Narrow Results

The diffusion of a Brownian particle exploring a meta-stable potential energy landscape with fluctuations is studied theoretically and numerically. The inverse harmonic part of the potential is replaced by a Gaussian approximated curve in the neighborhood of the saddle point and a new type of Monte-Carlo simulation algorithm is presented to simulate the random fluctuations of the potential energy. The probability of successful barrier surmounting and terminal arrival was calculated and compared with previous results. It is shown that, the replacement we have made is reasonable for the study of diffusion, which is primarily affected by the fluctuation of the barrier height, while other variations have little influence on the diffusion process. The Gaussian permutation and random Gaussian algorithms proposed here are expected to bring new ideas to the research of more complex problems.

A new methodology was introduced to investigate the pattern formation in time series systems due to their viscoelastic behavior. Four stochastic processes, uniform distribution, normal distribution, Nasdaq-100 stock market index, and a melody were studied within this context. The time series data were converted into vectorial forms in a scattering diagram. The sequential vectors can be split into its in-line (or conservative) and out-of-line (or dissipative) components. Thus, one can define the storage and loss modulus for conservative, and dissipative components, respectively. Instead of using the geometric Brownian equation which involves Wiener noise term, the changes were taken into consideration at every step by introducing “lethargy” concept and the deviation from it. Thus, the mathematics is somehow simplified, and the dynamical behavior of time series systems can be elucidated at every step of change. The viscoelastic behavior of time series systems reveals patterns of the viscoelastic parameters such as storage and loss modulus, and also of thermodynamic work-like and heat-like properties. Besides, there occur some minima and maxima in the distribution of the angles between the sequential vectors in the scattering diagram. The same is true for the change of entropy of the system.

We consider the presence of cosmic string induced density fluctuations in the universe at temperatures below the electroweak phase transition temperature. Resulting temperature fluctuations can restore the electroweak symmetry locally, depending on the amplitude of fluctuations and the background temperature. The symmetry will be spontaneously broken again in a given fluctuation region as the temperature drops there (for fluctuations with length scales smaller than the horizon), resulting in the production of baryon asymmetry. The time scale of the transition will be governed by the wavelength of fluctuation and, hence, can be much smaller than the Hubble time. This leads to strong enhancement in the production of baryon asymmetry for a second order electroweak phase transition as compared to the case when transition happens due to the cooling of the universe via expansion. For a two-Higgs extension of the Standard Model (with appropriate CP violation), we show that one can get the required baryon to entropy ratio if fluctuations propagate without getting significantly damped. If fluctuations are damped rapidly, then a volume factor suppresses the baryon production. Still, the short scale of the fluctuation leads to enhancement of the baryon to entropy ratio by at least 3–4 orders of magnitude compared to the conventional case of second order transition where the cooling happens due to expansion of the universe.

We review the main aspects of the warm inflation scenario, focusing on the inflationary dynamics and the predictions related to the primordial spectrum of perturbations, to be compared with the recent cosmological observations. We study in detail three different classes of inflationary models, chaotic, hybrid models and hilltop models, and discuss their embedding into supersymmetric models and the consequences for model building of the warm inflationary dynamics based on first principles calculations. Due to the extra friction term introduced in the inflaton background evolution generated by the dissipative dynamics, inflation can take place generically for smaller values of the field, and larger values of couplings and masses. When the dissipative dynamics dominates over the expansion, in the so-called strong dissipative regime, inflation proceeds with sub-Planckian inflaton values. Models can be naturally embedded into a supergravity framework, with SUGRA corrections suppressed by the Planck mass now under control, for a larger class of Kähler potentials. In particular, this provides a simpler solution to the "eta" problem in supersymmetric hybrid inflation, without restricting the Kähler potentials compatible with inflation. For chaotic models dissipation leads to a smaller prediction for the tensor-to-scalar ratio and a less tilted spectrum when compared to the cold inflation scenario. We find in particular that a small component of dissipation renders the quartic model now consistent with the current CMB data.

