Stability of a class of transformations of distribution-valued processes and stochastic evolution equations

Stability of a class of linear transformations of distribution-valued stochastic processes is studied. Two types of applications to convergence of solutions of stochastic evolution equations are given. One of them, for the case of continuous limits, simplifies the tightness problem considerably due to a recent result of Aldous.Centro de Investigación y de Estudios Avanzados.     

Femtosecond laser-induced damage of gold films

Single- and multi-shot ablation thresholds of gold films in the thickness range of 31-1400 nm were determined employing a Ti:sapphire laser delivering pulses of 28 fs duration, 793 nm center wavelength at 1 kHz repetition rate. The gold layers were deposited on BK7 glass by an electron beam evaporation process and characterized by atomic force microscopy and ellipsometry. A linear dependence of the ablation threshold fluence F_th on the layer thickness d was found for d ≤ 180 nm. If a film thickness of about 180 nm was reached, the damage threshold remained constant at its bulk value. For different numbers of pulses per spot (N-on-1), bulk damage thresholds of ∼0.7 J cm⁻² (1-on-1), 0.5 J cm⁻² (10-on-1), 0.4 J cm⁻² (100-on-1), 0.25 J cm⁻² (1000-on-1), and 0.2 J cm⁻² (10000-on-1) were obtained experimentally indicating an incubation behavior. A characteristic layer thickness of L_c ≈ 180 nm can be defined which is a measure for the heat penetration depth within the electron gas before electron-phonon relaxation occurs. L_c is by more than an order of magnitude larger than the optical absorption length of α⁻¹ ≈ 12 nm at 793 nm wavelength.     

Relating neural dynamics to neural coding

We demonstrate that two key theoretical objects used widely in computational neuroscience, the phase-resetting curve (PRC) from dynamics and the spike triggered average (STA) from statistical analysis, are closely related when neurons fire in a nearly regular manner and the stimulus is sufficiently small. We prove that the STA due to injected noisy current is proportional to the derivative of the PRC. We compare these analytic results with numerical calculations for the Hodgkin-Huxley neuron and we apply the method to neurons in the olfactory bulb of mice. This observation allows us to relate the stimulus-response properties of a neuron to its dynamics, bridging the gap between dynamical and information theoretic approaches to understanding brain computations and facilitating the interpretation of changes in channels and other cellular properties as influencing the representation of stimuli.     

Electro-flow focusing: the high-conductivity low-viscosity limit

Electro-flow focusing, a technique combining the features of electrospray (ES) and flow focusing (FF), provides a reliable tool to reach parametrical microjetting ranges not attainable by ES or FF alone under specific operational regimes (liquid properties and flow rate). In this Letter, we provide not only a closed theoretical model predicting the diameter of a high electrical conductivity electro-flow focused liquid microjet, but also its convective or absolute instability, linked to the jetting-to-dripping transition and the minimum liquid flow rate that can be ejected in steady jetting regime, in which the smallest droplets are issued. Good agreement is found with experimental values.     

Physics, mind, society: Back and forth

The life course of the physicist and biologist George Feher may be seen as an epitome of science of the second half of the 20th century and the beginning of the 21st century. Feher, a native of Slovakia, barely escaped Nazism and communism and became a scientist in the USA. The Nazi concentration camps and the communist gulags have become a symbol of the 20th century. This symbol stands here to pose a question: How the two totalitarian systems, fraught with irrationality, may have arisen and thrived in parallel with an unprecedented expansion of science, the paragon of rationalism? The question has become even more urgent in the 21st century. The Ground Zero, an empty spot left after the collapse of the twin towers of the World Trade Center on 11 September 2001, has become the symbol of the entrance of humankind into the new millennium. We can do much, but we understand too little about who we are and what we are doing — this is a message that the two symbols convey about the precarious stage of our evolution. The second message concerns the role of artifacts, specifically scientific instruments, in the advancement of science. Human cultural evolution has been steadily progressing, in a form of a ratchet, only because artifacts have been continually evolving. Contrary to the common Popperian wisdom, the demarcation in science may not consist in the amenability to theoretical falsification, but rather in the amenability to instrumental grasping. Scientific instruments have empowered humans for impressive feats of manipulation with Nature and themselves. Knowledge arising in the course of autonomous evolution of artifacts may surpass the horizon of human understanding and grasping. New knowledge may still be power, but no longer the power of humans. We may need a revision of some fundamental ideas of European thought. Our understanding of the human mind may entirely reshape our comprehension of the nature of physical knowledge, and vice versa.     

