Oscillations vs. chaotic waves: Attractor selection in bistable stochastic reaction–diffusion systems

In bistable systems, the long-term behavior of solutions depends on the location of the initial conditions. In a deterministic setting, where the initial condition is kept fixed in one particular basin of attraction, repeated numerical simulations will always lead to the same long-term behavior. The other possible asymptotic solution type will never be observed. This clear distinction does not hold anymore if the system is forced by random fluctuations. In this case, both asymptotic solutions can be attained, and the relative frequency of different long-term behaviors observed in many repeated simulation runs will follow a certain probability distribution. We present a simple reaction–diffusion model of spatial predator–prey interaction, where depending on the initial spatial distribution of the two populations either spatially homogeneous or spatiotemporal irregular oscillations may be observed. We show by repeated stochastic simulations that, when starting in the basin of attraction of the spatiotemporal irregular solution, in the randomly forced system the probability to observe spatially homogeneous oscillations instead of spatiotemporally irregular oscillations follows a non-trivial bimodal distribution.     

Reactive diffusion in the Ti–Si system and the significance of the parabolic growth constant

Solid diffusion couple experiments are conducted to analyse the growth mechanism of the phases and the diffusion mechanism of the components in the Ti–Si system. The calculation of the parabolic growth constants and the integrated diffusion coefficients substantiates that the analysis is intrinsically prone to erroneous conclusions if it is based on just the parabolic growth constants determined for a multiphase interdiffusion zone. The location of the marker plane is detected based on the uniform grain morphology in the TiSi₂ phase, which indicates that this phase grows mainly because of Si diffusion. The growth mechanism of the phases and morphological evolution in the interdiffusion zone are explained with the help of imaginary diffusion couples. The activation enthalpies for the integrated diffusion coefficient of TiSi₂ and the Si tracer diffusion are calculated as 190 ± 9 and 197 ± 8?kJ/mol, respectively. The crystal structure, details on the nearest neighbours of the components, and their relative mobilities indicate that the vacancies are mainly present on the Si sublattice.     

On the effects of a varied diffusion time in vivo: is the diffusion in white matter restricted?

The aim of this work was to study the diffusion-related signal attenuation curves (signal-vs.-b curves) measured perpendicular and parallel to the neuronal fibers of the corticospinal tract in vivo and to determine whether effects of restricted diffusion could be observed when varying the diffusion time (T_D). A biexponential model and a two-compartment model including exchange according to the Kärger formalism were employed to analyze the signal-vs.-b curves. To validate the two-compartment model, restricted diffusion with exchange was simulated for uniformly sized cylinders, using different diameters and exchange times. The model was shown to retrieve the simulated parameters well, also when the short gradient pulse approximation was not met. The in vivo measurements performed perpendicular to the tracts, using b values up to 28000 s/mm² and T_D values between 64 and 256 ms, did not show the effects of restricted diffusion as expected from previous ex vivo studies. The applied two-compartment model yielded an average axonal diameter of about 4 μm and an intracellular exchange time of about 300 ms, but did not fit statistically well to the data. In conclusion, this study indicates that if the diffusion is modeled as two compartments, of which one is restricted, exchange must be included in the model.     

Arnol’d diffusion in a system with 2.5 degrees of freedom: Classical and quantum mechanical approaches

Arnol’d diffusion, a universal phenomenon in nonlinear dynamics, is analyzed for a model system with 2.5 degrees of freedom. Only the three primary order resonances are taken into account, and the results obtained by using classical and quantum mechanical approaches are compared. It is shown that the parameter dependence of the rate of quantum Arnol’d diffusion is similar to the classical one, but the quantum diffusion coefficient is smaller by approximately an order of magnitude. It is found that the existence of a threshold with respect to perturbation parameters, pointed out earlier, is not an indispensable feature of quantum Arnol’d diffusion. It is shown that a quantum system with weakly overlapping resonances can exhibit mixed dynamics that has no classical counterpart (diffusion along a resonance superimposed by oscillations across the overlapped resonances).     

