Non-Existence of Positive Stationary Solutions for a Class of Semi-Linear PDEs with Random Coefficients

We consider a so-called random obstacle model for the motion of a hypersurface through a field of random obstacles, driven by a constant driving field. The resulting semi-linear parabolic PDE with random coefficients does not admit a global nonnegative stationary solution, which implies that an interface that was flat originally cannot get stationary. The absence of global stationary solutions is shown by proving lower bounds on the growth of stationary solutions on large domains with Dirichlet boundary conditions. Difficulties arise because the random lower order part of the equation cannot be bounded uniformly

Entropic and gradient flow formulations for nonlinear diffusion

Nonlinear diffusion $\partial_t \rho = \Delta(\Phi(\rho))$ is considered for a class of nonlinearities $\Phi$. It is shown that for suitable choices of $\Phi$, an associated Lyapunov functional can be interpreted as thermodynamics entropy. This information is used to derive an associated metric, here called thermodynamic metric. The analysis is confined to nonlinear diffusion obtainable as hydrodynamic limit of a zero range process. The thermodynamic setting is linked to a large deviation principle for the underlying zero range process and the corresponding equation of fluctuating hydrodynamics. For the latter connections, the thermodynamic metric plays a central role

Hamiltonian statistical mechanics

A framework for statistical-mechanical analysis of quantum Hamiltonians is introduced. The approach is based upon a gradient flow equation in the space of Hamiltonians such that the eigenvectors of the initial Hamiltonian evolve toward those of the reference Hamiltonian. The nonlinear double-bracket equation governing the flow is such that the eigenvalues of the initial Hamiltonian remain unperturbed. The space of Hamiltonians is foliated by compact invariant subspaces, which permits the construction of statistical distributions over the Hamiltonians. In two dimensions, an explicit dynamical model is introduced, wherein the density function on the space of Hamiltonians approaches an equilibrium state characterised by the canonical ensemble. This is used to compute quenched and annealed averages of quantum observables.Comment: 8 pages, 2 figures, references adde

Tightness for a stochastic Allen--Cahn equation

We study an Allen-Cahn equation perturbed by a multiplicative stochastic noise which is white in time and correlated in space. Formally this equation approximates a stochastically forced mean curvature flow. We derive uniform energy bounds and prove tightness of of solutions in the sharp interface limit, and show convergence to phase-indicator functions.Comment: 27 pages, final Version to appear in "Stochastic Partial Differential Equations: Analysis and Computations". In Version 4, Proposition 6.3 is new. It replaces and simplifies the old propositions 6.4-6.

The study of degradation mechanisms of glyco-engineered plant produced anti-rabies monoclonal antibodies E559 and 62-71-3

Rabies is an ancient and neglected zoonotic disease caused by the rabies virus, a neurotropic RNA virus that belongs to the Rhabdoviridae family, genus Lyssavirus. It remains an important public health problem as there are cost and health concerns imposed by the current human post exposure prophylaxis therapy. The use of monoclonal antibodies (mAbs) is therefore an attractive alternative. Rabies mostly affects people that reside in resource-limited areas where there are occasional failures in the cold-chain. These environmental changes may upset the stability of the mAbs. This study focused on mAbs 62-71-3 and E559; their structures, responses to freeze/thaw (F/T) and exposure to reactive oxygen species were therefore studied with the aid of a wide range of biophysical and in silico techniques in order to elucidate their stability and identify aggregation prone regions. E559 was found to be less stable than 62-71-3. The complementarity determining regions (CDR) contributed the most to its instability, more specifically: peptides (EIWD102)-E-99 and (92)ATSPYT(97) found in CDR3, Trp33 found in CDR1 and the oxidised Met34. The constant region "(158)SWNSGALTGHTFPAVL(175)" was also flagged by the special aggregation propensity (SAP) tool and F/T experiments to be highly prone to aggregation. The E559 peptides "(4)LQESGSVL(11) from the heavy chain and (4)LTQSPSSL(11) from the light chain, were also highly affected by F/T. These residues may serve as good candidates for mutation, in the aim to bring forward more stable therapeutic antibodies, thus paving a way to a more safe and efficacious antibody-based cocktail treatment against rabies

