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Analytical representations of the solutions of Kolmogorov's forward (i.e., Fokker-Planck) and backward partial differential equations are obtained by employing Girsanov's (1960) transformation. The equations considered are restricted to those with the drift vector being the gradient of a function and the diffusion matrix being nonsingular and dependent upon time only.
The relativistic motion of electrons in an intense electromagnetic wave packet propagating obliquely to a uniform magnetic field is analytically studied on the basis of the Fokker-Planck-Kolmogorov (FPK) approach. The wavepacket consists of circularly polarized electron-cyclotron waves. The dynamical system in question is shown to be reducible to one with three degrees of freedom. Within the framework of the Hamiltonian analysis the nonlinear diffusion tensor is derived, and it is shown that this tensor can be separated into zeroth-, first-, and second-order parts with respect to the relative bandwidth. The zeroth-order part describes diffusive acceleration along lines of constant unperturbed Hamiltonian. The second-order part, which corresponds to the longest time scale, describes diffusion across those lines. A possible transport theory is outlined on the basis of this separation of the time scales.
The relativistic motion of an ensemble of electrons in an intense monochromatic electromagnetic wave propagating obliquely in a uniform external magnetic field is studied. The problem is formulated from the viewpoint of Hamiltonian theory and the Fokker-Planck-Kolmogorov approach analyzed by Hizanidis (1989), leading to a one-dimensional diffusive acceleration along paths of constant zeroth-order generalized Hamiltonian. For values of the wave amplitude and the propagating angle inside the analytically predicted stochastic region, the numerical results suggest that the diffusion probes proceeds in stages. In the first stage, the electrons are accelerated to relatively high energies by sampling the first few overlapping resonances one by one. During that stage, the ensemble-average square deviation of the variable involved scales quadratically with time. During the second stage, they scale linearly with time. For much longer times, deviation from linear scaling slowly sets in.
Nambu-Goldstone modes are sensitive to the effects of physics at energies comparable to the scale of spontaneous symmetry breaking. We show that as a consequence of this the global texture proposal for structure formation requires rather severe assumptions about the nature of physics at the Planck scale.
Motivated by experiments in which an applied electric field translocates polynucleotides through an alpha-hemolysin protein channel causing ionic current transient blockade, a hybrid simulation model is proposed to predict the conductance properties of the open channel. Time scales corresponding to ion permeation processes are reached using the Poisson-Nemst-Planck (PNP) electro-diffusion model in which both solvent and local ion concentrations are represented as a continuum. The diffusion coefficients of the ions (K(+) and Cl(-)) input in the PNP model are, however, calculated from all-atom molecular dynamics (MD). In the MD simulations, a reduced representation of the channel is used. The channel is solvated in a 1 M KCI solution, and an external electric field is applied. The pore specific diffusion coefficients for both ionic species are reduced 5-7 times in comparison to bulk values. Significant statistical variations (17-45%) of the pore-ions diffusivities are observed. Within the statistics, the ionic diffusivities remain invariable for a range of external applied voltages between 30 and 240mV. In the 2D-PNP calculations, the pore stem is approximated by a smooth cylinder of radius approx. 9A with two constriction blocks where the radius is reduced to approx. 6A. The electrostatic potential includes the contribution from the atomistic charges. The MD-PNP model shows that the atomic charges are responsible for the rectifying behaviour and for the slight anion selectivity of the a-hemolysin pore. Independent of the hierarchy between the anion and cation diffusivities, the anionic contribution to the total ionic current will dominate. The predictions of the MD-PNP model are in good agreement with experimental data and give confidence in the present approach of bridging time scales by combining a microscopic and macroscopic model.
Hydrogen sorption crycoolers are being developed for the European Space Agency Planck mission to provide nominal 19 K cooling to instruments for measuring the temperature anisotropy of the cosmic microwave background with extreme sensitivity and resolution.
JPL is developing a continuous hydrogen sorption cryocooler for the ESA Planck mission, which will measure the anisotropy in the cosmic microwave background.
JPL is developing a continuous hydrogen sorption cryocooler for the ESA Planck mission to measure the anisotropy in the cosmic microwave background.
Two continuous operation 18 K/20 K sorption coolers are being developed by JPL for the ESA Planck mission to provide about 200 mW of cooling at 18 K and 1.4 W at 20 K. A detailed performance prediction model has been developed to support the design process and to evaluate the results of a prototype testing.
We present the general principles of gas gap heat switches that impact their performances for the Planck cryocooler, develop two figures of merit relevant to this application, and present initial characterization results of switches using uranium or ZrNi as the hydriding material.
Two continuous opertation 18K/20K sorption coolers are being developed by the Jet Propulsion Laboratory (JPL) as a NASA contribution to the European Space Agency (ESA) Planck mission that is currently planned for a 2007 launch.
We are developing metal-hydride based sorption cryocoolers for the Planck Surveyor mission.
We present the results of a finite difference implementation of the kinetic Fokker-Planck model with an exact form of the nonlinear collisional operator, The model is time dependent and three-dimensional; one spatial dimension and two in velocity space. The spatial dimension is aligned with the local magnetic field, and the velocity space is defined by the magnitude of the velocity and the cosine of pitch angle. An important new feature of model, the concept of integration along the particle trajectories, is discussed in detail. Integration along the trajectories combined with the operator time splitting technique results in a solution scheme which accurately accounts for both the fast convection of the particles along the magnetic field lines and relatively slow collisional process. We present several tests of the model's performance and also discuss simulation results of the evolution of the plasma distribution for realistic conditions in Earth's plasmasphere under different scenarios.
We discuss the performance prediction of the Planck sorption cooler and initial validation.
We discuss a simple ID model of the modification of Planck blackbody radiation by photonic band-gap materials (PBGs).
Continuous-duty hydrogen sorption cryocoolers are being developed for the European Space Agency (ESA) Planck mission. To achieve an acceptable level of performance and robust operation with these hydride refrigerators during flight, detailed investigations have been performed on the sorbent materials and on critical hardware components.
JPL is developing two continuous 20 K nominal sorption-based coolers for the European Space Agency (ESA) Planck mission.
New determinations are presented of the cosmic infrared background monopole brightness in thePlanckHFI bands from 100 to 857 GHz. Planck was not designed to measure the monopole component of sky brightness, so cross-correlation of the 2015 HFI maps with COBE/FIRAS data is used to recalibrate the zero level of the HFI maps. For the HFI 545 and 857 GHz maps, the brightness scale is also recalibrated. Correlation of the recalibrated HFI maps with a linear combination of Galactic HI and Hα data is used to separate the Galactic foreground emission and determine the cosmic infrared background brightness in each of the HFI bands. We obtain CIB values of 0.007, ±0.014, 0.010, ±0.019, 0.060, ±0.023, 0.149, ±0.017, 0.371, ±0.018, and 0.576, ±0.034 MJy sr−1at100, 143, 217, 353, 545, and 857 GHz, respectively. The estimated uncertainties for the 353–857 GHz bands are about 3–6 times smaller than those of previous direct CIB determinations at these frequencies. Our results are compared with integrated source brightness results from selected recent submillimeter and millimeter wavelength imaging surveys.