general solution to be a superposition of Kelvinon solutions with different winding numbers.Alexander Migdalwork_qrlmjshh65cfddfvw4x3lbhb44Wed, 28 Sep 2022 00:00:00 GMTGeneral invariance and equilibrium conditions for lattice dynamics in 1D, 2D, and 3D materials
https://scholar.archive.org/work/dzjyacva5zctdlp7ifcjeck2wm
The long-wavelength behavior of vibrational modes plays a central role in carrier transport, phonon-assisted optical properties, superconductivity, and thermomechanical and thermoelectric properties of materials. Here, we present general invariance and equilibrium conditions of the lattice potential; these allow to recover the quadratic dispersions of flexural phonons in low-dimensional materials, in agreement with the phenomenological model for long-wavelength bending modes. We also prove that for any low-dimensional material the bending modes can have a purely out-of-plane polarization in the vacuum direction and a quadratic dispersion in the long-wavelength limit. In addition, we propose an effective approach to treat invariance conditions in crystals with non-vanishing Born effective charges where the long-range dipole-dipole interactions induce a contribution to the lattice potential and stress tensor. Our approach is successfully applied to the phonon dispersions of 158 two-dimensional materials, highlighting its critical relevance in the study of phonon-mediated properties of low-dimensional materials.Changpeng Lin, Samuel Poncé, Nicola Marzariwork_dzjyacva5zctdlp7ifcjeck2wmTue, 20 Sep 2022 00:00:00 GMTRotating shallow water equations with bottom drag: bifurcations and growth due to kinetic energy backscatter
https://scholar.archive.org/work/khsz4v6cavgh7e7dzash3z4qie
The rotating shallow water equations with f-plane approximation and nonlinear bottom drag are a prototypical model for mid-latitude geophysical flow that experience energy loss through simple topography. Motivated by numerical schemes for large-scale geophysical flow, we consider this model on the whole space with horizontal kinetic energy backscatter source terms built from negative viscosity and stabilizing hyperviscosity with constant parameters. We study its interplay with linear and non-smooth quadratic bottom drag through the existence of coherent flows. Our results highlight that backscatter can have undesired amplification and selection effects, generating obstacles to energy distribution. We find that decreasing linear bottom drag destabilizes the trivial flow and generates nonlinear flows that can be associated with Rossby and inertia-gravity waves (IGWs). The IGWs are periodic travelling waves, while the Rossby waves are stationary and can be studied by a plane wave reduction. We show that for isotropic backscatter both bifurcate simultaneously and supercritically, while for anisotropic backscatter the primary bifurcation are Rossby waves. In all cases presence of non-smooth quadratic bottom drag implies unusual scaling laws. For the rigorous bifurcation analysis by Lyapunov-Schmidt reduction care has to be taken due to this lack of smoothness and since the hyperviscous terms yield a lack of spectral gap at large wave numbers. For purely smooth bottom drag, we identify a class of explicit such flows that behave linearly within the nonlinear equations: amplitudes can be steady and arbitrary, or grow exponentially and unboundedly. We illustrate the results by numerical computations and present extended branches in parameter space.Artur Prugger, Jens D. M. Rademacher, Jichen Yangwork_khsz4v6cavgh7e7dzash3z4qieWed, 14 Sep 2022 00:00:00 GMTOctonionic Magical Supergravity, Niemeier Lattices, and Exceptional and Hilbert Modular Forms
https://scholar.archive.org/work/tervfiwarzd4dgq2jb5wh2pwei
We show that the quantum degeneracies of spherically symmetric stationary BPS black holes of octonionic magical supergravity in five dimensions are given by the Fourier coefficients of the modular forms of the arithmetic subgroup of the exceptional group E_7(-25) that had been proposed as a spectrum generating extension of its U-duality group E_6(-26). Arithmetic group E_7(-25)(ℤ) acts as the discrete conformal group of the exceptional Jordan algebra J_3^𝕆(ℛ) over the integral octonions of Coxeter ℛ. The charges of the black holes take values on the lattice defined by J_3^𝕆(ℛ). Degeneracies of rank one and rank two quantum BPS black holes are given by the Fourier