Onset of Rayleigh-Bénard convection in a ternary liquid system and the Onsager law with generalized thermal diffusion

For the ternary system isopropanol-ethanol-water, a model was proposed to estimate the cross diffusion coefficients from measurements of the critical parameters for the onset of Rayleigh-Bénard convection, together with the consideration of the reciprocity laws of Onsager. Among the three forms of the chemical potentials used, not a single chemical potential was found to provide a correlation between the Onsager laws and the experimental data. The present study shows that consideration of a generalized thermal diffusion term taking account of all components is adequate to estimate quantitative values of the cross diffusion coefficients.     

Cooperative emission from an ensemble of three-level Λ radiators in a cavity: An insight from the viewpoint of dynamics of nonlinear systems

Cooperative radiation emitted by an ensemble of three-level optical systems with a doublet in the ground state (Λ scheme), which is placed into a cyclic cavity, is studied theoretically. In contrast to the two-level model of emitters, this process with such a configuration of operating transitions may occur without population inversion in the whole, if the doublet is prepared at the initial instant in a superposition (coherent) state. In the ideal case of a Hamilton system, in which the cavity losses and relaxation in the radiator ensemble are disregarded, the conservation laws are derived, which allow a substantial reduction of the dimension of the phase space of the model (?¹¹ → ?⁵) and the application of methods of dynamics of nonlinear systems for analyzing the three-level superradiance under these conditions. The possibility of different (both quasiperiodic and chaotic) scenarios of the three-level superradiance is demonstrated on the basis of Poincaré’s mappings. Global bifurcation of the system upon a transition from the conventional superradiance regime to inversionless one is revealed. The effects of cavity losses, as well as homogeneous and inhomogeneous broadening in the system of radiators on the regularities found are also discussed.     

Influence of structure disorders and temperaturesof systems on the bio-energy transport in proteinmolecules (Ⅱ)

The influence of molecular structure disorders and physiological temperature on the states and properties of solitons as transporters of bio-energy are numerically studied through the fourth-order Runge-Kutta method and a new theory based on my paper [Front. Phys. China, 2007, 2(4): 469]. The structure disorders include fluctuations in the characteristic parameters of the spring constant, dipole-dipole interaction constant and exciton-phonon coupling constant, as well as the chain-chain interaction coefficient among the three channels and ground state energy resulting from the disorder distributions of masses of amino acid residues and impurities. In this paper, we investigate the behaviors and states of solitons in a single protein molecular chain, and in α-Helix protein molecules with three channels. In the former we prove first that the new solitons can move without dispersion, retaining its shape, velocity and energy in a uniform and periodic protein molecule. In this case of structure disorder, the fluctuations of the spring constant, dipole-dipole interaction constant and exciton-phonon coupling constant, as well as the ground state energy and the disorder distributions of masses of amino acid residues of the proteins influence the states and properties of motion of solitons. However, they are still quite stable and are very robust against these structure disorders, even in the presence of larger disorders in the sequence of masses, spring constants and coupling constants. Still, the solitons may disperse or be destroyed when the disorder distribution of the masses and fluctuations of structure parameters are quite great. If the effect of thermal perturbation of the environment on the soliton in nonuniform proteins is considered again, it is still thermally stable at the biological temperature of 300 K, and at the longer time period of 300 ps and larger spacing of 400 amino acids. The new soliton is also thermally stable in the case of motion over a long time period of 300 ps in the region of 300–320 K under the influence of the above structure disorders. However, the soliton disperses in the case of a higher temperature of 325 K and in larger structure disorders. Thus, we determine that the soliton’s lifetime and critical temperature are 300 ps and 300–320 K, respectively. These results are also consistent with analytical data obtained via quantum perturbed theory. In α-Helix protein molecules with three channels, results obtained show that these structure disorders and quantum fluctuations can change the states and features of solitons, decrease their amplitudes, energies and velocities, but they still cannot destroy the solitons, which can still transport steadily along the molecular chains while retaining energy and momentum when the quantum fluctuations are small, such as in structure disorders and quantum fluctuations of and and . Therefore, the solitons in the improved model are quite robust against these disorder effects. However, the solitons may be dispersed or disrupted in cases of very large structure disorders. When the influence of temperature on solitons is considered, we find that the new solitons can transport steadily over 333 amino acid residues in the case of motion over a long time period of 120 ps, and can retain their shapes and energies to travel forward along protein molecules after mutual collision of the solitons at the biological temperature of 300 K. Therefore, the soliton is also very robust against thermal perturbation of the α-helix protein molecules at 300 K. However, the soliton disperses in cases of higher temperatures at 325 K and in larger structure disorders. Thus, their critical temperature is about 320 K. When the effects of structure disorder and temperature are considered simultaneously, the soliton has high thermal stability and can transport for a long time along the protein molecular chains while retaining its amplitude, energy and velocity, even though the fluctuations of the structure parameters and temperature of the medium increase continually. However, the soliton disperses in the larger fluctuations of and at T=300 K, and at temperatures higher than 315 K when the fluctuations are and . This means that the critical temperature of the soliton is only 315 K in this condition. In a word, we can conclude from the above investigations that the soliton in the improved model is very robust against the structure disorders and thermal perturbation of proteins at the biological temperature of 300 K in α-helix protein molecules, and is a possible bio-energy transport carrier; the improved model is a possible candidate for the mechanism of this transport.      

