Random hysteresis loops

Gioia Carinci

Displaying similar documents to “Random hysteresis loops”

Bulk superconductivity in Type II superconductors near the second critical ﬁeld

Soren Fournais, Bernard Helffer (2010)

Journal of the European Mathematical Society

Similarity:

We consider superconductors of Type II near the transition from the ‘bulk superconducting’ to the ‘surface superconducting’ state. We prove a new $L^{\infty}$ estimate on the order parameter in the bulk, i.e. away from the boundary. This solves an open problem posed by Aftalion and Serfaty [AS].

Stability and semiclassics in self-generated fields

László Erdős, Soren Fournais, Jan Philip Solovej (2013)

Journal of the European Mathematical Society

Similarity:

We consider non-interacting particles subject to a fixed external potential $V$ and a self-generated magnetic field $B$ . The total energy includes the field energy $β \int B^{2}$ and we minimize over all particle states and magnetic fields. In the case of spin-1/2 particles this minimization leads to the coupled Maxwell-Pauli system. The parameter $β$ tunes the coupling strength between the field and the particles and it effectively determines the strength of the field. We investigate the stability and...

A $C^{*}$ -Algebra Approach to Field Theory

D. Kastler (1968)

Recherche Coopérative sur Programme n°25

Similarity:

Existence of a positive ground state solution for a Kirchhoff type problem involving a critical exponent

Lan Zeng, Chun Lei Tang (2016)

Annales Polonici Mathematici

Similarity:

We consider the following Kirchhoff type problem involving a critical nonlinearity: ⎧ $- [a + b (\int_{Ω} {| \nabla u | ² d x)}^{m} {] Δ u = f (x, u) + | u |}^{2 * - 2} u$ in Ω, ⎨ ⎩ u = 0 on ∂Ω, where $Ω \subset ℝ^{N}$ (N ≥ 3) is a smooth bounded domain with smooth boundary ∂Ω, a > 0, b ≥ 0, and 0 < m < 2/(N-2). Under appropriate assumptions on f, we show the existence of a positive ground state solution via the variational method.

Asymptotic properties of ground states of scalar field equations with a vanishing parameter

Vitaly Moroz, Cyrill B. Muratov (2014)

Journal of the European Mathematical Society

Similarity:

We study the leading order behaviour of positive solutions of the equation $- Δ u + ϵ u - {| u |}^{p - 2} u + {| u |}^{q - 2} u = 0, x \in ℝ^{N}$ , where $N \geq 3$ , $q > p > 2$ and when $ϵ > 0$ is a small parameter. We give a complete characterization of all possible asymptotic regimes as a function of $p$ , $q$ and $N$ . The behavior of solutions depends sensitively on whether $p$ is less, equal or bigger than the critical Sobolev exponent $2^{*} = \frac{2 N}{N - 2}$ . For $p < 2^{*}$ the solution asymptotically coincides with the solution of the equation in which the last term is absent. For $p > 2^{*}$ the solution asymptotically...

Fourth-order nonlinear elliptic equations with critical growth

David E. Edmunds, Donato Fortunato, Enrico Jannelli (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

In this paper we consider a nonlinear elliptic equation with critical growth for the operator $\Delta^{2}$ in a bounded domain $\Omega\subset\mathbb{R}^{n}$ . We state some existence results when $n\geq 8$ . Moreover, we consider $5\leq n\leq 7$ , expecially when $\Omega$ is a ball in $\mathbb{R}^{n}$ .

The critical barrier for the survival of branching random walk with absorption

Bruno Jaffuel (2012)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

We study a branching random walk on $ℝ$ with an absorbing barrier. The position of the barrier depends on the generation. In each generation, only the individuals born below the barrier survive and reproduce. Given a reproduction law, Biggins et al. [ (1991) 573–581] determined whether a linear barrier allows the process to survive. In this paper, we refine their result: in the boundary case in which the speed of the barrier matches the speed of the minimal position of a...