Precession and Interference in the Aharonov–Casher and Scalar Aharonov–Bohm Effects

The ideal scalar Aharonov–Bohm (SAB) and Aharonov–Casher (AC) effect involve a magnetic dipole pointing in a certain fixed direction: along a purely time dependent magnetic field in the SAB case and perpendicular to a planar static electric field in the AC case. We extend these effects to arbitrary direction of the magnetic dipole. The precise conditions for having nondispersive precession and interference effects in these generalized set ups are delineated both classically and quantally. Under these conditions the dipole is affected by a nonvanishing torque that causes pure precession around the directions defined by the ideal set ups. It is shown that the precession angles are in the quantal case linearly related to the ideal phase differences, and that the nonideal phase differences are nonlinearly related to the ideal phase differences. It is argued that the latter nonlinearity is due to the appearance of a geometric phase associated with the nontrivial spin path. It is further demonstrated that the spatial force vanishes in all cases except in the classical treatment of the nonideal AC set up, where the occurring force has to be compensated by the experimental arrangement. Finally, for a closed space-time loop the local precession effects can be inferred from the interference pattern characterized by the nonideal phase differences and the visibilities. It is argued that this makes it natural to regard SAB and AC as essentially local and nontopological effects.     

Photo-orientation at liquid crystal—polymer interfaces

It is suggested that liquid crystal—polymer interfaces are coupled systems, in which the components mutually influence the orientational state of each other. The photo-orientation process at liquid crystal-polymer interfaces provides a striking example of such a coupling. Experiments show that the anisotropic structure generated by polarised light at a polymer surface is strongly affected by the phase of the liquid crystal covering the polymer. Photo-orientation is significantly more efficient when the liquid crystal is in the isotropic phase than when it exhibits orientational order. The observations are interpreted by assuming that in the smectic and nematic phases the liquid crystal stabilises to a large extent polymer chain-segments aligned parallel to the director, while it blocks the photo-induced formation of chain-segments in the perpendicular direction. Other situations, in which the coupling between the liquid crystal and the polymer can be important, are also discussed briefly.     

Dynamics of photoluminescence in GaInNAs saturable absorber mirrors

Femtosecond time-resolved photoluminescence experiments have been used to study the nonlinear dynamics of novel monolithic GaInNAs/GaAs semiconductor saturable absorber mirrors at 1.08 and 1.55 m. The mirror structures were grown using molecular-beam epitaxy followed by Ni-ion implantation and thermal annealing. We present photoluminescence measurements showing the critical role of post-growth processing on the response time of GaInNAs/GaAs absorber mirrors. PACS 42.65.Re; 42.50.Nn; 42.70.Nq     

Generalized Sasaki Projections and Riesz Ideals in Pseudoeffect Algebras

A noncommutative version of generalized Sasaki projections in pseudoeffect algebras is introduced. It is proved that an ideal in a pseudoeffect algebra is Riesz if and only if it is closed under the right and left Sasaki projections. In lattice ordered pseudoeffect algebras, it is shown that generalized Sasaki projections are one-element sets, and their explicit form is found. It is shown that if a supremum of a normal Riesz ideal in a lattice ordered pseudoeffect algebra exists, it is a central element. These results extend those obtained recently by Avallone and Vitolo for effect algebras.