Evolution of spatially anisotropic perturbation created in the system formed after Relativistic Heavy Ion Collisions has been studied. The microscopic evolution of the fluctuations has been examined within the ambit of Boltzmann Transport Equation (BTE) in a hydrodynamically expanding background. The expansion of the background composed of quark gluon plasma (QGP) is treated within the framework of relativistic hydrodynamics. Spatial anisotropic fluctuations with different geometries have been evolved through Boltzmann equation. It is observed that the trace of such fluctuation survives the evolution. Within the relaxation time approximation, analytical results have been obtained for the evolution of these anisotropies. Explicit relations between fluctuations and transport coefficients have been derived. The mixing of various Fourier (or k) modes of the perturbations during the evolution of the system has been explicitly demonstrated. This study is very useful in understanding the presumption that the measured anisotropies in the data from heavy ion collisions at relativistic energies imitate the initial state effects. The evolution of correlation function for the perturbation in pressure has been studied and shows that the initial correlation between two neighbouring points in real space evolves to a constant value at later time which gives rise to Dirac delta function for the correlation function in Fourier space. The power spectrum of the fluctuation in thermodynamic quantities (like temperature estimated in this work) can be connected to the fluctuation in transverse momentum of the thermal hadrons measured experimentally. The bulk viscous coefficient of the QGP has been estimated by using correlations of pressure fluctuation with the help of Green–Kubo relation. Angular power spectrum of the anisotropies has been estimated in the appendix.

The power spectrum of the momentum distributions of particles have been estimated with Optical Glauber and Monte Carlo Glauber initial conditions for relativistic heavy ion collisions. The evaluation procedure adopted in this work is analogous to the one used in the calculation of power spectrum in Cosmic Microwave Background Radiation (CMBR). The power spectrum due to perturbations in the phase space distribution of the particles has also been evaluated. The perturbation in phase space has been evolved through the Boltzmann transport equation in an expanding quark–gluon plasma (QGP) background. The expansion of the QGP has been treated within the purview of (3+1)-dimensional relativistic hydrodynamics. We observe that the nonequilibrium effects introduced as perturbations in the phase space distributions can be traced through its variation with temperature which is distinctly different from the case of vanishing perturbation. A relation has been derived between the power spectrum and the flow harmonics.

The dynamic behaviors of the new soliton in the improved Davydov model in the protein molecules at biological temperature have been numerically simulated by utilizing the dynamic equations for the bio-energy transport and the Runge–Kutta way. In this simulation the influences of the temperature and structure disorders of the protein molecules on the soliton transporting the bio-energy have been completely considered. We find that the new soliton is quite stable in the cases of motion of a long time of 300 ps and of disorders of the structures of the proteins at biological temperatures of 300 K–320 K. The disorders of the structures contain the disorder of mass sequence of amino acids and the fluctuations of the coupling constant, force constant and dipole- dipole interaction constant and ground state energy of the proteins, designating the features of its structure and interactions between the particles in it. However, the soliton disperses in the cases of higher temperature of 325 K and larger structure disorders. The numerical results show that the new soliton is very robust against the influences of the thermal perturbation and structure disorders at biological temperature 300 K, its lifetime and critical temperature are at least 300 ps at 300 K and 320 K, respectively. These results are also consistent with analytical data.

Electro-rheological (ER) fluid is a smart suspension which can be changed promptly from Newtonian to Bingham plastic material when subjected to a high-intensity electric field. This property of ER fluid makes it possible to be applied in adaptive energy absorbers. As the impact velocity encountered in applications could be very large, it is necessary to characterize the ERF under high shear rate. In this study, a capillary rheo-meter with parallel duct was designed and manufactured which is capable of producing a shear rate as high as 5000(1/s). Two giant ER fluids with mass concentration C = 51% and 44.5% and a commercial density-matched ER fluid with C = 37.5% were characterized. The experimental results show that when the ER fluids are free of electric field (E = 0kV/mm), they are Newtonian. However, for the former two ER fluids, the deposition effect is very remarkable and stirring has to be made continuously to keep the suspension stable. With the increase of the electric field intensity, the yield shear stresses of ER fluids increase exponentially but their viscosities do not change much. It is also found that within the parallel duct, the flow of ER fluids exhibits notable fluctuations, whose period increases with the increase of electric field intensity and is independent of the shear rate.