Semi-classical standing waves for nonlinear Schrödinger equations at structurally stable critical points of the potential

Jaeyoung Byeon, Kazunaga Tanaka (2013)

Journal of the European Mathematical Society

Similarity:

We consider a singularly perturbed elliptic equation $ϵ^{2} Δ u - V (x) u + f (u) = 0, u (x) > 0$ on $ℝ^{N}$ , ${𝚕𝚒𝚖}_{|x| \to \infty} u (x) = 0$ , where $V (x) > 0$ for any $x \in ℝ^{N}$ . The singularly perturbed problem has corresponding limiting problems $Δ U - c U + f (U) = 0, U (x) > 0$ on $ℝ^{N}$ , ${𝚕𝚒𝚖}_{|x| \to \infty} U (x) = 0, c > 0$ . Berestycki-Lions found almost necessary and sufficient conditions on nonlinearity $f$ for existence of a solution of the limiting problem. There have been endeavors to construct solutions of the singularly perturbed problem concentrating around structurally stable critical points of potential $V$ under possibly general conditions...

On gradient at infinity of semialgebraic functions

Didier D&#039;Acunto, Vincent Grandjean (2005)

Annales Polonici Mathematici

Similarity:

Let f: ℝⁿ → ℝ be a C² semialgebraic function and let c be an asymptotic critical value of f. We prove that there exists a smallest rational number $ϱ_{c} \leq 1$ such that |x|·|∇f| and ${| f (x) - c |}^{ϱ_{c}}$ are separated at infinity. If c is a regular value and $ϱ_{c} < 1$ , then f is a locally trivial fibration over c, and the trivialisation is realised by the flow of the gradient field of f.

Quasi-polynomial mixing of the 2D stochastic Ising model with “plus” boundary up to criticality

Eyal Lubetzky, Fabio Martinelli, Allan Sly, Fabio Lucio Toninelli (2013)

Journal of the European Mathematical Society

Similarity:

We considerably improve upon the recent result of [37] on the mixing time of Glauber dynamics for the 2D Ising model in a box of side $L$ at low temperature and with random boundary conditions whose distribution $P$ stochastically dominates the extremal plus phase. An important special case is when $P$ is concentrated on the homogeneous all-plus configuration, where the mixing time $T_{M I X}$ is conjectured to be polynomial in $L$ . In [37] it was shown that for a large enough inverse-temperature $β$ and...

On the Law of Large Numbers for Nonmeasurable Identically Distributed Random Variables

Alexander R. Pruss (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

Let Ω be a countable infinite product $Ω ₁^{ℕ}$ of copies of the same probability space Ω₁, and let Ξₙ be the sequence of the coordinate projection functions from Ω to Ω₁. Let Ψ be a possibly nonmeasurable function from Ω₁ to ℝ, and let Xₙ(ω) = Ψ(Ξₙ(ω)). Then we can think of Xₙ as a sequence of independent but possibly nonmeasurable random variables on Ω. Let Sₙ = X₁ + ⋯ + Xₙ. By the ordinary Strong Law of Large Numbers, we almost surely have $E_{*} [X ₁] \leq l i m i n f S ₙ / n \leq l i m s u p S ₙ / n \leq E * [X ₁]$ , where $E_{*}$ and E* are the lower and upper expectations....

Linking and the Morse complex

Michael Usher (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

Similarity:

For a Morse function $f$ on a compact oriented manifold $M$ , we show that $f$ has more critical points than the number required by the Morse inequalities if and only if there exists a certain class of link in $M$ whose components have nontrivial linking number, such that the minimal value of $f$ on one of the components is larger than its maximal value on the other. Indeed we characterize the precise number of critical points of $f$ in terms of the Betti numbers of $M$ and the behavior of $f$ with respect...

Fourth-order nonlinear elliptic equations with critical growth

David E. Edmunds, Donato Fortunato, Enrico Jannelli (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Similarity:

Collisions of random walks

Martin T. Barlow, Yuval Peres, Perla Sousi (2012)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

A recurrent graph $G$ has the infinite collision property if two independent random walks on $G$ , started at the same point, collide infinitely often a.s. We give a simple criterion in terms of Green functions for a graph to have this property, and use it to prove that a critical Galton–Watson tree with finite variance conditioned to survive, the incipient infinite cluster in $ℤ^{d}$ with $d \geq 19$ and the uniform spanning tree in $ℤ^{2}$ all have the infinite collision property. For power-law combs and spherically...

