Dewetting of cellular monolayers

We investigate the physical principles of cellular layer stability. We show that cohesive cellular layers deposited on non-adhesive substrates are metastable and "dewet" by nucleation and growth of dry patches. The dewetting process can be induced either chemically by a non-adhesive surface treatment or, unlike simple liquids, physically by a decrease in the substrate rigidity. We thus unveil two mechanisms by which the integrity of cellular layers can be compromised. We interpret the opening dynamics by an analogy with the dewetting of viscous films. This analogy can be exploited to estimate parameters characterizing the mechanical response of a cellular layer.     

Ground state of magnetic dimers on metal surfaces

We present model studies of the ground state for magnetic dimers on metal surfaces. We find it can be neither ferromagnetic nor antiferromagnetic, but is often canted for nearest neighbors. Thus, the system cannot be described using bilinear exchange. We give a criterion which can be used quite generally to interrogate the local stability of ferromagnetically or antiferromagnetically aligned dimers, and which also may be used to infer the canting angle when canted states are stable.     

Entropic characteristics of photon tomograms

We study the electromagnetic-field tomograms for classical and quantum states. We use the violation of the positivity of entropy for the photon-probability distributions for distinguishing the classical and quantum domains. We show that the photon-probability distribution expressed in terms of optical or symplectic tomograms of the photon quantum state must be a nonnegative function, which yields the nonnegative Shannon entropy. We also show that the optical tomogram of the photon classical state provides the expression for the Shannon entropy, which can be nonpositive.     

Low-energy signatures of charge and spin fluctuations in Raman and optical spectra of the cuprates

We calculate the optical and Raman response within a phenomenological model of fermion quasiparticles coupled to nearly critical collective modes. We find that, whereas critical scaling properties might be masked in optical spectra due to charge conservation, distinct critical signatures of charge and spin fluctuations can be detected in Raman spectra exploiting specific symmetry properties. We compare our results with recent experiments on the cuprates.     

On instability of excited states of the nonlinear Schrödinger equation

We introduce a new notion of linear stability for standing waves of the nonlinear Schrödinger equation (NLS) which requires not only that the spectrum of the linearization be real, but also that the generalized kernel be not degenerate and that the signature of all the positive eigenvalues be positive. We prove that excited states of the NLS are not linearly stable in this more restrictive sense. We then give a partial proof that this more restrictive notion of linear stability is a necessary condition to have orbital stability.     

Stability of functions in Boolean models of gene regulatory networks

Boolean networks are used to model large nonlinear systems such as gene regulatory networks. We will present results that can be used to understand how the choice of functions affects the network dynamics. The so called bias-map and its fixed points depict much of the function's dynamical role in the network. We define the concept of stabilizing functions and show that many Post and canalizing functions are also stabilizing functions. Boolean networks constructed using the same type of stabilizing functions are always stable regardless of the average in-degree of network functions. We derive the number of all stabilizing functions and find it to be much larger than the number of Post and canalizing functions. We also discuss the implementation of functions and apply the presented results to biological data that give an approximation of the distribution of regulatory functions in eucaryotic cells. We find that the obtained theoretical results on the number of active genes are biologically plausible. Finally, based on the presented results, we discuss why canalizing and Post regulatory functions seem to be common in cells.     

The production of high-energy protons in central relativistic nuclear collisions

We extend our model of transport theory to be applicable to the inclusive production of protons with very high energy. We then consider the angular distribution of such protons, produced in a central collision of Ar on KC1 at 800 MeV per nucleon. The slight anisotropy observed in the data can be explained by a finite value of the friction constant which in turn determines the number of collisions needed for equilibrium to be reached. We also show that these data are quite sensitive to the reaction geometry and cannot be explained by the firestreak model.     

Initial applications of the molecular model to compute defect vibrations of oxygen in silicon

Abstract

We have employed the molecular model introduced first by Jaswal to compute the vibrational spectra of oxygen bearing defects in a silicon crystal. This was done in the context of a silicon molecular cluster with outer valencies terminated by hydrogen. We employ the MINDO/3 semi-empirical electronic structure method to compute the total energy of the molecular cluster. We examine the conditions in applications of the molecular model required for accurate predictions of oxygen local-mode vibrational frequencies. We find that the oxygen atom and its nearest neighbor silicon atoms must be allowed to vibrate. The nearest-neighbor and next nearest-neighbor shells of silicon atoms must be allowed to relax from their lattice positions. The outermost relaxed shell of silicon atoms should be bonded to silicon atoms in their lattice positions. We apply the molecular model to three defects of crystalline silicon; interstitial oxygen, oxygen in a vacancy (the A-center), and two oxygen atoms in a vacancy. Comparison of our computed local-mode oxygen vibration frequencies with experiment shows the computed oxygen local-mode frequencies to be almost uniformly 10% greater than those observed. Isotope shifts fit experiment equally well. We conclude that the molecular model represents an accurate and efficient approach for the computation of defect local mode vibrational frequencies for oxygen and other defects in crystalline silicon.     

Jump diffusion models and the evolution of financial prices

We analyze a stochastic model to describe the evolution of financial prices. We consider the stochastic term as a sum of the Wiener noise and a jump process. We point to the effects of the jumps on the return time evolution, a central concern of the econophysics literature. The presence of jumps suggests that the process can be described by an infinitely divisible characteristic function belonging to the De Finetti class. We then extend the De Finetti functions to a generalized nonlinear model and show the model to be capable of explaining return behavior.     