Evaluation of eigenfunctions from compound matrix variables in non-linear elasticity – I. Fourth order systems

We show how the compound matrix method can be used to produce eigenfunctions as well as eigenvalues for bifurcation problems in non-linear elasticity. For typical problems in elasticity the boundary conditions require a different treatment to that required for typical problems in fluid mechanics. For elasticity problems we have to use an additional shooting method to ensure that the boundary conditions are satisfied.     

Temporal Fluctuations of Radiation of π and σ Components of a Mercury Capillary Lamp in the Presence of the Transverse Zeeman Effect

Russian Physics Journal - Temporal fluctuations of the intensity of radiation of the π component and of the sum of the σ+ and σ components of capillary low-pressure lamps filled with...     

Analytic modeling of instabilities driven by higher-order modes in the HLS Ⅱ RF system with a higher-harmonic cavity

The utility of a passive fourth-harmonic cavity plays a key role in suppressing longitudinal beam instabilities in the electron storage ring and lengthens the bunch by a factor of 2.6 for the phase Ⅱ project of the Hefei Light Source (HLS Ⅱ ). Meanwhile, instabilities driven by higher-order modes (HOM) may limit the performance of the higher-harmonic cavity. In this paper, the parasitic coupled-bunch instability, which is driven by narrow band parasitic modes, and the microwave instability, which is driven by broadband HOM, are both modeled analytically. The analytic modeling results are in good agreement with those of our previous simulation study and indicate that the passive fourth-harmonic cavity suppresses parasitic coupled-bunch instabilities and microwave instability. The modeling suggests that a fourth-harmonic cavity may be successfully used at the HLS Ⅱ .     

Mössbauer probe spectroscopy of the initial stage of mechanical alloying in a binary Mg-Fe system in comparison to Al-Fe and Si-Fe systems

This work compares the results from investigating a Mg-⁵⁷Fe binary system with a 99: 1 atomic ratio to previously obtained data for systems based on Al and Si. It is shown that the necessary conditions of the process are the formation of a nanostructure state and the penetration of Fe atoms into the boundaries of the grains of the basic elements. Substantial differences are observed in the kinetics of nanostructure state formation and the consumption of Fe in the Mg → Al → Si series, due to the determining role of the chemical interaction of Mg (Al, Si) with Fe.     

