We construct a discrete model of fluid particles according to a two generator formalism for nonequilibrium thermodynamics. The model has the form of smoothed particle hydrodynamics including correct thermal fluctuations. A slight variation of the model reproduces the dissipative particle dynamics model with any desired thermodynamic behavior. The resulting algorithms have the following properties: mass, momentum, and energy are conserved, entropy is a nondecreasing function of time, and the thermal fluctuations produce the correct Einstein distribution function at equilibrium.

The drift mobility of ${\mathrm{O}}_2^{-}$ ions in argon gas near the liquid-vapor critical point has been measured as a function of the density $N$. Near $T_c$ the density-normalized ion mobility ${\mu }_{0}N$ shows a deep minimum for $N<\mathrm{}{N}_c$. This phenomenon was previously intepreted as the result of the formation of a correlated cluster of argon atoms around the ion because of the strong electrostriction exerted on the highly polarizable and compressible gas. We now suggest that a possible explanation is related to the onset of a parametric resonance of the bubble surrounding the ion. At resonance, additional energy is dissipated by sound waves, resulting in the observed mobility drop.

There exists a variety of physically interesting situations described by continuous maps that are nondifferentiable on some surface in phase space. Such systems exhibit novel types of bifurcations in which multiple coexisting attractors can be created simultaneously. The striking feature of these bifurcations is that in the presence of arbitrarily small noise they lead to fundamentally unpredictable behavior of orbits as a system parameter is varied slowly through its bifurcation value. This unpredictability gradually disappears as the speed of variation of the system parameter through the bifurcation is reduced to zero.

A new approach to nonlinear modeling is presented which, by incorporating the global behavior of the model, lifts shortcomings of both least squares and total least squares parameter estimates. Although ubiquitous in practice, a least squares approach is fundamentally flawed in that it assumes independent, normally distributed (IND) forecast errors: nonlinear models will not yield IND errors even if the noise is IND. A new cost function is obtained via the maximum likelihood principle; superior results are illustrated both for small data sets and infinitely long data streams.

The superposition of selected higher order harmonics and continuous background, produced in Ar gas through two time delayed 60 fs pulses at 800 nm, is measured as a function of their delay time. An isolated less than 100 as sharp feature, indicative for pulse production in the attosecond regime, followed by a subfemtosecond beating, indicative for the production of trains of sub-fs XUV pulses, is clearly observable in the resulting temporal trace. The trace Fourier transforms to a frequency spectrum composed of harmonics from the selected ensemble and a continuous background that correlates with the observed ultrashort feature. Numerical simulation spectra encompass similar temporal localization.

We show the existence of a region in the parameter space that defines the field dynamics in a Fabry-Pérot cylindrical cavity, where three output stable stationary states of the light are possible for a given localized incident field. Two of these states do not preserve the bilateral (i.e., left-right) symmetry of the entire system. These broken-symmetry states are the high-transmission nonlinear modes of the system. We also discuss how to excite these states.

Computer simulations of radiation processes in an air bubble and an argon bubble are performed under a condition of single-bubble sonoluminescence (SBSL) based on a quasiadiabatic compression model of a bubble collapse. It is clarified that emissions from excited molecules are strongly quenched by high pressure and temperature inside a SBSL bubble and SBSL originates in the emissions from plasma. It is pointed out that sonoluminescence from cavitation fields (MBSL) originates in emissions from excited molecules, which is not quenched due to the much lower pressure and temperature inside the MBSL bubbles.

We describe the electromagnetic theory of second-harmonic generation from the surface of a sphere that is small compared to the wavelength of light. In a leading-order expansion, the second-harmonic radiation is emitted in nonlocally excited electric dipole and locally excited electric quadrupole modes. We analyze the problem with particular emphasis on experimental aspects, such as the radiation pattern, polarization selection rules, determination of nonlinear susceptibilities, radiation efficiency, and spectral characteristics.

We demonstrate an efficient nonlinear process in which Stokes and anti-Stokes components are generated spontaneously in a multilevel medium coherently prepared by resonant, counterpropagating fields. A medium of this kind combines large nonlinear gain and efficient intrinsic feedback, thereby allowing for very weak optical fields to induce nonlinear processes. Mirrorless self-oscillation induced by microwatts of light power (nanojoules of pulse energy) is observed.

Experiments are performed to demonstrate the generation and propagation of acoustic solitary waves in an air-filled tube with a periodic array of Helmholtz resonators connected axially. The purpose is to verify the theoretical findings made so far that nonlinear acoustic waves do not evolve into a shock but into a solitary wave propagating steadily without any change of its smooth profile. To identify the solitary wave, the temporal pressure profile is compared directly with the theoretical profile of the solitary wave. Also checked are the relation between the peak sound pressure of the solitary wave and its half-value width in time, and the relation between the peak sound pressure and the deviation of propagation speed from sound speed. The experimental results show good quantitative agreement with the theory.

