In this paper, we study the optimal time problem for the one-dimensional, linear heat equation, in the presence of a scaling parameter. To begin with, we build an exact solution. The dependence of this solution as regards the scaling parameter naturally opens the way to study the existence and uniqueness of an optimal time control. If, moreover, one assumes the L∞− null controllability, it enab...

To describe the small-scale intermittency of turbulence, a self-similarity is assumed for the probability density function of a logarithm of the rate of energy dissipation smoothed over a length scale among those in the inertial range. The result is an extension of Kolmogorov's classical theory [A. N. Kolmogorov, Dokl. Akad. Nauk SSSR 30, 301 (1941)], i.e., a one-parameter framework where the l...

The finite temperature transition of QCD with two degenerate light quarks is studied on the lattice with a renormalization group improved gauge action and the Wilson quark action. We have made simulations on an 8 3 × 4 lattice near the chiral transition point. It is shown that the chiral condensate which is the order parameter of chiral symmetry satisfies remarkably a scaling relation with the ...

We present a constructive approach to obtain information about the compactness and shape of large-scale lowest excitations in disordered systems by studying order parameter fluctuations (OPF) at low temperatures. We show that the parameter G that measures OPF is 1/3 at T = 0 provided the ground state is unique and the probability distribution for the lowest excitations is gapless and with finit...

Experiments measuring DNA extension in nanochannels are at odds with even the most basic predictions of current scaling arguments for the conformations of confined semiflexible polymers such as DNA. We show that a theory based on a weakly self-avoiding, one-dimensional "telegraph" process collapses experimental data and simulation results onto a single master curve throughout the experimentally...

Products of random matrices associated to one-dimensional random media satisfy a central limit theorem assuring convergence to a gaussian centered at the Lyapunov exponent. The hypothesis of single parameter scaling states that its variance is equal to the Lyapunov exponent. We settle discussions about its validity for a wide class of models by proving that, away from anomalies, single paramete...

We investigate the problem of a decomposition of a dissipative dynamical map, which is used in quantum dynamics of a finite open quantum system, into two distinct types of mapping on a Hilbert-Schmidt space of quantum states represented by density matrices. One type corresponds to reversible behaviours, while the other to irreversible characteristics. For a finite dimensional system, in which o...

Early-type galaxies are characterized by many scaling relations. Evolutionary classifications find that some of these correlations are indeed generated by diversification. With a simple mathematical formalism, we show (Fraix-Burnet 2011) that even the so-called fundamental plane, a relatively tight correlation between three variables, can be easily explained as the artifact of the effect of ano...

[Abstract] It is a challenge to produce a practical design of an electron storage ring with a theoretical minimum emittance (TME) lattice of ultra low emittance, e.g. down to a level of several pico-meters, due to the very strong focusing and the extremely large natural chromaticity associated with the lattice design. To help dealing with this challenge, it is customary to scale the parameters ...

In this paper we developed a general primal-dual nonlinear rescaling method with dynamic scaling parameter update (PDNRD) for convex optimization. We proved the global convergence, established 1.5Q-superlinear rate of convergence under the standard second order optimality conditions. The PDNRD was numerically implemented and tested on a number of nonlinear problems from COPS and CUTE sets. We p...