- journal articles metadata
European Mathematical Society Publishing House
2024-03-28 15:27:20
11
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=RLM&vol=29&iss=1&update_since=2024-03-28
Rendiconti Lincei - Matematica e Applicazioni
Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur.
RLM
1120-6330
1720-0768
General
10.4171/RLM
http://www.ems-ph.org/doi/10.4171/RLM
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2006)
29
2018
1
A Morse index invariant reduction of non-equilibrium thermodynamics
Franco
Cardin
Università degli Studi di Padova, Italy
Leonardo
Masci
Università degli Studi di Padova, Italy
Non-equilibrium thermodynamics, reaction-di¤usion system, Lyapunov–Schmidt reduction, collective variables, Morse theory
We consider the finite dimensional reduction of the well known non-equilibrium thermodynamics theory developed through the last two decades by a team of researchers lead by Giovanni Jona-Lasinio, realized by considering a simplified version – a reaction-diffusion-like dynamics – of that theory. We begin with a clear axiomatic format of that framework, showing that the reaction-diffusion dynamics emerge in a direct way after a few assumptions. Our goal is to put focus on the relations between the reduced and the full theory and to underline some topological features of this theory, more precisely, by first showing that the Morse index distribution of the equilibria of the finite dimensional reduced system is exactly the same of the full original system, thus giving us eventually a good measure of the robustness of the reduction, and secondly, moving our framework to a Morse–Smale setting, by proposing an alternative way to compute the Morse index of the equilibria. In order to realize this last program, we propose a weak infinite-dimensional Maslov–Hörmander theorem.
Partial differential equations
Differential geometry
Global analysis, analysis on manifolds
1
29
10.4171/RLM/791
http://www.ems-ph.org/doi/10.4171/RLM/791
4
10
2018
An axiomatic framework for the mechanics of generalized continua
Gianpietro
Del Piero
Università di Ferrara, Italy and Università dell’Aquila, Cisterna di Latina, Italy
Foundations of continuum mechanics, virtual power, generalized continua, micromorphic continua, microstructure
The foundations of the mechanics of generalized continua are revisited in the light of the theoretical progress made in the last decades. The resulting axiomatic framework is independent of the concepts of motion and inertia, and provides a simple and unifying formulation for several classes of generalized continua.
Mechanics of deformable solids
31
61
10.4171/RLM/792
http://www.ems-ph.org/doi/10.4171/RLM/792
4
10
2018
A continuum model of interlocking structural systems
Maurizio
Brocato
ENS d’Architecture Paris-Malaquais, Université Paris-Est, France
Continua with microstructure, configurational forces, interlocking structures, stereotomy
Masonry systems made of interlocking square-cut stones have long been studied by mathematicians and architects. It so happens that, under appropriate boundary conditions, ashlars interlock, and a stable structure results. Recently, the idea that new masonry-like materials can be designed on the basis of this archetypal principle has been put forward and applications have been proposed under the name of topological interlocking materials. In this paper, a mathematical model is proposed, that describes these materials as a special class of continua with microstructure. The system is viewed as a continuous body, the material elements of which are ashlar blocks endowed with an interaction structure based, to within certain approximations, on their interlocking geometry. The case of rigid ashlars with purely plastic interactions is developed in detail.
Mechanics of deformable solids
63
83
10.4171/RLM/793
http://www.ems-ph.org/doi/10.4171/RLM/793
4
10
2018
On Professor Grioli’s last riddle: What boundary and initial conditions make sense for microstructured continua?
Paolo
Podio-Guidugli
Accademia Nazionale dei Lincei, Roma, Italy and Università di Roma Tor Vergata, Italy
Microstructured continua, initial/boundary conditions, Cosserat continua
An abridged but faithful exposition of Professor Grioli’s version of the theory of microstructured continua of Cosserat type is given, so as to reformulate and discuss the title question. This exposition prompts some reflections on how to bridge by the use of continuum theories the gap between microscopic and macroscopic mathematical descriptions of matter.
Mechanics of deformable solids
Numerical analysis
85
92
10.4171/RLM/794
http://www.ems-ph.org/doi/10.4171/RLM/794
4
10
2018
Compactness and $s$-numbers for polynomials
Erhan
Çalışkan
Istanbul University, Vezneciler, Istanbul, Turkey
Pilar
Rueda
Universitat de Valencia, Burjassot, Spain
Homogeneous polynomials, $s$-numbers sequences, approximation numbers, Kolmogorov numbers, the measure of non-compactness
We extend the measure of non compactness notion to the polynomial setting by means of Approximation, Kolmogorov and Gelfand numbers, that are introduced for homogeneous polynomials. As an application, we study diagonal polynomials between sequence spaces.