The behavior of a phase separating binary mixture in uniform shear flow is investigated by numerical simulations and in a renormalization group approach. Results show the simultaneous existence of domains of two characteristic scales. Stretching and cooperative ruptures of the network produce a rich interplay where the recurrent prevalence of thick and thin domains determines log-time periodic oscillations. A power-law growth $R\left(t\right)\sim t^{\alpha }$ of the average domain size, with $\alpha =4\mathrm{}/3$ and $\alpha =1\mathrm{}/3$ in the flow and shear direction, respectively, is shown to be obeyed.

We use numerical simulations to prove that the dynamics of the small-scale vorticity in two-dimensional incompressible fluids is nearly passive and that the feedback of the small scales onto the large-scale dynamics is important only for the part of the large-scale range which is adjacent or close to the small-scale range.

Kinematic dynamo theory is presented here for turbulent conductive fluids. We describe how inhomogeneous magnetic fluctuations are generated below the viscous scale of turbulence where the spatial smoothness of the velocity permits a systematic analysis of the Lagrangian path dynamics. We find analytically the moments and multipoint correlation functions of the magnetic field at small yet finite magnetic diffusivity. We show that the field is concentrated in long narrow strips and describe anomalous scalings and angular singularities of the multipoint correlation functions which are manifestations of the field's intermittency. The growth rate of the magnetic field in a typical realization is found to be half the difference of two Lyapunov exponents of the same sign.

We provide a simple physical picture which suggests that the asymptotic dynamics of inelastic gases in one dimension is independent of the degree of inelasticity. Statistical characteristics, including velocity fluctuations and the velocity distribution, are identical to those of a perfectly inelastic sticky gas, which in turn is described by the inviscid Burgers equation. Asymptotic predictions of this continuum theory, including the $t^{-2\mathrm{}/3}$ temperature decay and the development of discontinuities in the velocity profile, are verified numerically for inelastic gases.

We describe the two generic instabilities which arise in quasireversible systems and show that their normal forms are the well-known real Lorenz equations and the Maxwell-Bloch equations. We present for the first time analytic predictions for the appearance of Lorenz chaos and we describe a simple mechanical system which experimentally displays this chaotic behavior.

Taming chaos by weak harmonic perturbations has been a hot topic in recent years. This paper clarifies the mechanism for taming chaos theoretically. The model we consider in this paper is a forced Rayleigh oscillator with a diode. To simplify analyses, we consider the degenerate case, where the diode in the circuit operates as a switch. In this case, the governing equation of the circuit is represented by a constrained equation, and the Poincaré map is derived rigorously as a one-dimensional map. By the analysis of the Poincaré map, we clarify that taming chaos occurs by a saddle-node bifurcation.

We describe the first coherent generation of continuous wave radiation at 121.56 nm. A yield of $3\times {10}^8\mathrm{photons}/\sec$ (0.5 nW) has been achieved by four-wave mixing in mercury vapor. This continuous Lyman- $\alpha$ source could be used for laser cooling and precision spectroscopy of both hydrogen and antihydrogen.

Heap formations of granular materials in a vertical vibrating bed are studied by a simulation model in which the effect of decrease in local density due to vibration is modeled by the creation of empty sites in the bulk. Dynamics of empty sites are introduced to simulate the bulk flow while the surface flow is modeled by rules similar to the sandpile model. Phenomena such as heap formation and downward and upward convection modes can be reproduced. Phase diagrams similar to experimental observations can be constructed. A continuum model based on the empty site dynamics is also proposed. Predictions from the continuum model compare favorably with experimental observations.

The minimal surfaces bounded by a frame formed of a double helix and two horizontal rods are studied. The vibration equation shows that the helicoid is the stable surface when its winding number is small. The catenoid is locally isometric to the helicoid so that their vibration spectra are strongly related. While the catenoid is known to undergo a discontinuous transition to two disks, the helicoid is shown to become unstable through a continuous transition to a ribbon-shaped surface obtained experimentally, numerically, and analytically in the limit of infinite height. The normal forms of the bifurcations confirm the analysis.

Global bifurcations such as crises of attractors, explosions of chaotic saddles, and metamorphoses of basin boundaries play a crucial role in understanding the dynamical evolution of physical systems. Global bifurcations in dissipative planar maps are typically caused by collisions of invariant manifolds of periodic orbits, whose dynamical behaviors are described by rotation numbers. We show that the rotation numbers of the periodic orbits created at certain important tangencies are determined by the continued fraction expansion of the rotation number of the orbit involved in the collision.