Search results for: Kramers vs. Kramers

Authors: Huailei Wen

Abstract:

The Kramers vs. Kramers (1979) is a film that comprehensively examines the role and status of women under the traditional secular vision, where women have become subordinate to the patriarchal society and family. Through the construction of the protagonist Joanna's dissatisfaction with the social and ethical status quo, her struggle to subvert the existing status of women, and her return to her own self, the story comprehensively reflects the difficult journey of women, represented by Joanna, to subvert the stereotypes and return to their own selves in the specific historical context of the time, revealing the self-value of Joanna's phenomenon to modern women.

Keywords: star image, feminism, Kramers vs. Kramers, Hollywood

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Authors: Adriano Valdes-Gomez, Francisco Javier Sevilla

Abstract:

We devise a numerical algorithm to simulate the diffusion of a Brownian particle restricted to the surface of a three-dimensional sphere when the particle is under the effects of an external potential that is coupled linearly. It is obtained using elementary geometry, yet, it converges, in the weak sense, to the solutions to the Smoluchowski equation. Rotations on the sphere, which are the analogs of linear displacements in euclidean spaces, are calculated using algebraic operations and then by a proper scaling, which makes the algorithm efficient and quite simple, especially to what may be the short-time propagator approach. Our findings prove that the global effects of curvature are taken into account in both dynamic and stationary processes, and it is not restricted to work in configuration space, neither restricted to the overdamped limit. We have generalized it successfully to simulate the Kramers or the Ornstein-Uhlenbeck process, where it is necessary to work directly in phase space, and it may be adapted to other two dimensional surfaces with non-constant curvature.

Keywords: diffusion on the sphere, Fokker-Planck equation on the sphere, non equilibrium processes on the sphere, numerical methods for diffusion on the sphere

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Authors: Jyoti Wadhwa, Arvinder Singh

Abstract:

This work presents the theoretical investigation of an enhanced second-harmonic generation of higher-order Gaussian laser beam in plasma having a density ramp. The mechanism responsible for the self-focusing of a laser beam in plasma is considered to be the relativistic mass variation of plasma electrons under the effect of a highly intense laser beam. Using the moment theory approach and considering the Wentzel-Kramers-Brillouin approximation for the non-linear Schrodinger wave equation, the differential equation is derived, which governs the spot size of the higher-order Gaussian laser beam in plasma. The nonlinearity induced by the laser beam creates the density gradient in the background plasma electrons, which is responsible for the excitation of the electron plasma wave. The large amplitude electron plasma wave interacts with the fundamental beam, which further produces the coherent radiations with double the frequency of the incident beam. The analysis shows the important role of the different modes of higher-order Gaussian laser beam and density ramp on the efficiency of generated harmonics.

Keywords: density rippled plasma, higher order Gaussian laser beam, moment theory approach, second harmonic generation.

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Authors: Jannes Quer, Amir Niknejad, Marcus Weber

Abstract:

Computational Drug Design is often based on Molecular Dynamics simulations of molecular systems. Molecular Dynamics can be used to simulate, e.g., the binding and unbinding event of a small drug-like molecule with regard to the active site of an enzyme or a receptor. However, the time-scale of the overall binding event is many orders of magnitude longer than the time-scale of simulation. Thus, there is a need to speed-up molecular simulations. In order to speed up simulations, the molecular dynamics trajectories have to be ”steared” out of local minimizers of the potential energy surface – the so-called metastabilities – of the molecular system. Increasing the kinetic energy (temperature) is one possibility to accelerate simulated processes. However, with temperature the entropy of the molecular system increases, too. But this kind ”stearing” is not directed enough to stear the molecule out of the minimum toward the saddle point. In this article, we give a new mathematical idea, how a potential energy surface can be changed in such a way, that entropy is kept under control while the trajectories are still steared out of the metastabilities. In order to compute the unsteared transition behaviour based on a steared simulation, we propose to use extrapolation methods. In the end we mathematically show, that our method accelerates the simulations along the direction, in which the curvature of the potential energy surface changes the most, i.e., from local minimizers towards saddle points.

Keywords: extrapolation, Eyring-Kramers, metastability, multilevel sampling

Procedia PDF Downloads 297