One of the major issues concerning the study of a dynamical system is the response to perturbations. In climate dynamics, for example, it is of major interest to understand how a given variable, e.g., the temperature, is sensitive to alterations of some other component of the system, e.g., the greenhouse gas concentration. We review the connection between equilibrium and non-equilibrium properties, also known as Fluctuation-Relaxation Relation, and its main aspects in chaotic and turbulent systems. We consider, in particular, the effects of the fast variables on the slow variables in a multiscale system, as far as the sensitivity properties are concerned. Two examples about (widely speaking) climate modelling are discussed: the Lorenz-96 model and the double-potential well model. Both of them, despite their apparent simplicity, hide the same kind of interesting features of much more complex systems.

The concrete mixer possesses the basic performance "mixing efficiency", and is one of the most important construction machines on the step that manufactures concrete. The bi-axial forced-mixing type of the mixer is high and the mixing efficiency is the highest. The flow patterns of this type mixer are divided into two: the locally crossing flow and the globally circulating flow. The globally circulating flow uniformly mixes fine particle materials that differ greatly the grain size turned on and are various and cement active. The locally crossing flow contributes to "Knead" to improve the contact frequency of the cement particle and water.

In the research, concrete was assumed to be a viscous model of one phase system for the model mixer of two types with different area of the locally crossing flow, the mixing efficiency curve of the model concrete of the high viscosity and the low viscosity was a process of becoming uniform with the axial rotation, and quantification was attempted. The second research tried the quantification of the crossing flow around the blade generated when two circulating flows crossed by the pressure fluctuation of the pressure sensor installed in the surface of the blade of the mixer was attempted, and the magnitude of the crossing Flow generated in the model mixer of two types and the correlation of the mixing efficiency curve were considered.

The present paper reviews some general aspects of the stochastic analysis performed by the author in the field of statistical physics, particularly concerning the order formation from unstable states. First, a brief review and some new results are given on the generalization of the Itô-type and Stratonovich-type stochastic integrals. Their physical meaning is also discussed form the viewpoint of symmetry. Secondly, Kubo's stochastic Liouville equation is presented from the viewpoint of separation of procedures, to give a simple derivation of the Fokker–Planck equation. Thirdly, the scaling theory of order formation from the unstable point is re-formulated by introducing here a new order parameter to characterize macroscopic order formation and to clarify the synergetic effect of the initial fluctuation, random noise and nonlinearity. Finally, some discussions are given, particularly concerning applications of the Hida calculus based on the Gelfand triplet space.

Based on the theory of non-equilibrium statistics and density operator equation, the generalized master equation satisfied by characteristic function for the non-extensive reaction-diffusion systems affected by pressure is derived by calculating the time variation of probability distribution function, where the pressure of the non-extensive systems is given in the framework of Tsallis statistics. This new equation not only depends on the non-extensive parameter but also has more nonlinear terms as compared with the master equation in the phenomenological theory and thus has more generality.

The mesoscopic single RLC (resistance-inductance-capacitance) circuit and the RLC circuit including complicated coupling are quantized by employing Dirac's standard canonical quantization method. The thermal effects for the systems are investigated by virtue of GHFT (the generalized Hellmann–Feynman theorem). The results distinctly show the effect of temperature on the quantum fluctuation.

An externally activated nonequilibrium anomalous reactive rate process is studied by taking into account both internal and external fluctuations in a unified way. The probability of diffusion passing over the saddle point and the reactive rate together with the effective transmission coefficient are calculated by the method of reactive flux. It is found that the fierceness of internal fluctuation is always harmful to the diffusion of particles. However, the external activation may be beneficial to the rate process.

