Search results for "Planck"
showing 9 items of 159 documents
Exact stationary solution for a class of non-linear systems driven by a non-normal delta-correlated process
1995
In this paper the exact stationary solution in terms of probability density function for a restricted class of non-linear systems under both external and parametric non-normal delta-correlated processes is presented. This class has been obtained by imposing a given probability distribution and finding the corresponding dynamical system which satisfies the modified Fokker-Planck equation. The effectiveness of the results has been verified by means of a Monte Carlo simulation.
On the a posteriori error analysis for linear Fokker-Planck models in convection-dominated diffusion problems
2018
This work is aimed at the derivation of reliable and efficient a posteriori error estimates for convection-dominated diffusion problems motivated by a linear Fokker-Planck problem appearing in computational neuroscience. We obtain computable error bounds of the functional type for the static and time-dependent case and for different boundary conditions (mixed and pure Neumann boundary conditions). Finally, we present a set of various numerical examples including discussions on mesh adaptivity and space-time discretisation. The numerical results confirm the reliability and efficiency of the error estimates derived.
Fabrication of Single Cylindrical Au-Coated Nanopores with Non-Homogeneous Fixed Charge Distribution Exhibiting High Current Rectifications
2014
We have designed and characterized a cylindrical nanopore that exhibits high electrochemical current rectification ratios at low and intermediate electrolyte concentrations. For this purpose, the track-etched single cylindrical nanopore in polymer membrane is coated with a gold (Au) layer via electroless plating technique. Then, a non-homogeneous fixed charge distribution inside the Au-coated nanopore is obtained by incorporating thiol-terminated uncharged poly(N-isopropylacrylamide) (PNIPAM) chains in series to poly(4-vinyl pyridine) (PVP) chains, which are positively charged at acidic pH values. The functionalization reaction is checked by measuring the current–voltage (I–V) curves prior …
Non-thermal pressure support in X-COP galaxy clusters
2018
Galaxy clusters are the endpoints of structure formation and are continuously growing through the merging and accretion of smaller structures. Numerical simulations predict that a fraction of their energy content is not yet thermalized, mainly in the form of kinetic motions (turbulence, bulk motions). Measuring the level of non-thermal pressure support is necessary to understand the processes leading to the virialization of the gas within the potential well of the main halo and to calibrate the biases in hydrostatic mass estimates. We present high-quality measurements of hydrostatic masses and intracluster gas fraction out to the virial radius for a sample of 12 nearby clusters with availab…
The dissipative linear Boltzmann equation for hard spheres
2005
The authors prove existence and uniqueness of a Maxwellian, normalized equilibrium state for a dissipative linear Boltzmann equation with hard-sphere collision kernel modeling a granular gas and, for initial data with finite temperature and entropy, strong L 1 convergence (obtained through compactness arguments) toward the equilibrium of the solutions in the space-homogeneous case. The form of the equilibrium state, which is universal for the family of collision operators including hard, soft and Maxwellian interactions, is guessed through a grazing collision asymptotics and then proved to be the equilibrium state through Fourier analysis. Uniqueness and strong L 1 convergence proofs follow…
CALIBRATION OF LÉVY PROCESSES USING OPTIMAL CONTROL OF KOLMOGOROV EQUATIONS WITH PERIODIC BOUNDARY CONDITIONS
2018
We present an optimal control approach to the problem of model calibration for L\'evy processes based on a non parametric estimation procedure. The calibration problem is of considerable interest in mathematical finance and beyond. Calibration of L\'evy processes is particularly challenging as the jump distribution is given by an arbitrary L\'evy measure, which form a infinite dimensional space. In this work, we follow an approach which is related to the maximum likelihood theory of sieves. The sampling of the L\'evy process is modelled as independent observations of the stochastic process at some terminal time $T$. We use a generic spline discretization of the L\'evy jump measure and selec…
Duality-invariant dispersion relations for electromagnetic and gravitational waves at Planck scales
2012
In this paper we explore some mathematical aspects of a duality-invariant Einstein-Planck relation on electromagnetic waves and gravitational waves at a Planckian scale. We explore a generalized version of Maxwell's equations leading to the proposed duality-invariant dispersion relation for electromagnetic waves. We also study the analogous aspects of duality in a post-Newtonian description of gravitational waves.
Itô-Stratonovitch Formula for the Wave Equation on a Torus
2010
We give an Ito-Stratonovitch formula for the wave equation on a torus, where we have no stochastic process associated to this partial differential equation. This gives a generalization of the classical Ito-Stratonovitch equation for diffusion in semi-group theory established by ourself in [18], [20].
Self-Defence Against Non-State Actors: Impulses from the Max Planck Trialogues on the Law of Peace and War
2017
The legality of self-defence against non-state actors is currently one of the most contested issues of the jus contra bellum. How should we interpret state practice – has it already given rise, in law, to a broader concept of self-defence, or is the traditional state centred view still good law? Under which specific requirements should self-defence against non-state actors, if at all, be regarded as lawful and how can an abuse of an extended right to self-defence be prevented? The “Impulses from the Max Planck Trialogues on the Law of Peace and War” consist of short essays dealing with these questions. The essays are grouped in four categories: 1) restrictivist positions upholding a state-c…