‘Planetodiversity’: the variety of planets and planetary systems in the Universe

‘Planetodiversity’ is a composite word from planetary diversity. This denomination wants to parallel the common use of the term biodiversity employed in biology but translated here to the context of planetary sciences due to the proliferating variety of planets discovered outside the Solar System and theoretically proposed to exist. There are two properties that allow us a classification of a body as a planet or more generally as a ‘planetary mass object’: the orbital configuration and the physical structure (mass, energy and chemical composition). This leads respectively to the concepts that we term the ‘orbital planetodiversity’ and the ‘physical planetodiversity’. We present in a comparative way the basic planetary types observed or expected to exist within the framework of these two concepts.     

Secondary dislocation structures in a Ni–TiN system from the GMS and O-lattice theory

The preferred state in an interface is the key to evaluating misfit strain, especially for the interphase interfaces in secondary preferred state. The structure of good matching site (GMS) in a GMS clusters offers a guidance for the preferred state, especially for identifying the coincidence site lattice in two dimension for secondary preferred state and the Burgers vectors in a large misfit system. Here, we combine the GMS with O-lattice theory to calculate the secondary dislocation structure in the habit planes of the type II and III TiN precipitates in a Ni–TiN system. We find that under a slight elastic strain, the type III habit plane contains a single set of secondary dislocations, consistent with the experimental observation. The type II habit plane contains three sets of secondary dislocations, two of which can be relaxed to be nearly parallel and another of which may be invisible in diffraction contrast due to its short Burgers vector. The present study provides a reasonable interpretation to the observed interfacial dislocations, and also suggests Burgers vectors for the dislocations that are not determined experimentally.     

Gravitational field of quasistationary concentrated systems with rotation in the newman — penrose formalism. I

A series of solutions of Einstein's equations with term is found; it describes the gravitational field of quasistationary concentrated systems containing electric and magnetic charges. The metrics are of Petrov type D and have rotation and expansion. The solutions are interpreted physically. In this, the first part of the paper, the problem is formulated in terms of the spin coefficient method.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 113–117, March, 1976.     

Monte Carlo simulations in the isothermal—isobaric ensemble: the requirement of a ‘shell’ molecule and simulations of small systems

A modification of the widely used Monte Carlo method for determining thermophysical properties in the isothermal-isobaric ensemble is presented. The new Monte Carlo method, now consistent with recent derivations describing the proper statistical mechanical formulation of the constant pressure ensemble for small systems, requires a ‘shell’ molecule to uniquely identify the volume of the system, thereby avoiding the redundant counting of configurations. Ensemble averages obtained with the new algorithm differ from averages calculated with the old Monte Carlo method, particularly for small system sizes, although both sets of averages become equal in the thermodynamic limit. Monte Carlo simulations in the constant pressure ensemble applied to the Lennard-Jones fluid demonstrate these differences for small systems. Peculiarities of small systems are also discussed, revealing that ‘shape’ is an important thermodynamic variable. Finally, an extension of the Monte Carlo method to mixtures is presented.     

Translation–rotation coupling in the self–diffusion of fluids: molecular dynamic investigation and a generalized exponential approach

Detailed molecular dynamics simulations are carried out to investigate the translation–rotation coupling in linear molecules. We calculated the moment of inertia ratio dependence of the self–diffusion coefficients D, the so–called dynamic isotope effect on the self–diffusion, in pure fluids. Our model systems consist of linear homonuclear pseudo–triatomic rigid molecules for three different molecular sizes over a wide range of density for a given temperature. For a compact representation of our results an exponential approach is employed, which demonstrates a strong translation–rotation coupling on the self–diffusion coefficient in a linear molecule. We find as a main result that in contrast to the low density behaviour at high densities the change of the rotation–translation coupling as a function of the moments of inertia is quite similar for all investigated molecules and we could explain this finding by a careful inspection of the corresponding velocity autocorrelation functions. Finally we present a comparison of experimental data for 20 neat molecular liquids and the corresponding theoretical predictions based on our findings for linear molecules. The good overall agreement indicates that our approach can be generalized and is therefore not only a compact representation of the calculated data but has also large predictive capabilities.