Global Well-Posedness of Incompressible Navier-Stokes Equations with Two Slow Variables

In this paper, the global well-posedness of the three-dimensional incompressible Navier-Stokes equations with a linear damping for a class of large initial data slowly varying in two directions are proved by means of a simpler approach.

Slow and Intraseasonal Modes of the Boreal Winter Atmospheric Circulation Simulated by CMIP5 Models

Abstract The authors evaluate the performance of models from Coupled Model Intercomparison Project Phase 5(CMIP5)in simulating the historical(1951-2000)modes of interannual variability in the seasonal mean Northern Hemisphere(NH)500 hPa geopotential height during winter(December-January-February,DJF).The analysis is done by using a variance decomposition method,which is suitable for studying patterns of interannual variability arising from intraseasonal variability and slow variability(time scales of a season or longer).Overall,compared with reanalysis data,the spatial structure and variance of the leading modes in the intraseasonal component are generally well reproduced by the CMIP5 models,with few clear differences between the models.However,there are systematic discrepancies among the models in their reproduction of the leading modes in the slow component.These modes include the dominant slow patterns,which can be seen as features of the Pacific-North American pattern,the North Atlantic Oscillation/Arctic Oscillation,and the Western Pacific pattern.An overall score is calculated to quantify how well models reproduce the three leading slow modes of variability.Ten models that reproduce the slow modes of variability relatively well are identified.

Onsager principle as a tool for approximation

Onsager principle is the variational principle proposed by Onsager in his celebrated paper on the reciprocal relation.The principle has been shown to be useful in deriving many evolution equations in soft matter physics.Here the principle is shown to be useful in solving such equations approximately.Two examples are discussed：the diffusion dynamics and gel dynamics.Both examples show that the present method is novel and gives new results which capture the essential dynamics in the system.

Quantum theory on protein folding

The conformational change of biological macromolecule is investigated from the point of quantum transition.A quantum theory on protein folding is proposed.Compared with other dynamical variables such as mobile electrons,chemical bonds and stretching-bending vibrations the molecular torsion has the lowest energy and can be looked as the slow variable of the system.Simultaneously,from the multi-minima property of torsion potential the local conformational states are well defined.Following the idea that the slow variables slave the fast ones and using the nonadiabaticity operator method we deduce the Hamiltonian describing conformational change.It is shown that the influence of fast variables on the macromolecule can fully be taken into account through a phase transformation of slow variable wave function.Starting from the conformation-transition Hamiltonian the nonradiative matrix element was calculated and a general formulas for protein folding rate was deduced.The analytical form of the formula was utilized to study the temperature dependence of protein folding rate and the curious non-Arrhenius temperature relation was interpreted.By using temperature dependence data the multi-torsion correlation was studied.The decoherence time of quantum torsion state is estimated.The proposed folding rate formula gives a unifying approach for the study of a large class problems of biological conformational change.

Stochastic fluctuations of permittivity coupling regulate seizure dynamics in partial epilepsy

Partial epilepsy is characterized by recurrent seizures that arise from a localized pathological brain region. During the onset of partial epilepsy, the seizure evolution commonly exhibits typical timescale separation phenomenon. This timescale separation behavior can be mimicked by a paradigmatic model termed as Epileptor, which consists of coupled fast-slow neural populations via a permittivity variable. By incorporating permittivity noise into the Epileptor model, we show here that stochastic fluctuations of permittivity coupling participate in the modulation of seizure dynamics in partial epilepsy. In particular, introducing a certain level of permittivity noise can make the model produce more comparable seizure-like events that capture the temporal variability in realistic partial seizures. Furthermore, we observe that with the help of permittivity noise our stochastic Epileptor model can trigger the seizure dynamics even when it operates in the theoretical nonepileptogenic regime. These findings establish a deep mechanistic understanding on how stochastic fluctuations of permittivity coupling shape the seizure dynamics in partial epilepsy,and provide insightful biological implications.