coefficients of singular modular forms E_4(Z) of weight 4 and E_8(Z)=(E_4(Z))^2 of weight 8 of E_7(-25)(ℤ). The degeneracies of rank 3 BPS black holes are given by the Fourier coefficients of the powers (E_4(Z))^n of E_4(Z) for n>2. Using the results of Elkies and Gross on the embeddings of cubic rings A into the exceptional Jordan algebra and their action on the 24 dimensional orthogonal quadratic subspace of J_3^𝕆(ℛ), we show that the degeneracies of rank one black holes described by such embeddings are given by the Fourier coefficients of the Hilbert modular forms of SL(2,A) which is a discrete subgroup of SL(2,ℤ)^3. If the discriminant of the cubic ring is D=p^2 with p a prime number then the isotropic lines in the 24 dimensional quadratic space define a pair of Niemeier lattices which can be taken as charge lattices of some BPS black holes. For p=7 they are the Leech lattice with no roots and the lattice A_6^4 with 168 root vectors. We also review the current status of the searches for the M/superstring theoretic origins of the octonionic magical supergravity.Murat Gunaydin, Abhiram Kidambiwork_tervfiwarzd4dgq2jb5wh2pweiMon, 12 Sep 2022 00:00:00 GMTSingle eigenvalue fluctuations of general Wigner-type matrices
https://scholar.archive.org/work/7nu76t5fbrhohcr3yrnrw4arwy
We consider the single eigenvalue fluctuations of random matrices of general Wigner-type, under a one-cut assumption on the density of states. For eigenvalues in the bulk, we prove that the asymptotic fluctuations of a single eigenvalue around its classical location are Gaussian with a universal variance. Our method is based on a dynamical approach to mesoscopic linear spectral statistics which reduces their behavior on short scales to that on larger scales. We prove a central limit theorem for linear spectral statistics on larger scales via resolvent techniques and show that for certain classes of test functions, the leading-order contribution to the variance agrees with the GOE/GUE cases.Benjamin Landon, Patrick Lopatto, Philippe Sosoework_7nu76t5fbrhohcr3yrnrw4arwyWed, 31 Aug 2022 00:00:00 GMTA Bayesian Analysis of Physical Parameters for 783 Kepler Close Binaries: Extreme-mass-ratio Systems and a New Mass Ratio versus Period Lower Limit
https://scholar.archive.org/work/rma7so2zufapvarv3gtbgssshm
Contact binary star systems represent the long-lived penultimate phase of binary evolution. Population statistics of their physical parameters inform an understanding of binary evolutionary pathways and end products. We use light curves and new optical spectroscopy to conduct a pilot study of ten (near) contact systems in the long-period (P > 0.5 days) tail of close binaries in the Kepler field. We use PHOEBE light-curve models to compute Bayesian probabilities on five principal system parameters. Mass ratios and third-light contributions measured from spectra agree well with those inferred from the light curves. Pilot study systems have extreme mass ratios q < 0.32. Most are triples. Analysis of the unbiased sample of 783 0.15 d < P < 2 days (near) contact binaries results in 178 probable contact systems, 114 probable detached systems, and 491 ambiguous systems for which we report best-fitting and 16th-/50th-/84th-percentile parameters. Contact systems are rare at periods P > 0.5 days, as are systems with q > 0.8. There exists an empirical mass ratio lower limit q min ( P ) ≈ 0.05–0.15 below which contact systems are absent, supporting a new set of theoretical predictions obtained by modeling the evolution of contact systems under the constraints of mass and angular momentum conservation. Premerger systems should lie at long periods and near this mass ratio lower limit, which rises from q = 0.044 for P = 0.74 days to q = 0.15 at P = 2.0 days. These findings support a scenario whereby nuclear evolution of the primary (more massive) star drives mass transfer to the primary, thus moving systems toward extreme q and larger P until the onset of the Darwin instability at q min precipitates a merger.Henry A. Kobulnicky, Lawrence A. Molnar, Evan M. Cook, Lauren E. Hendersonwork_rma7so2zufapvarv3gtbgssshmFri, 19 Aug 2022 00:00:00 GMTLectures on modular forms and strings
https://scholar.archive.org/work/rra4lqiauzezpnt4kq5ag3axnu
