Search results for "classical"

Riemann type integrals for functions taking values in a locally convex space

2006

The McShane and Kurzweil-Henstock integrals for functions taking values in a locally convex space are defined and the relations with other integrals are studied. A characterization of locally convex spaces in which Henstock Lemma holds is given.

Enclosure method for the p-Laplace equation

2014

We study the enclosure method for the p-Calder\'on problem, which is a nonlinear generalization of the inverse conductivity problem due to Calder\'on that involves the p-Laplace equation. The method allows one to reconstruct the convex hull of an inclusion in the nonlinear model by using exponentially growing solutions introduced by Wolff. We justify this method for the penetrable obstacle case, where the inclusion is modelled as a jump in the conductivity. The result is based on a monotonicity inequality and the properties of the Wolff solutions.

Corallaria

2021

Prima delle sette commedie composte dall’umanista ferrarese Tito Livio Frulovisi (1400-1463 c.), la Corallaria è caratterizzata da un doppio intreccio, entro il quale si individuano frequenti contaminazioni fra temi di tradizione comica classica e motivi di origine novellistica. Rappresentata a Venezia nel 1432, probabilmente da una compagnia di attori professionisti, la Corallaria si configura come una commedia “stataria”, dal momento che la maggiore parte degli eventi che vi si verificano, piuttosto che direttamente rappresentata, viene raccontata dai personaggi. Il titolo, di stampo evidentemente plautino, deriva dai coralli che il giovane Miles si fa prestare da Faceto e regala alla vec…

Connectivity Influences on Nonlinear Dynamics in Weakly-Synchronized Networks: Insights from Rössler Systems, Electronic Chaotic Oscillators, Model a…

2019

Natural and engineered networks, such as interconnected neurons, ecological and social networks, coupled oscillators, wireless terminals and power loads, are characterized by an appreciable heterogeneity in the local connectivity around each node. For instance, in both elementary structures such as stars and complex graphs having scale-free topology, a minority of elements are linked to the rest of the network disproportionately strongly. While the effect of the arrangement of structural connections on the emergent synchronization pattern has been studied extensively, considerably less is known about its influence on the temporal dynamics unfolding within each node. Here, we present a compr…

A note on correlation and local dimensions

2015

Abstract Under very mild assumptions, we give formulas for the correlation and local dimensions of measures on the limit set of a Moran construction by means of the data used to construct the set.

Kinematically corrected correlation functions for inclusive reactions

1972

Signorini problem with Coulomb's law of friction. Shape optimization in contact problems

1992

Similarity Solutions and Collapse in the Attractive Gross-Pitaevskii Equation

2000

We analyse a generalised Gross-Pitaevskii equation involving a paraboloidal trap potential in $D$ space dimensions and generalised to a nonlinearity of order $2n+1$. For {\em attractive} coupling constants collapse of the particle density occurs for $Dn\ge 2$ and typically to a $\delta$-function centered at the origin of the trap. By introducing a new dynamical variable for the spherically symmetric solutions we show that all such solutions are self-similar close to the center of the trap. Exact self-similar solutions occur if, and only if, $Dn=2$, and for this case of $Dn=2$ we exhibit an exact but rather special D=1 analytical self-similar solution collapsing to a $\delta$-function which …

Monte Carlo study of surface critical behavior in the XY model.

1989

We have used Monte Carlo simulations to study the behavior of $L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}D$ slabs containing classical spins which interact via nearest-neighbor $\mathrm{XY}$ coupling. The coupling constant ${J}_{S}$ for spins in the surface layer is fixed at $0.5J$. Finite-size scaling is used to analyze data for $D=59$ and to extract estimates for the surface critical exponents. We find that ${\ensuremath{\beta}}_{1}$ is in good agreement with theoretical predictions.

Statistical Mechanics of the Integrable Models

1987

There is an infinity of classically integrable models. The only ones we can consider here, and these only briefly, are: the sine-Gordon (s-G) model $${\phi _{{\rm{xx}}}}{}^ - {\phi _{{\rm{tt}}}} = {{\rm{m}}^2}\sin \phi ,$$ (1.1) the sinh-Gordon (sinh-G) model $${\phi _{{\rm{xx}}}}{}^ - {\phi _{{\rm{tt}}}} = {{\rm{m}}^2}\sinh \phi ,$$ (1.2) and the repulsive and attractive non-linear Schrodinger (NLS) models $${}^ - {\rm{i}}{\phi _{\rm{t}}} = {\phi _{{\rm{xx}}}}{}^ - 2{\rm{c}}\phi {\left| \phi \right|^2}.$$ (1.3) The “attractive” NLS has real coupling constant c 0; φ is complex. In (1.1) and (1.2) m is a mass (ħ = c = 1) and φ is real. These 4 integrable models are in one space and one time …