In this work we analyze the pressure motor patterns used by canaries (Serinus canaria) during song, both in the cases of males and testosterone treated females. We found a qualitative difference between them which was not obvious from the acoustical features of the uttered songs. We also show the diversity of patterns, both for males and females, to be consistent with a recently proposed model for the dynamics of the oscine respiratory system. The model not only allows us to reproduce qualitative features of the different pressure patterns, but also to account for all the diversity of pressure patterns found in females.

We investigate the effects of anisotropy on finite-size scaling of site percolation in two dimensions. We consider a lattice of size $n_x\times n_y$. We define an aspect ratio $\omega =n_x∕n_y$ and consider the mean connected fraction $P$ (averaged over the realizations) as a function of the site occupancy probability $\left(p\right)$, the system size $\left(n_x\right)$, and this aspect ratio. It is clear that there is an easy direction for percolation, which is in the short direction (i.e., $y$ if $\omega >1$) and a difficult direction which is along the long axis. We define an apparent percolation threshold in each direction as the value of $p$ when 50% of realizations connect in that direction. We show that standard finite-size scaling applies if we use this apparent threshold. We also find a finite-size scaling for the fluctuations about this mean connected fraction.

D. Stauffer and A. Aharony, Introduction to Percolation Theory (Taylor and Francis, London, 1992).

We study the effects of thermal noise in a stochastic Langevin formulation of a typical example of a pattern-forming system with two-dimensional circular domain. A greater tendency towards dynamic cellular states is observed when the pattern-forming system is subjected to noise, which seems to explain the prevailing behavior of related laboratory experiments. We also report on two-dimensional numerical observations of certain dynamic states, homoclinic intermittent states, which until now, had only been observed in laboratory experiments.

In very compressible fluids, such as fluids near their critical point, the bulk fluid is adiabatically thermalized by the expansion of a hot boundary layer. Thanks to this thermomechanical process (the so-called piston effect) the fluid velocity at the edge of the boundary layer can become very high when the heating power is concentrated in a fissure. Spectacular jets are then observed in $\mathrm{S}{\mathrm{F}}_6$ and $\mathrm{C}{\mathrm{O}}_2$. Data obtained under weightlessness (in order to remove convection) and data obtained under earth gravity are compared and analyzed. They emphasize the key role of the boundary layer expansion for thermal phenomena in compressible fluids and the hydrodynamic nature of the piston effect.

We study the effect of pulse duration on the heating of single van der Waals bound argon and deuterium clusters by a strong laser field using a two-dimensional (2D) electrostatic particle-in-cell (PIC) code in the range of laser-cluster parameters such that kinetic as well as hydrodynamic effects are active. Heating is dominated by a collisionless resonant absorption process that involves energetic electrons transiting through the cluster. A size-dependent intensity threshold defines the onset of this resonance [T. Taguchi et al., Physical Review Letters, 92, 20 (2004)]. It is seen that increasing the laser pulse duration lowers this intensity threshold and the energetic electrons take multiple laser periods to transit the cluster instead of one laser period. Our simulations also show that strong electron heating is accompanied by the generation of a high-energy peak in the ion energy distribution function. We also calculate the yield of thermonuclear fusion neutrons from exploding deuterium clusters using the PIC model with periodic boundary conditions that allows for the interaction of ions from neighboring clusters.

We consider the coupled propagation of the pump and Stokes waves in a Raman active medium accounting for the group velocity walk off and group velocity dispersion. Interplay of the Raman coherence and the dispersion can lead to the formation of a complete band gap in the spectrum of linear waves consisting of the two consecutive subgaps located at different frequencies. Using an approximate analytic technique, we find exponentially localized solitons residing in the complete gap, and find algebraic solitons when the gap is closed. Feasibility of observation of these structures in hollow fibers is discussed.

A formulation of the intermolecular force in the nonideal-gas lattice Boltzmann equation method is examined. Discretization errors in the computation of the intermolecular force cause parasitic currents. These currents can be eliminated to roundoff if the potential form of the intermolecular force is used with compact isotropic discretization. Numerical tests confirm the elimination of the parasitic currents.

Experiments show that the spatiotemporal spectral broadening of an intense pump pulse in a Kerr medium in the presence of strong higher-order dispersion does not lead to symmetric profiles, and hence cannot be interpreted as standard modulational instability of a plane and monochromatic nonlinear eigenmode. The highly asymmetric features of the generated $(K_{\perp },\Omega )$ spectrum are due to odd-order dispersion terms and are interpreted in terms of spontaneous formation of stationary conical waves.

We consider the escape over a fluctuating potential barrier with a three-state Markovian noise. The resonant activations (RA’s) for the mean first-passage times as functions of the transition rates ${\gamma }_1$, ${\gamma }_2$, and ${\gamma }_3$ of the three-state Markovian noise are obtained, respectively. The effect of the three values of the three-state Markovian noise on the RA’s is investigated.

We suggest a procedure to identify those parts of the spectrum of the equal-time correlation matrix $\mathbf{C}$ where relevant information about correlations of a multivariate time series is induced. Using an ensemble average over each of the distances between eigenvalues, all nearest-neighbor distributions can be calculated individually. We present numerical examples, where (a) information about cross correlations is found in the so-called “bulk” of eigenvalues (which generally is thought to contain only random correlations) and where (b) the information extracted from the lower edge of the spectrum of $\mathbf{C}$ is statistically more significant than that extracted from the upper edge. We apply the analysis to electroencephalographic recordings with epileptic events.

