45 research outputs found
Geometric structure and geodesic in a solvable model of nonequilibrium process
We investigate the geometric structure of a nonequilibrium process and its geodesic solutions. By employing an exactly solvable model of a driven dissipative system (generalized nonautonomous Ornstein-Uhlenbeck process), we compute the time-dependent probability density functions (PDFs) and investigate the evolution of this system in a statistical metric space where the distance between two points (the so-called information length) quantifies the change in information along a trajectory of the PDFs. In this metric space, we find a geodesic for which the information propagates at constant speed, and demonstrate its utility as an optimal path to reduce the total time and total dissipated energy. In particular, through examples of physical realizations of such geodesic solutions satisfying boundary conditions, we present a resonance phenomenon in the geodesic solution and the discretization into cyclic geodesic solutions. Implications for controlling population growth are further discussed in a stochastic logistic model, where a periodic modulation of the diffusion coefficient and the deterministic force by a small amount is shown to have a significant controlling effect
A reconstruction of the initial conditions of the Universe by optimal mass transportation
Reconstructing the density fluctuations in the early Universe that evolved
into the distribution of galaxies we see today is a challenge of modern
cosmology [ref.]. An accurate reconstruction would allow us to test
cosmological models by simulating the evolution starting from the reconstructed
state and comparing it to the observations. Several reconstruction techniques
have been proposed [8 refs.], but they all suffer from lack of uniqueness
because the velocities of galaxies are usually not known. Here we show that
reconstruction can be reduced to a well-determined problem of optimisation, and
present a specific algorithm that provides excellent agreement when tested
against data from N-body simulations. By applying our algorithm to the new
redshift surveys now under way [ref.], we will be able to recover reliably the
properties of the primeval fluctuation field of the local Universe and to
determine accurately the peculiar velocities (deviations from the Hubble
expansion) and the true positions of many more galaxies than is feasible by any
other method.
A version of the paper with higher-quality figures is available at
http://www.obs-nice.fr/etc7/nature.pdfComment: Latex, 4 pages, 3 figure
Multidimensional Conservation Laws: Overview, Problems, and Perspective
Some of recent important developments are overviewed, several longstanding
open problems are discussed, and a perspective is presented for the
mathematical theory of multidimensional conservation laws. Some basic features
and phenomena of multidimensional hyperbolic conservation laws are revealed,
and some samples of multidimensional systems/models and related important
problems are presented and analyzed with emphasis on the prototypes that have
been solved or may be expected to be solved rigorously at least for some cases.
In particular, multidimensional steady supersonic problems and transonic
problems, shock reflection-diffraction problems, and related effective
nonlinear approaches are analyzed. A theory of divergence-measure vector fields
and related analytical frameworks for the analysis of entropy solutions are
discussed.Comment: 43 pages, 3 figure
Stability of flows associated to gradient vector fields and convergence of iterated transport maps
In this paper we address the problem of stability of flows
associated to a sequence of vector fields under minimal regularity requirements
on the limit vector field, that is supposed to be a gradient. We apply this
stability result to show the convergence of iterated compositions of optimal
transport maps arising in the implicit time discretization (with respect to the
Wasserstein distance) of nonlinear evolution equations of a diffusion type.
Finally, we use these convergence results to study the gradient flow of a
particular class of polyconvex functionals recently considered by Gangbo, Evans
ans Savin. We solve some open problems raised in their paper and obtain
existence and uniqueness of solutions under weaker regularity requirements and
with no upper bound on the jacobian determinant of the initial datum
On Landau damping
Going beyond the linearized study has been a longstanding problem in the
theory of Landau damping. In this paper we establish exponential Landau damping
in analytic regularity. The damping phenomenon is reinterpreted in terms of
transfer of regularity between kinetic and spatial variables, rather than
exchanges of energy; phase mixing is the driving mechanism. The analysis
involves new families of analytic norms, measuring regularity by comparison
with solutions of the free transport equation; new functional inequalities; a
control of nonlinear echoes; sharp scattering estimates; and a Newton
approximation scheme. Our results hold for any potential no more singular than
Coulomb or Newton interaction; the limit cases are included with specific
technical effort. As a side result, the stability of homogeneous equilibria of
the nonlinear Vlasov equation is established under sharp assumptions. We point
out the strong analogy with the KAM theory, and discuss physical implications.Comment: News: (1) the main result now covers Coulomb and Newton potentials,
and (2) some classes of Gevrey data; (3) as a corollary this implies new
results of stability of homogeneous nonmonotone equilibria for the
gravitational Vlasov-Poisson equatio
Moderate rate of transmitted resistance mutations to antiretrovirals and genetic diversity in newly HIV-1 patients diagnosed in Benin
ObjectiveSeventeen years after the start of the IBAARV (Beninese initiative for access to antiretrovirals), transmitted drug resistance mutations in ARV-naive patients and HIV-1 genetic diversity were investigated in Benin.ResultsDrug resistance mutations were detected in (27/248; 10.9%) according to the WHO SDRM 2009 list, with a predominance of mutations directed against NNRTIs drugs (24/248; 10%). Phylogenetic and recombination analyses showed a predominance of CRF02_AG strains (165/248; 66.5%) and a high genetic diversity with five other variants and 39 URFs (15.7%) which contained portions of strains that co-circulate in Benin. Eight recent transmission chains revealed active ongoing transmission of HIV-1 strains among ARV-naive patients. Our study showed a moderate primary drug resistance mutations rate and also provided recent data on the HIV-1 variants that circulate in Benin. Regular monitoring of primary drug resistance is required to adapt HIV-1 treatment strategies and adoption of new WHO recommendations in Benin