Upscaling from particle models to entropic gradient flows

We prove that, for the case of Gaussians on the real line, the functional derived by a time discretization of the diffusion equation as entropic gradient flow is asymptotically equivalent to the rate functional derived from the underlying microscopic process. This result strengthens a conjecture that the same statement is actually true for all measures with second finite moment

Large deviations for the macroscopic motion of an interface

We study the most probable way an interface moves on a macroscopic scale from an initial to a final position within a fixed time in the context of large deviations for a stochastic microscopic lattice system of Ising spins with Kac interaction evolving in time according to Glauber (non-conservative) dynamics. Such interfaces separate two stable phases of a ferromagnetic system and in the macroscopic scale are represented by sharp transitions. We derive quantitative estimates for the upper and the lower bound of the cost functional that penalizes all possible deviations and obtain explicit error terms which are valid also in the macroscopic scale. Furthermore, using the result of a companion paper about the minimizers of this cost functional for the macroscopic motion of the interface in a fixed time, we prove that the probability of such events can concentrate on nucleations should the transition happen fast enough

Beyond Kinetic Relations

We introduce the concept of kinetic equations representing a natural extension of the more conventional notion of a kinetic relation. Algebraic kinetic relations, widely used to model dynamics of dislocations, cracks and phase boundaries, link the instantaneous value of the velocity of a defect with an instantaneous value of the driving force. The new approach generalizes kinetic relations by implying a relation between the velocity and the driving force which is nonlocal in time. To make this relations explicit one needs to integrate the system of kinetic equations. We illustrate the difference between kinetic relation and kinetic equations by working out in full detail a prototypical model of an overdamped defect in a one-dimensional discrete lattice. We show that the minimal nonlocal kinetic description containing now an internal time scale is furnished by a system of two ordinary differential equations coupling the spatial location of defect with another internal parameter that describes configuration of the core region.Comment: Revised version, 33 pages, 9 figure

Flavaglines Alleviate Doxorubicin Cardiotoxicity: Implication of Hsp27

Background: Despite its effectiveness in the treatment of various cancers, the use of doxorubicin is limited by a potentially fatal cardiomyopathy. Prevention of this cardiotoxicity remains a critical issue in clinical oncology. We hypothesized that flavaglines, a family of natural compounds that display potent neuroprotective effects, may also alleviate doxorubicininduced cardiotoxicity. Methodology/Principal Findings: Our in vitro data established that a pretreatment with flavaglines significantly increased viability of doxorubicin-injured H9c2 cardiomyocytes as demonstrated by annexin V, TUNEL and active caspase-3 assays. We demonstrated also that phosphorylation of the small heat shock protein Hsp27 is involved in the mechanism by which flavaglines display their cardioprotective effect. Furthermore, knocking-down Hsp27 in H9c2 cardiomyocytes completely reversed this cardioprotection. Administration of our lead compound (FL3) to mice attenuated cardiomyocyte apoptosis and cardiac fibrosis, as reflected by a 50 % decrease of mortality. Conclusions/Significance: These results suggest a prophylactic potential of flavaglines to prevent doxorubicin-induce

Un élément fini de poutre fissurée application à la dynamique des arbres tournants

International audienceDans ce travail on présente une méthode originale de construction d'un élément fini de poutre affectée de fissurations. La souplesse additionnelle due à la présence des fissures est identifiée à partir de calculs éléments finis tridimensionnels tenant compte des conditions de contact unilatéral entre les lèvres. Cette souplesse est répartie sur toute la longueur de l'élément dont on se propose de construire la matrice de rigidité. La démarche permet un gain considérable en temps de calcul par rapport à la représentation nodale de la section fissurée lors de l'intégration temporelle de systèmes différentiels en dynamique des structures