The goal of these lectures is to present an informal but precise introduction to a body of concepts and methods of interest in number theory and string theory revolving around modular forms and their generalizations. Modular invariance lies at the heart of conformal field theory, string perturbation theory, Montonen-Olive duality, Seiberg-Witten theory, and S-duality in Type IIB superstring theory. Automorphic forms with respect to higher arithmetic groups as well as mock modular forms enter in toroidal string compactifications and the counting of black hole microstates. After introducing the basic mathematical concepts including elliptic functions, modular forms, Maass forms, modular forms for congruence subgroups, vector-valued modular forms, and modular graph forms, we describe a small subset of the countless applications to problems in Mathematics and Physics, including those mentioned above.Eric D'Hoker, Justin Kaidiwork_rra4lqiauzezpnt4kq5ag3axnuMon, 15 Aug 2022 00:00:00 GMTSpectral signatures and properties of carbon defects in GaN and AlN
https://scholar.archive.org/work/4llnus7pdzartio5rq4hdiz5o4
Semi-insulating GaN and UV-transparent AlN are in demand in optoelectronics based on III-nitrides. Carbon (C) as an impurity is responsible for these properties of the materials. However, neither the compensation mechanism for С-doping of GaN nor the nature of the 4.7 eV absorption band in AlN is fully understood since C impurity is amphoteric. The variety of possible defect types is enormous and includes also complexes and intrinsic defects (such as nitrogen vacancies) while the proportion between the defects can change de-pending on the growth parameters and impurity concentrations. Unfortunately, usually, only indirect methods can be used for the identification of the point defect structure, which sometimes leads to excessive speculation. In this work, the structure of C-contained defects is determined by the isotopemass effect in vibration spectra, which is one of the most direct methods of analysis. Then, the new properties related to particular types of C-containing defects are investigated in GaN and AlN. In Chapter 5 of this work, the signatures of the defects in vibrational spectra are investigated. Seven types of C-containing defects in GaN and two in AlN are described by means of Fourier-Transform Infrared absorption Spectroscopy (FTIR) and Raman scattering. An excellent match of experimental results with calculated vibration frequencies is observed for numerous vibrational modes. In most cases, the isotopemass analysis leaves no doubt about the origin of the vibrations. It is illustrated how the chemical carbon concentration [C] defines the proportion between the defects in GaN and affects the (self-) compensation mechanism of C-doping. Signal intensities at different [C] in two series of GaN samples are discussed in Chapter 6. The defectrelated vibrations are found in all intentionally doped samples at [C] from 2×1017 to 3.5×1019 cm-3. Thus, it has been demonstrated that Raman scattering under the condition of resonant excitation of defects improves the sensitivity threshold by 1 - 2 orders of doping [...]Ivan Gamov, Technische Universität Berlin, Matthias Bickermannwork_4llnus7pdzartio5rq4hdiz5o4Thu, 21 Jul 2022 00:00:00 GMTDynamical change under slowly changing conditions: the quantum Kruskal-Neishtadt-Henrard theorem
https://scholar.archive.org/work/dkt46vieurbvbiiyewihcjbjhi
Adiabatic approximations break down classically when a constant-energy contour splits into separate contours, forcing the system to choose which daughter contour to follow; the choices often represent qualitatively different behavior, so that slowly changing conditions induce a sudden and drastic change in dynamics. The Kruskal-Henrard-Neishtadt theorem relates the probability of each choice to the rates at which the phase space areas enclosed by the different contours are changing. This represents a connection within closed-system mechanics, and without dynamical chaos, between spontaneous change and increase in phase space measure, as required by the Second Law of Thermodynamics. Quantum mechanically, in contrast, dynamical tunneling allows adiabaticity to persist, for very slow parameter change, through a classical splitting of energy contours; the classical and adiabatic limits fail to commute. Here we show that a quantum form of the Kruskal-Neishtadt-Henrard theorem holds nonetheless, due to unitarity.Peter Stabel, James R. Anglinwork_dkt46vieurbvbiiyewihcjbjhiTue, 05 Jul 2022 00:00:00 GMTTo Shell Model, or Not to Shell Model, That Is the Question