The new mathematical framework based on the free energy of pure classical fluids presented by Rohrmann [Physica A 347, 221 (2005)] is extended to multicomponent systems to determine thermodynamic and structural properties of chemically complex fluids. Presently, the theory focuses on $D$-dimensional mixtures in the low-density limit (packing factor $\eta <0.01$). The formalism combines the free-energy minimization technique with space partitions that assign an available volume $v$ to each particle. $v$ is related to the closeness of the nearest neighbor and provides a useful tool to evaluate the perturbations experimented by particles in a fluid. The theory shows a close relationship between statistical geometry and statistical mechanics. New, unconventional thermodynamic variables and mathematical identities are derived as a result of the space division. Thermodynamic potentials ${\mu }_{il}$, conjugate variable of the populations $N_{il}$ of particles class $i$ with the nearest neighbors of class $l$ are defined and their relationships with the usual chemical potentials ${\mu }_i$ are established. Systems of hard spheres are treated as illustrative examples and their thermodynamics functions are derived analytically. The low-density expressions obtained agree nicely with those of scaled-particle theory and Percus-Yevick approximation. Several pair distribution functions are introduced and evaluated. Analytical expressions are also presented for hard spheres with attractive forces due to Kac-tails and square-well potentials. Finally, we derive general chemical equilibrium conditions.

The gap between the eigenvalues of the dominant and subdominant eigenvectors of the evolution operator associated with the contact process in one dimension is studied by perturbative series expansions in powers of the creation rate. The series expansion for the gap was computed with 49 coefficients. An analysis by Padé approximants allowed the determination of the critical creation rate and the time correlation critical exponent.

We characterize the kinematics of bubbles in a sheared two-dimensional foam using statistical measures. We consider the distributions of both bubble velocities and displacements. The results are discussed in the context of the expected behavior for a thermal system and simulations of the bubble model. There is general agreement between the experiments and the simulation, but notable differences in the velocity distributions point to interesting elements of the sheared foam not captured by prevalent models.

We derive from first principles (without resorting to the replica trick) a density-functional theory for fluids in quenched disordered matrices (QA-DFT). We show that the disorder-averaged free energy of the fluid is a functional of the average density profile of the fluid as well as the pair correlation of the fluid and matrix particles. For practical reasons it is preferable to use another functional: the disorder-averaged free energy plus the fluid-matrix interaction energy, which, for fixed fluid-matrix interaction potential, is a functional only of the average density profile of the fluid. When the matrix is created as a quenched configuration of another fluid, the functional can be regarded as depending on the density profile of the matrix fluid as well. In this situation, the replica Ornstein-Zernike equations which do not contain the blocking parts of the correlations can be obtained as functional identities in this formalism, provided the second derivative of this functional is interpreted as the connected part of the direct correlation function. The blocking correlations are totally absent from QA-DFT, but nevertheless the thermodynamics can be entirely obtained from the functional. We apply the formalism to obtain the exact functional for an ideal fluid in an arbitrary matrix, and discuss possible approximations for nonideal fluids.

The motion of chemically driven droplets is analyzed by applying a solvability condition of perturbed hydrodynamic equations affected by the adsorbate concentration. Conditions for traveling bifurcation analogous to a similar transition in activator-inhibitorsystems are obtained. It is shown that interaction of droplets leads to either scattering of mobile droplets or the formation of regular patterns, respectively, at low or high adsorbate diffusivity. The same method is applied to droplets running on growing terrace edges during surface freezing.

We investigate different states of synchronization in a ring of four mutually coupled van der Pol oscillators. The stability analysis and numerical simulation are performed to determine the suitable coupling parameters leading to high-quality synchronization. The consequences of parameter mismatch are also highlighted. Experimental realization is then used to show the existence of complete and partial synchronization.

We analytically investigate quantum wave functions with localizations on classical periodic orbits (POs) in the circular billiards. We construct the coherent states which are the coherent superpositions of nearly degenerate eigenstates and found to be localized around single classical POs. With the constructed coherent states, we can analytically express the mesoscopic eigenstates in the weakly perturbed systems, which are found to be localized on the ensemble of classical POs. Furthermore, these coherent states can be utilized to study the quantum vortex structures in quantum billiards.

Depending on the parameters of two-dimensional excitable or oscillatory media rigidly rotating or meandering spiral waves are observed. The transition from rigid rotation to meandering motion occurs via a supercritical Hopf bifurcation. To stabilize rigid rotation in a parameter range beyond the Hopf bifurcation, we propose and successfully apply a proportional control algorithm as well as time delay autosynchronization. Both control methods are noninvasive. This allows for determination of the parameters of unstable rigid rotation of spiral waves either for a model or an experimental system. Using the Oregonator model for the light-sensitive Belousov-Zhabotinsky reaction as a representative example we show that quite naturally some latency time appears in the control loop, and propose an efficient method to overcome its destabilizing influence.

Finite-size left-handed material (LHM) slabs are studied both analytically and numerically. The analytical method is based on Huygens’ principles using truncated current sheets that cover only the apertures of the slabs. It is shown that the main effects on the images’ spectra due to the size of the slabs can be predicted by the proposed analytical method, which can, therefore, be used as a fast alternative to the numerical simulations. Furthermore, the property of negative-energy streams at the image plane is explained. This unique property is found to be due to the interactions between propagating and evanescent waves and can only occur with LHM slabs, both finite size and infinite.

We present a finite-difference scheme for computing the Green’s function of a one-dimensional crystal. The method enables one to derive the band structure and the density of states of this type of structures, whatever the particular values of the potential energy. The technique also enables one to compute the influence of defects on the density of states and on the scattering of the eigenstates of the crystal. The technique is applied to the Krönig-Penney potential. In particular, we study the bound states of a square potential introduced in the crystal and their influence on the conductance of the system. We also determine the surface states induced by a termination of the Krönig-Penney potential. Our results turn out to be in excellent agreement with analytical expressions, which proves their validity and the versatility of the technique.