Derivation of Hartree’s theory for mean-field Bose gases

Mathieu Lewin (2013)

Journées Équations aux dérivées partielles

Similarity:

This article is a review of recent results with Phan Thành Nam, Nicolas Rougerie, Sylvia Serfaty and Jan Philip Solovej. We consider a system of $N$ bosons with an interaction of intensity $1 / N$ (mean-field regime). In the limit $N \to \infty$ , we prove that the first order in the expansion of the eigenvalues of the many-particle Hamiltonian is given by the nonlinear Hartree theory, whereas the next order is predicted by the Bogoliubov Hamiltonian. We also discuss the occurrence of Bose-Einstein condensation...

On a bifurcation problem arising in cholesteric liquid crystal theory

Carlo Greco (2017)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

In a cholesteric liquid crystal the director field $n (x, y, z)$ tends to form a right-angle helicoid around a twist axis in order to minimize the internal energy; however, a fixed alignment of the director field at the boundary (strong anchoring) can give rise to distorted configurations of the director field, as oblique helicoid, in order to save energy. The transition to this distorted configurations depend on the boundary conditions and on the geometry of the liquid crystal, and it is known...

A class number criterion for the equation $(x^{p} - 1) / (x - 1) = p y^{q}$

Benjamin Dupuy (2007)

Acta Arithmetica

Similarity:

Bubbling along boundary geodesics near the second critical exponent

Manuel del Pino, Monica Musso, Frank Pacard (2010)

Journal of the European Mathematical Society

Similarity:

The role of the second critical exponent $p = (n + 1) / (n - 3)$ , the Sobolev critical exponent in one dimension less, is investigated for the classical Lane–Emden–Fowler problem $Δ u + u^{p} = 0$ , $u > 0$ under zero Dirichlet boundary conditions, in a domain $Ω$ in $ℝ^{n}$ with bounded, smooth boundary. Given $Γ$ , a geodesic of the boundary with negative inner normal curvature we find that for $p = (n + 1) / (n - 3 - ε)$ , there exists a solution $u_{ε}$ such that $| \nabla u_{ε} |^{2}$ converges weakly to a Dirac measure on $Γ$ as $ε \to 0^{+}$ , provided that $Γ$ is nondegenerate in the sense of second...

About the generating function of a left bounded integer-valued random variable

Charles Delorme, Jean-Marc Rinkel (2008)

Bulletin de la Société Mathématique de France

Similarity:

We give a relation between the sign of the mean of an integer-valued, left bounded, random variable $X$ and the number of zeros of $1 - Φ (z)$ inside the unit disk, where $Φ$ is the generating function of $X$ , under some mild conditions

Random ε-nets and embeddings in $ℓ_{\infty}^{N}$

Y. Gordon, A. E. Litvak, A. Pajor, N. Tomczak-Jaegermann (2007)

Studia Mathematica

Similarity:

We show that, given an n-dimensional normed space X, a sequence of $N = {(8 / ε)}^{2 n}$ independent random vectors ${(X_{i})}_{i = 1}^{N}$ , uniformly distributed in the unit ball of X*, with high probability forms an ε-net for this unit ball. Thus the random linear map $Γ : ℝ \to ℝ^{N}$ defined by $Γ x = {(⟨ x, X_{i} ⟩)}_{i = 1}^{N}$ embeds X in $ℓ_{\infty}^{N}$ with at most 1 + ε norm distortion. In the case X = ℓ₂ⁿ we obtain a random 1+ε-embedding into $ℓ_{\infty}^{N}$ with asymptotically best possible relation between N, n, and ε.