A class of delayed ratio-dependent Gause-type predator–prey model is considered. We study the eigenvalue problem for the linearized system at the coexisting equilibrium. For a critical case when the characteristic equation has a single zero root and a simple pair of pure imaginary roots, a complete bifurcation analysis is presented by employing the center manifold reduction and the normal form method. We analyzed the influence of the time delay on the Hopf–Fold bifurcation and showed the occurrence of quasi-periodic motion and bursting behavior. This phenomenon is in line with the seasonal variation law of the population.

Self-affine multiplicity scaling is investigated in the framework of two-dimensional factorial moment methodology using the concept of the Hurst exponent (H) considering different bins of the phase space. We have investigated the fluctuation pattern of emitted pions in ²⁴Mg-AgBr interactions at 4.5 AGeV and this study reveals that the fluctuation is self-similar in some bins, whereas it is self-affine in other bins, that is, the multiplicity scaling is bin-dependent.

We studied the effects of the Tsallis distribution on the transverse momentum fluctuation in high energy collisions. The parton–hadron duality and the Bose–Einstein type correlation between partons were assumed. The fluctuation was calculated in the boost-invariant picture for the expectation value used in the Boltzmann–Gibbs (BG) statistics and for the expectation value used in the Tsallis nonextensive statistics. It was shown that the fluctuation is a function of $\eta$ which is the ratio of the inverse temperature to the correlation length. We found the following points: (1) the fluctuation depends on the form of the distribution and depends weakly on the definition of the expectation value used in the statistics, (2) the fluctuation increases as the entropic parameter value of the Tsallis distribution increases, and (3) the variation of the fluctuation as a function of the entropic parameter for the expectation value used in the BG statistics is larger than that for the expectation value used in the Tsallis nonextensive statistics in the wide range of $\eta$.

A noninteracting hadron resonance gas model is used often to study the hadronic phase formed in heavy ion collisions. Interaction among various hadronic constituents can be included using an S-matrix-based virial expansion approach. The virial coefficients require the dynamical information about the scattering phase shifts, which is used to compute various thermodynamic observables of an interacting hadronic gas. The attractive part of the phase shifts are calculated using K-matrix formalism while the repulsive part is obtained by fitting to experimental data. Calculation of various thermodynamic variables like pressure, energy density, specific heat capacity, etc., along with the second and higher-order correlations and fluctuations of conserved charges are done, first with only attraction and then with both attraction and repulsion included. Comparison of S-matrix results indicate a better agreement with lattice QCD data than the ideal HRG model across all thermodynamic variables.

Correlation among singly charged particles emitted in the forward and backward pseudo-rapidity cones is measured in ${}^{16}$O-Ag/Br and ${}^{32}$S-Ag/Br interactions at an incident energy of $200$ GeV/nucleon. Event-by-event fluctuations in the charged particle multiplicities and their pseudo-rapidity values are also investigated in terms of some known statistical measures. Evidences of short-ranged particle correlation and cluster formation in the pseudo-rapidity space are found from our analysis. A microscopic transport model based on the Ultra-relativistic Quantum Molecular Dynamics could not match the experimental results. The differences between experimental observation and corresponding simulation could neither be accounted for even when a Bose–Einstein type of correlation effect is implemented into the simulated data.

This paper deals with the target excitation dependence of the multifractal specific heat of pions produced in nucleus-nucleus collisions at 60 and 200 AGeV. Fluctuation pattern of pions is studied in two dimensions considering anisotropy of phase space. The parameter characterizing the anisotropy of phase space, Hurst exponent, is extracted by fitting one-dimensional factorial moment saturation curves. Values of intermittency exponent α_q and generalized dimension D_q are determined. The fluctuation pattern reveals multifractal behavior at all target excitations at both energies. The multifractal specific heat c is found to depend on target excitation and the dependence is found to be more pronounced at lower energy. The results are discussed in detail.