https://scholar.archive.org/work/cp7os4eqvfhjlbzxsuyqouqm6e
The present review takes steps from the domain of the shell model into open shell nuclei. The question posed in the title is to dramatize how far shell model approaches, i.e., many nucleons occupying independent-particle configurations and interacting through two-body forces (a configuration interaction problem) can provide a description of nuclei as one explores the structure observed where neither proton nor neutron numbers match closed shells. Features of doubly closed and singly closed shell nuclei and adjacent nuclei are sketched, together with the roles played by seniority, shape coexistence, triaxial shapes and particle–core coupling in organizing data. An illuminating step is taken here to provide a detailed study the reduced transition rates, B(E2;21+→01+), in the singly closed shell nuclei with doubly closed shell plus or minus a pair of identical nucleons, and the confrontation between such data and state-of-the-art shell model calculations: this amounts to a review of the effective charge problem. The results raise many questions and point to the need for much further work. Some guidance on criteria for sharpening the division between the domain of the shell model and that of deformation-based descriptions of nuclei are provided. The paper is closed with a sketch of a promising direction in terms of the algebraic structure embodied in the symplectic shell model.Andrew E. Stuchbery, John L. Woodwork_cp7os4eqvfhjlbzxsuyqouqm6eWed, 29 Jun 2022 00:00:00 GMTMajorana nanowires for topological quantum computation: A tutorial
https://scholar.archive.org/work/rsn6pak6ibag5gn2ulpkducu7i
Majorana bound states are quasiparticle excitations localized at the boundaries of a topologically nontrivial superconductor. They are zero-energy, charge-neutral, particle-hole symmetric, and spatially-separated end modes which are topologically protected by the particle-hole symmetry of the superconducting state. Due to their topological nature, they are robust against local perturbations and, in an ideal environment, free from decoherence. Furthermore, unlike ordinary fermions and bosons, the adiabatic exchange of Majorana modes is noncommutative, i.e., the outcome of exchanging two or more Majorana modes depends on the order in which exchanges are performed. These properties make them ideal candidates for the realization of topological quantum computers. In this tutorial, I will present a pedagogical review of 1D topological superconductors and Majorana modes in quantum nanowires. I will give an overview of the Kitaev model and the more realistic Oreg-Lutchyn model, discuss the experimental signatures of Majorana modes, and highlight their relevance in the field of topological quantum computation. This tutorial may serve as a pedagogical introduction for graduate and undergraduate students and researchers new to the field.Pasquale Marrawork_rsn6pak6ibag5gn2ulpkducu7iWed, 29 Jun 2022 00:00:00 GMTInterior Hölder continuity for singular-degenerate porous medium type equations with an application to a biofilm model
https://scholar.archive.org/work/w3sjwe4arjbtflagqaujjp6doa
We show interior H\"older continuity for a class of quasi-linear degenerate reaction-diffusion equations. The diffusion coefficient in the equation has a porous medium type degeneracy and its primitive has a singularity. The reaction term is locally bounded except in zero. The class of equations we analyse is motivated by a model that describes the growth of biofilms. Our method is based on the original proof of interior H\"older continuity for the porous medium equation. We do not restrict ourselves to solutions that are limits in the weak topology of a sequence of approximate continuous solutions of regularized problems, which is a common assumption.V. Hissink Mullerwork_w3sjwe4arjbtflagqaujjp6doaFri, 24 Jun 2022 00:00:00 GMTFrom local degrees of freedom to correlated states in anisotropic 3d transition metal compounds
https://scholar.archive.org/work/ssbk75bxvfbmbaavwrffsqlzpu