Operator theory
Functional analysis
93
107
10.4171/RLM/795
http://www.ems-ph.org/doi/10.4171/RLM/795
4
10
2018
On a $(p,q)$-Laplacian problem with parametric concave term and asymmetric perturbation
Salvatore
Marano
Università degli Studi di Catania, Italy
Sunra
Mosconi
Università degli Studi di Catania, Italy
Nikolaos
Papageorgiou
National Technical University of Athens, Greece
$(p,q)$-Laplacian, asymmetric perturbation, concave term, extremal constant-sign and nodal solution
A Dirichlet problem driven by the $(p,q)$-Laplace operator and an asymmetric concave reaction with positive parameter is investigated. Four nontrivial smooth solutions (two positive, one negative, and the remaining nodal) are obtained once the parameter turns out to be suffciently small. Under a oddness condition near the origin for the perturbation, a whole sequence of sign-changing solutions, which converges to zero, is produced.
Partial differential equations
Global analysis, analysis on manifolds
109
125
10.4171/RLM/796
http://www.ems-ph.org/doi/10.4171/RLM/796
4
10
2018
Sign-changing solutions for a class of Schrödinger equations with vanishing potentials
Vincenzo
Ambrosio
Università degli Studi di Urbino „Carlo Bo“, Urbino, Italy
Teresa
Isernia
Università di Napoli Federico II, Italy
Fractional Laplacian, sign-changing solutions, Deformation Lemma
In this paper we consider a class of fractional Schrödinger equations with potentials vanishing at infinity. By using a minimization argument and a quantitative Deformation Lemma, we prove the existence of a sign-changing solution.
Partial differential equations
Integral equations
127
152
10.4171/RLM/797
http://www.ems-ph.org/doi/10.4171/RLM/797
4
10
2018
Inverse mean curvature flow in quaternionic hyperbolic space
Giuseppe
Pipoli
Università degli Studi dell'Aquila, Italy
Inverse mean curvature flow, quaternionic hyperbolic space, qc-curvature
In this paper we complete the study started in [Pi2] of evolution by inverse mean curvature flow of star-shaped hypersurface in non-compact rank one symmetric spaces. We consider the evolution by inverse mean curvature flow of a closed, mean convex and star-shaped hypersurface in the quaternionic hyperbolic space. We prove that the flow is defined for any positive time, the evolving hypersurface stays star-shaped and mean convex. Moreover the induced metric converges, after rescaling, to a conformal multiple of the standard sub-Riemannian metric on the sphere defined on a codimension 3 distribution. Finally we show that there exists a family of examples such that the qc-scalar curvature of this sub-Riemannian limit is not constant.
Differential geometry
153
171
10.4171/RLM/798
http://www.ems-ph.org/doi/10.4171/RLM/798
4
10
2018
On the spline transform of step-wise functions
Jean-Paul
Calvi
Université Toulouse III, France
Livio
Tilatti
Office National des Forêts, Foix, France
Histograms, natural cubic splines, spline transform
We establish some properties of the classical area-preserving spline transform of step-wise functions and propose a regularization algorithm for the positive step-wise functions whose spline transform fails to be non negative.
Approximations and expansions
Numerical analysis
173
193
10.4171/RLM/799
http://www.ems-ph.org/doi/10.4171/RLM/799
4
10
2018
Eigenvalue problem for fractional Kirchhoff Laplacian
Jagmohan
Tyagi
Indian Institute of Technology Gandhinagar, India
Fractional Laplacian, variational methods, simplicity and isolatedness
In this note, we discuss the isolatedness, simplicity and nodal estimate for the first eigenvalue of fractional Laplacian of Kirchhoff type. This work is motivated by the recent works on the fractional eigenvalues.
Partial differential equations
195
203
10.4171/RLM/800
http://www.ems-ph.org/doi/10.4171/RLM/800
4
10
2018
Stochastic heat equations with values in a Riemannian manifold
Michael
Röckner
Universität Bielefeld, Germany
Bo
Wu
Fudan University, Shanghai, China and University of Bonn, Germany
Rongchan
Zhu
Bejing Institute of Technology, China and University of Bielefeld, Germany
Xiangchan
Zhu
Bejing Jiaotong University, China and University of Bielefeld, Germany
Stochastic heat equation, Ricci curvature, functional inequality, quasi-regular Dirichlet form
The main result of this note is the existence of martingale solutions to the stochastic heat equation (SHE) in a Riemannian manifold by using suitable Dirichlet forms on the corresponding path/loop space. Moreover, we present some characterizations of the lower bound of the Ricci curvature by functional inequalities of various associated Dirichlet forms.
Probability theory and stochastic processes
Global analysis, analysis on manifolds
205
213
10.4171/RLM/801
http://www.ems-ph.org/doi/10.4171/RLM/801
4
10
2018