Scale-free percolation

Maria Deijfen, Remco van der Hofstad, Gerard Hooghiemstra (2013)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

We formulate and study a model for inhomogeneous long-range percolation on $ℤ^{d}$ . Each vertex $x \in ℤ^{d}$ is assigned a non-negative weight $W_{x}$ , where ${(W_{x})}_{x \in ℤ}^{d}$ are i.i.d. random variables. Conditionally on the weights, and given two parameters $α, λ g t; 0$ , the edges are independent and the probability that there is an edge between $x$ and $y$ is given by $p_{x y} = 1 - exp {- λ W_{x} W_{y} {/ | x - y |}^{α}}$ . The parameter $λ$ is the percolation parameter, while $α$ describes the long-range nature of the model. We focus on the degree distribution in the resulting graph, on whether...

Convergence of minimax structures and continuation of critical points for singularly perturbed systems

Benedetta Noris, Hugo Tavares, Susanna Terracini, Gianmaria Verzini (2012)

Journal of the European Mathematical Society

Similarity:

In the recent literature, the phenomenon of phase separation for binary mixtures of Bose–Einstein condensates can be understood, from a mathematical point of view, as governed by the asymptotic limit of the stationary Gross–Pitaevskii system $- Δ u + u^{3} + β u v^{2} = λ u, - Δ v + v^{3} + β u^{2} v = μ v, u, v \in H_{0}^{1} (Ω), u, v > 0$ , as the interspecies scattering length $β$ goes to $+ \infty$ . For this system we consider the associated energy functionals $J_{β}, β \in (0, + \infty)$ , with $L^{2}$ -mass constraints, which limit $J_{\infty}$ (as $β \to + \infty$ ) is strongly irregular. For such functionals, we construct multiple critical points...

Giant component and vacant set for random walk on a discrete torus

Itai Benjamini, Alain-Sol Sznitman (2008)

Journal of the European Mathematical Society

Similarity:

We consider random walk on a discrete torus $E$ of side-length $N$ , in sufficiently high dimension $d$ . We investigate the percolative properties of the vacant set corresponding to the collection of sites which have not been visited by the walk up to time $u N^{d}$ . We show that when $u$ is chosen small, as $N$ tends to infinity, there is with overwhelming probability a unique connected component in the vacant set which contains segments of length const $log N$ . Moreover, this connected component occupies a...

Rigidity of critical circle mappings I

Edson de Faria, Welington de Melo (1999)

Journal of the European Mathematical Society

Similarity:

We prove that two $C^{3}$ critical circle maps with the same rotation number in a special set $𝔸$ are $C^{1 + α}$ conjugate for some $α > 0$ provided their successive renormalizations converge together at an exponential rate in the $C^{0}$ sense. The set $𝔸$ has full Lebesgue measure and contains all rotation numbers of bounded type. By contrast, we also give examples of $C^{\infty}$ critical circle maps with the same rotation number that are not $C^{1 + β}$ conjugate for any $β > 0$ . The class of rotation numbers for which such examples exist...

Location of the critical points of certain polynomials

Somjate Chaiya, Aimo Hinkkanen (2013)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

Similarity:

Let $𝔻$ denote the unit disk ${z : | z | < 1}$ in the complex plane $ℂ$ . In this paper, we study a family of polynomials $P$ with only one zero lying outside $\bar{𝔻}$ . We establish criteria for $P$ to satisfy implying that each of $P$ and $P^{'}$ has exactly one critical point outside $\bar{𝔻}$ .

Soft local times and decoupling of random interlacements

Serguei Popov, Augusto Teixeira (2015)

Journal of the European Mathematical Society

Similarity:

In this paper we establish a decoupling feature of the random interlacement process $ℐ^{u} \subset ℤ^{d}$ at level $u$ , $d \geq 3$ . Roughly speaking, we show that observations of $ℐ^{u}$ restricted to two disjoint subsets $A_{1}$ and $A_{2}$ of $ℤ^{d}$ are approximately independent, once we add a sprinkling to the process $ℐ^{u}$ by slightly increasing the parameter $u$ . Our results differ from previous ones in that we allow the mutual distance between the sets $A_{1}$ and $A_{2}$ to be much smaller than their diameters. We then provide an important application...