Anisotropy plays a crucial role in a wide variety of magnetic systems. In low-dimensional materials it can stabilise magnetic structures, overcoming the tendency for thermal fluctuations to disorder the magnetic correlations. It can also give rise to exotic dynamics such as nonlinear excitations and amplitude fluctuations that are not present in purely isotropic magnets. The origin of magnetic anisotropy lies in the physics of the individual magnetic ion and the crystallographic environment in which it nds itself. The nature of the magnetocrystalline anisotropy is therefore highly dependent on both the crystal structure and the species of magnetic ion. This dependence on the particulars of the system gives rise to starkly different phenomena in different compounds. In this Thesis, the physics of a number of anisotropic 3d transition metal compounds will be investigated, with a particular focus on the interplay between the single-ion physics and correlated phenomena. The Thesis begins with a discussion of the nature of magnetic interactions in the solid state, focusing on the quantum mechanical nature of the spin and orbital degrees of freedom that give rise to magnetism. Chapter 2 then provides an overview of neutron scattering { the principle experimental technique employed in this Thesis. This chapter concentrates on the instrumentation and neutron scattering theory required to interpret the results detailed in the later chapters and includes sections on both time-of-flight and triple-axis spectroscopy. Following the two introductory chapters, Chapter 3 explores the low energy dynamics of quasi-one-dimensional, large-S quantum antiferromagnets with easyaxis anisotropy. Such a situation is present in some 3d transition metal compounds based on ions such as Fe³⁺ or Mn²⁺. A description of these systems is developed using a semiclassical nonlinear δ model. The saddle point approximation leads to a sine-Gordon equation which supports soliton solutions. These correspond to the movement of spatially extended domain wa [...]Harry Lane, University Of Edinburgh, Caroline Kirk, Chris Stock, Paul Attfieldwork_ssbk75bxvfbmbaavwrffsqlzpuWed, 15 Jun 2022 00:00:00 GMTA Bayesian Analysis of Physical Parameters for 783 Kepler (Near-)Contact Binaries: Extreme-Mass-Ratio Systems and a New Mass Ratio versus Period Lower Limit
https://scholar.archive.org/work/ignnzd2bkbar7gcyldhocx6kdm
Contact binary star systems represent the long-lived penultimate phase of binary evolution. Population statistics of their physical parameters inform understanding of binary evolutionary pathways and end products. We use light curves and new optical spectroscopy to conduct a pilot study of ten (near-)contact systems in the long-period (P>0.5 d) tail of close binaries in the Kepler field. We use PHOEBE light curve models to compute Bayesian probabilities on five principal system parameters. Mass ratios and third-light contributions measured from spectra agree well with those inferred from the light curves. Pilot study systems have extreme mass ratios q<0.32. Most are triples. Analysis of the unbiased sample of 783 0.15 d0.5 d, as are systems with q>0.8. There exists an empirical mass ratio lower limit q_min(P)≈0.05–0.15 below which contact systems are absent, supporting a new set of theoretical predictions obtained by modeling the evolution of contact systems under the constraints of mass and angular momentum conservation. Pre-merger systems should lie at long periods and near this mass ratio lower limit, which rises from q=0.044 for P=0.74 d to q=0.15 at P=2.0 d. These findings support a scenario whereby nuclear evolution of the primary (more massive) star drives mass transfer to the primary, thus moving systems toward extreme q and larger P until the onset of the Darwin instability at q_min precipitates a merger.Henry A. Kobulnicky, Lawrence A. Molnar, Evan M. Cook, Lauren E. Hendersonwork_ignnzd2bkbar7gcyldhocx6kdmWed, 01 Jun 2022 00:00:00 GMTInvestigation of Game-Theoretic Mechanisms for the Valuation of Energy Resources
https://scholar.archive.org/work/p4hj2g3zrnbjhjkjdqoxbkolh4