Scaling properties of spatially extended chaotic systems

We investigate the scaling properties of Lyapunov eigenvectors and exponents in coupled-map lattices exhibiting space-time chaos. A deep interrelation between spatiotemporal chaos and kinetic roughening of surfaces is postulated. We show that the logarithm of unstable eigenvectors exhibits scale-invariance with roughness exponents that can be predicted by a simple scaling conjecture. We argue that these scaling properties should be generic in spatially homogeneous extended systems with local diffusive-like couplings.     

Employment of Jacobian elliptic functions for solving problems in nonlinear dynamics of microtubules

We show how Jacobian elliptic functions （JEFs） can be used to solve ordinary differential equations （ODEs） describing the nonlinear dynamics of microtubules （MTs）. We demonstrate that only one of the JEFs can be used while the remaining two do not represent the solutions of the crucial differential equation. We show that a kinkbtype soliton moves along MTs. Besides this solution, we also discuss a few more solutions that may or may not have physical meanings. Finally, we show what kind of ODE can be solved by using JEFs.     

Indications on the mass of the lightest electroweak baryon

In general, an effective low-energy Lagrangian model of composite electroweak symmetry breaking contains soliton solutions that may be identified with technibaryons. We recall how the masses of such states may be related to the coefficients of fourth-order terms in the effective Lagrangian, and review the qualitative success of this approach for baryons in QCD. We then show how the current theoretical and phenomenological constraints on the corresponding fourth-order coefficients in the electroweak theory could be used to estimate qualitative lower and upper bounds on the lightest electroweak baryon mass. We also discuss how the sensitivity of the LHC experiments could enable these bounds to be improved.     

On the quantum mechanical superposition of macroscopically distinguishable states

We consider the superposition of macroscopically distinguishable states for a measuring process whose time evolution is described by the Schrödinger equation. We ask whether it is possible to observe interference effects due to the above mentioned superposition and how to observe them, taking into consideration an experiment performed by other authors. We find a necessary condition in order to be able to observe these effects. We also point out some very serious difficulties in observing them and analyse the connection between some of these difficulties and the Wigner-Araki-Yanase theory. We try to explain why the whole problem seems to us to be far from having a solution and we suggest some paths we think worthy of further investigation.     

Negative partial density of states in mesoscopic systems

Since the experimental observation of quantum mechanical scattering phase shift in mesoscopic systems, several aspects of it have not yet been understood. The experimental observations have also accentuated many theoretical problems related to Friedel sum rule and negativity of partial density of states. We address these problems using the concepts of Argand diagram and Burgers circuit. We can prove the possibility of negative partial density of states in mesoscopic systems. Such a conclusive and general evidence cannot be given in one, two or three dimensions. We can show a general connection between phase drops and exactness of semi classical Friedel sum rule. We also show Argand diagram for a scattering matrix element can be of few classes based on their topology and all observations can be classified accordingly.     

Influence of the electron-hole density profile on the reflectivity of laser irradiated silicon

We study the influence of the spatial extension of the electron-hole plasma created by a pump pulse on the reflectivity of a probe pulse. We show that the density deduced from reflectivity measurements is the surface density value with a very good accuracy, except very close to the plasma resonance. We also show that the resonance broadening due to the spatial inhomogeneity can be larger than the one due to free carriers absorption and has to be included in the usual experimental determination of the plasma relaxation time.     

Complete Measurements of Quantum Observables

We define a complete measurement of a quantum observable (POVM) as a measurement of the maximally refined (rank-1) version of the POVM. Complete measurements give information on the multiplicities of the measurement outcomes and can be viewed as state preparation procedures. We show that any POVM can be measured completely by using sequential measurements or maximally refinable instruments. Moreover, the ancillary space of a complete measurement can be chosen to be minimal.     

Generalization of Nambu's mechanics

We look for a generalization of the mechanics of Hamilton and Nambu. We have found the equations of motion of a classical physical system ofS basic dynamic variables characterized byS – 1 constants of motion and by a function of the dynamical variables and the time whose value also remains constant during the evolution of the system. The numberS may be even or odd. We find that any locally invertible transformations are canonical transformations. We show that the equations of motion obtained can be put in a form similar to Nambu's equations by means of a time transformation. We study the relationship of the present formalism to Hamiltonian mechanics and consider an extension of the formalism to field theory.     

Suppression of nonlinear interactions in resonant macroscopic quantum devices: the example of the solid-state ring laser gyroscope

We report fine-tuning of nonlinear interactions in a solid-state ring laser gyroscope by vibrating the gain medium along the cavity axis. We demonstrate both experimentally and theoretically that nonlinear interactions vanish for some values of the vibration parameters, leading to quasi-ideal rotation sensing. We eventually point out that our conclusions can be mapped onto other subfields of physics such as ring-shaped superfluid configurations, where nonlinear interactions could be tuned by using Feshbach resonance.     

Effect of nonlinear correlations on the statistics of return intervals in multifractal data sets

We study the statistics of return intervals between events above a certain threshold in multifractal data sets without linear correlations. We find that nonlinear correlations in the record lead to a power-law (i) decay of the autocorrelation function of the return intervals, (ii) increase in the conditional return period, and (iii) decay in the probability density function of the return intervals. We show explicitly that all the observed quantities depend both on the threshold value and system size, and hence there is no simple scaling observed. We also demonstrate that this type of behavior can be observed in real economic records and can be used to improve considerably risk estimation.