q-Gaussians in the porous-medium equation: stability and time evolution

The stability of q-Gaussian distributions as particular solutions of the linear diffusion equation and its generalized nonlinear form, , the porous-medium equation, is investigated through both numerical and analytical approaches. An analysis of the kurtosis of the distributions strongly suggests that an initial q-Gaussian, characterized by an index q_i, approaches asymptotically the final, analytic solution of the porous-medium equation, characterized by an index q, in such a way that the relaxation rule for the kurtosis evolves in time according to a q-exponential, with a relaxation index q_rel ≡q_rel(q). In some cases, particularly when one attempts to transform an infinite-variance distribution (q_i ≥ 5/3) into a finite-variance one (q < 5/3), the relaxation towards the asymptotic solution may occur very slowly in time. This fact might shed some light on the slow relaxation, for some long-range-interacting many-body Hamiltonian systems, from long-standing quasi-stationary states to the ultimate thermal equilibrium state.     

关于态叠加原理的认同与争议

给出了不同学者关于量子力学态叠加原理的几种表述,分析比较了关于该原理的有关观点的争议,并对其中的原因进行了讨论。     

Step structure on the fivefold Al-Pd-Mn quasicrystal surface, and on related surfaces

We compare step morphologies on surfaces of Al-rich metallic alloys, both quasicrystalline and crystalline. We present evidence that the large-scale step structure observed on Al-rich quasicrystals after quenching to room temperature reflects equilibrium structure at an elevated temperature. These steps are relatively rough, i.e., have high diffusivity, compared to those on crystalline surfaces. For the fivefold quasicrystal surface, step diffusivity increases as step height decreases, but this trend is not obeyed in a broader comparison between quasicrystals and crystals. On a shorter scale, the steps on Al-rich alloys tend to exhibit local facets (short linear segments), with different facet lengths, a feature which could develop during quenching to room temperature. Facets are shortest and most difficult to identify for the fivefold quasicrystal surface.     

Lattice-BGK approach to simulating granular flows

Many continuum theories for granular flow produce an equation of motion for the fluctuating kinetic energy density (granular temperature) that accounts for the energy lost in inelastic collisions. Apart from the presence of an extra dissipative term, this equation is very similar in form to the usual temperature equation in hydrodynamics. It is shown how a lattice-kinetic model based on the Bhatnagar-Gross-Krook (BGK) equation that was previously derived for a miscible two-component fluid may be modified to model the continuum equations for granular flow. This is done by noting that the variable corresponding to the concentration of one species follows an equation that is essentially analogous to the granular temperature equation. A simulation of an unforced granular fluid using the modified model reproduces the phenomenon of clustering instability, namely the spontaneous agglomeration of particles into dense clusters, which occurs generically in all granular flows. The success of the continuum theory in capturing the gross features of this basic phenomenon is discussed. Some shear flow simulations are also presented.     

Rigid Motions in the Presence of a Magnetic Field

It is shown that, in the standard framework of non-relativistic quantum mechanics, the presence of a magnetic field implies that there are no operators representing those translations or rotations that do not leave invariant the magnetic field, and the corresponding components of the linear or angular momentum are undefined. Pacs: 03.65.-w. 02.20.-a     

Glafka 2004: Generalizing Quantum Mechanics for Quantum Gravity

Familiar quantum mechanics assumes a fixed spacetime geometry. Quantummechanics must therefore be generalized for quantum gravity where spacetime geometry is not fixed but rather a quantum variable. This extended abstract sketches a fully fourdimensional generalized quantum mechnics of cosmological spacetime geometries that is one such generalization.This contribution to the proceedings of the Glafka Conference is an extended abstract of the author's talk there. More details can be found in the references cited at the end of the abstract expecially (Hartle, 1995).     

Persistence in financial markets

Persistence is studied in a financial context by mapping the time evolution of the values of the shares quoted on the London Financial Times Stock Exchange 100 index (FTSE 100) onto Ising spins. By following the time dependence of the spins, we find evidence for power law decay of the proportion of shares that remain either above or below their 'starting' values. As a result, we estimate a persistence exponent for the underlying financial market to be θ_f∼0.5.     

Global symmetry breaking in the nonconserved order parameter system during phase ordering

We study global symmetry breaking in the 2D system of scalar nonconserved order parameter following a quench to zero temperature. We show that the instant of time when the symmetry is broken and the final morphology is chosen corresponds to the saturation of the order parameter inside the domains. There are three possible final morphologies: the positive and negative order parameter final morphology, and the state of the coexisting positive and negative order parameter subsystems with a flat interface between them. We find also that each type of the final morphology constitutes about 1/3 of all cases, what agrees with the results obtained recently by Spirin et al. [Phys. Rev. E 65, 016119 (2001)]. Our results are pertinent for the two dimensional systems, but we suspect that there is also a way to apply similar arguments for the three dimensional ones.     

Proton induced thermal stress-wave measurements using a Laser Doppler Vibrometer

Thermal stress-waves are generated in the solid target material when the proton beam interacts. These stress waves excite natural oscillations of the target or cause plastic deformations. Hence, an experimental setup with a laser Doppler vibrometer [CITE] was developed to investigate free surface vibrations of cylindrical targets. The target configurations for RIB and conventional neutrino beams (CNGS project) were investigated to analyze proton induced thermal stress-wave generation and propagation.