Electricity systems are facing the pressure to change in response to the effects of new technology, particularly the proliferation of renewable technologies (such as solar PV systems and wind generation) leading to the retirement of traditional generation technologies that provide stabilising inertia. These changes create an imperative to consider potential future market structures to facilitate the participation of distributed energy resources (DERs; such as EVs and batteries) in grid operation. However, this gives rise to general questions surrounding the ethics of market structures and how they could be fairly applied in future electricity systems. Particularly the most basic question "how should electricity be valued and traded" is fundamentally a moral question without any easy answer. We give a survey of philosophical attitudes around such a question, before presenting a series of ways that these intuitions have been cast into mathematics, including: the Vickrey-Clarke-Groves mechanism, Locational Marginal Pricing, the Shapley Value, and Nash bargaining solution concepts. We compared these different methods, and attempted a new synthesis that brought together the best features of each of them; called the 'Generalised Neyman and Kohlberg Value' or the GNK-value for short. The GNK value was developed as a novel bargaining solution concept for many player non-cooperative transferable utility generalised games, and thus it was intrinsically flexible in its application to various aspects of powersystems. We demonstrated the features of the GNK-value against the other mathematical solutions in the context of trading the immediate consumption/generation of power on small sized networks under linear-DC approximation, before extending the computation to larger networks. The GNK value proved to be difficult to compute for large networks but was shown to be approximable for larger networks with a series of sampling techniques and a proxy method. The GNK value was ethically compared to other mechanisms with the unfortu [...]Mark Burgess, University, The Australian Nationalwork_p4hj2g3zrnbjhjkjdqoxbkolh4Sat, 28 May 2022 00:00:00 GMTQuantum Control via Landau-Zener-Stückelberg-Majorana Transitions
https://scholar.archive.org/work/ba3l6el3efckzkh4amiuxwdngu
Since the pioneering works by Landau, Zener, St\"uckelberg, and Majorana (LZSM), it has been known that driving a quantum two-level system results in tunneling between its states. Even though the interference between these transitions is known to be important, it is only recently that it became both accessible, controllable, and useful for engineering quantum systems. Here, we study systematically various aspects of LZSM physics and review the relevant literature, significantly expanding the review article in [Shevchenko, S. N., S. Ashhab, and F. Nori (2010), "Landau-Zener-St\"uckelberg interferometry," Phys. Rep. 492, 1.].O. V. Ivakhnenko, S. N. Shevchenko, Franco Noriwork_ba3l6el3efckzkh4amiuxwdnguTue, 24 May 2022 00:00:00 GMTFirst principle studies on electronic and thermoelectric properties of Fe_2TiSn based multinary Heusler alloys
https://scholar.archive.org/work/3inv5xuj35dshlvcmszaqyjudm
The alloys with 8/18/24 valence electron count (VEC) are promising candidates for efficient energy conversion and refrigeration applications at low as well as high temperatures. The full potential linearized augmented plane wave method as implemented in WIEN2k code was used to investigate electronic structure and TE transport properties with the PBE-GGA and TB-mBJ exchange potentials and Boltzmann transport theory. The calculated single crystal elastic constants, phonon dispersion and phonon density of states confirm that these systems are mechanically and dynamically stable. The TE transport properties is calculated by including the lattice part of thermal conductivity (κ_L) obtained from two methods one from the calculated elastic properties calculation (κ^elastic_L) and the other from phonon dispersion curve (κ^phonon_L). The strong phonon-phonon scattering by large mass difference/strain fluctuation of isovalent/aliovalent substitution at Ti/Sn sites of Fe_2TiSn reduces the lattice thermal conductivity which results in high ZT value of 0.81 at 900 K for Fe_2Sc_0.25Ti_0.5Ta_0.25Al_0.5Bi_0.5. The comparative analysis of TE transport properties using the band structures calculated with the PBE-GGA and TB-mBJ functional shows that the ZT value obtained from TB-mBJ scheme is found to be significantly higher than that based on PBE-GGA. The calculated relatively low lattice thermal conductivity and high ZT values suggest that isovalent/aliovalent substituted Fe_2TiSn are promising candidates for medium to high temperature waste heat recovery.Mukesh K. Choudhary, H. Fjellvåg, P. Ravindranwork_3inv5xuj35dshlvcmszaqyjudmMon, 16 May 2022 00:00:00 GMTTracy-Widom distribution for heterogeneous Gram matrices with applications in signal detection
https://scholar.archive.org/work/f6lijnrherbefmxxz4yr6dxab4
Detection of the number of signals corrupted by high-dimensional noise is a fundamental problem in signal processing and statistics. This paper focuses on a general setting where the high-dimensional noise has an unknown complicated heterogeneous variance structure. We propose a sequential test which utilizes the edge singular values (i.e., the largest few singular values) of the data matrix. It also naturally leads to a consistent sequential testing estimate of the number of signals. We describe the asymptotic distribution of the test statistic in terms of the Tracy-Widom distribution. The test is shown to be accurate and have full power against the alternative, both theoretically and numerically. The theoretical analysis relies on establishing the Tracy-Widom law for a large class of Gram type random matrices with non-zero means and completely arbitrary variance profiles, which can be of independent interest.Xiucai Ding, Fan Yangwork_f6lijnrherbefmxxz4yr6dxab4Fri, 13 May 2022 00:00:00 GMTComplex Nanowrinkling in Chiral Liquid Crystal Surfaces: From Shaping Mechanisms to Geometric Statistics
https://scholar.archive.org/work/feo4zdo7fjfphinvrtnn24wfnq
Surface wrinkling is closely linked to a significant number of surface functionalities such as wetting, structural colour, tribology, frictions, biological growth and more. Given its ubiquity in nature's surfaces and that most material formation processes are driven by self-assembly and self-organization and many are formed by fibrous composites or analogues of liquid crystals, in this work, we extend our previous theory and modeling work on in silico biomimicking nanowrinkling using chiral liquid crystal surface physics by including higher-order anisotropic surface tension nonlinearities. The modeling is based on a compact liquid crystal shape equation containing anisotropic capillary pressures, whose solution predicts a superposition of uniaxial, equibiaxial and biaxial egg carton surfaces with amplitudes dictated by material anchoring energy parameters and by the symmetry of the liquid crystal orientation field. The numerical solutions are validated by analytical solutions. The blending and interaction of egg carton surfaces create surface reliefs whose amplitudes depend on the highest nonlinearity and whose morphology depends on the anchoring coefficient ratio. Targeting specific wrinkling patterns is realized by selecting trajectories on an appropriate parametric space. Finally, given its importance in surface functionalities and applications, the geometric statistics of the patterns up to the fourth order are characterized and connected to the parametric anchoring energy space. We show how to minimize and/or maximize skewness and kurtosis by specific changes in the surface energy anisotropy. Taken together, this paper presents a theory and simulation platform for the design of nano-wrinkled surfaces with targeted surface roughness metrics generated by internal capillary pressures, of interest in the development of biomimetic multifunctional surfaces.Ziheng Wang, Phillip Servio, Alejandro D. Reywork_feo4zdo7fjfphinvrtnn24wfnqWed, 04 May 2022 00:00:00 GMTUniform sup-norm bounds for Siegel cusp forms
https://scholar.archive.org/work/df6nnefc6bak5nsztnjwkhe5qu
Es sei Γ eine torsionsfreie arithmetische Untergruppe der symplektischen Gruppe Sp(n,R), die auf dem Siegelschen oberen Halbraum H_n vom Grad n wirkt. Wir betrachten den d-dimensionalen Raum der Siegelschen Spitzenformen vom Gewicht k zur Gruppe Γ, mit einer Orthonormalbasis {f_1,...,f_d}. In der vorliegenden Dissertation zeigen wir mit Hilfe des Wärmeleitungskerns, dass die Supremumsnorm von S_k(Z):=det(Y)^k (|f_1(Z)|^2+...+|f_d(Z)|^2) (Z∈H_n) für n=2 ohne zusätzliche Bedingungen und für n>2 unter Annahme einer vermuteten Determinanten-Ungleichung nach oben beschränkt ist. Wenn M:=Γ\H_n kompakt ist, dann ist die obere Schranke durch c_(n,Γ) k^{n(n+1)/2} gegeben. Wenn M nicht kompakt und von endlichem Volumen ist, dann ist die obere Schranke durch c_(n,Γ) k^{3n(n+1)/4} gegeben. In beiden Fällen ist c_(n,Γ) eine positive reelle Konstante, die nur vom Grad n und der Gruppe Γ abhängt. Wir zeigen weiter, dass die obere Schranke in dem Sinne gleichmäßig ist, dass bei fixierter Gruppe Γ_0 die Konstante c_(n,Γ) für Untergruppen Γ von endlichem Index nur vom Grad n und der Gruppe Γ_0 abhängt.Antareep Mandal, Humboldt-Universität Zu Berlinwork_df6nnefc6bak5nsztnjwkhe5quMon, 25 Apr 2022 00:00:00 GMT