A simple mathematical model is proposed to study the influence of cell fission on transport. The model describes fractional, in time, tumor development, which is a one-dimensional continuous-time random walk. The model is relevant for consideration of both solid and diffusive cancers.

In a recent paper [Phys. Rev. E 68, 011906 (2003)], Naef and Magnasco suggested that the “bright” mismatches observed in Affymetrix microarray experiments are caused by the fluorescent molecules used to label RNA target sequences, which would impede target-probe hybridization. Their conclusion is based on the observation of “unexpected” asymmetries in the affinities obtained by fitting microarray data from publicly available experiments. We point out here that the observed asymmetry is due to the inequivalence of RNA and DNA, and that the reported affinities are consistent with stacking free energies obtained from melting experiments of unlabeled nucleic acids in solution. The conclusion of Naef and Magnasco is therefore based on an unjustified assumption.

In their Comment, Carlon et al. correctly observe that hybridization experiments in solution have shown an asymmetry which we failed to notice. However, contrary to their statement, the stacking free energies of unlabeled nucleic acids in solution are not compatible with our (and other authors’) measurements, even qualitatively. Furthermore, to bolster our paper’s assertion that labeling of the nucleic acids materially modifies the observed affinities, we present experimental data in which a change of labeling protocol results in a clear change in the affinities in question. We must therefore agree with extant studies suggesting that the energies of hybridization in solution are a superficial approximation to the much more complex physicochemical process of hybridization of labeled nucleic acids in high-density oligonucleotide arrays.

Coupled nonlinear systems under certain conditions exhibit phase synchronization, which may change for different frequency bands or with the presence of additive system noise. In both cases, Fourier filtering is traditionally used to preprocess data. We investigate to what extent the phase synchronization of two coupled Rössler oscillators depends on (1) the broadness of their power spectrum, (2) the width of the bandpass filter, and (3) the level of added noise. We find that for identical coupling strengths, oscillators with broader power spectra exhibit weaker synchronization. Further, we find that within a broad bandwidth range, bandpass filtering reduces the effect of noise but can lead to a spurious increase in the degree of phase synchronization with narrowing bandwidth, even when the coupling between the two oscillators remains the same.

We study an inhomogeneous sandpile model in which two different toppling rules are defined. For any site only one rule is applied corresponding to either the Bak, Tang, and Wiesenfeld model [P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987)] or the Manna two-state sandpile model [S. S. Manna, J. Phys. A 24, L363 (1991)]. A parameter $c$ is introduced which describes a density of sites which are randomly deployed and where the stochastic Manna rules are applied. The results show that the avalanche area exponent ${\tau }_a$, avalanche size exponent ${\tau }_s$, and capacity fractal dimension $D_s$ depend on the density $c$. A crossover from multifractal scaling of the Bak, Tang, and Wiesenfeld model $(c=0)$ to finite-size scaling was found. The critical density $c$ is found to be in the interval $0<c<0.01$. These results demonstrate that local dynamical rules are important and can change the global properties of the model.

The spectroscopic properties of an open large Bunimovich cavity are studied numerically in the framework of the effective Hamiltonian formalism. The cavity is opened by attaching two leads to it in four different ways. In some cases, the transmission takes place via standing waves with an intensity that closely follows the profile of the resonances. In other cases, short-lived and long-lived resonance states coexist. The short-lived states cause traveling waves in the transmission while the long-lived ones generate superposed fluctuations. The traveling waves oscillate as a function of energy. They are not localized in the interior of the large chaotic cavity. In all considered cases, the phase rigidity fluctuates with energy. It is mostly near to its maximum value and agrees well with the theoretical value for the two-channel case.

In granular media, the characterization of the behavior of solitary waves around interfaces is of importance in order to look for more applications of these systems. We study the behavior of solitary waves at both interfaces of a symmetric granular container, a class of systems that has received recent attention because it possesses the feature of energy trapping. Hertzian contact is assumed. We have found that the scattering process is elastic at one interface, while at the other interface it is observed that the transmitted solitary wave has stopped its movement during a time that gets longer when the ratio between masses at the interfaces increases. The origin of this effect can be traced back to the phenomenon of gaps opening, recently observed experimentally.

An extended volumetric scheme is proposed for lattice Boltzmann (LB) models. This scheme is particularly desirable for multispeed LB models due to its removal of nonlocal advection. It recovers the same macroscopic hydrodynamics as the standard lattice Boltzmann method without any further treatments. This scheme achieves an effectively reduced Courant-Friedrichs-Lewy number so that numerical stability is significantly enhanced for high Reynolds number simulations while maintaining the same order of numerical accuracy.

Various model problems of “transport-limited dissolution” in two dimensions are analyzed using time-dependent conformal maps. For diffusion-limited dissolution (reverse Laplacian growth), several exact solutions are discussed for the smoothing of corrugated surfaces, including the continuous analogs of “internal diffusion-limited aggregation” and “diffusion-limited erosion.” A class of non-Laplacian, transport-limited dissolution processes is also considered, which raises the general question of when and where a finite solid will disappear. In a case of dissolution by advection-diffusion, a tilted ellipse maintains its shape during collapse, as its center of mass drifts obliquely away from the background fluid flow, but other initial shapes have more complicated dynamics.

The dynamics of small spheres that are held by linear springs in a low Reynolds number shear flow at neighboring locations is investigated. The flow elongates the beads, and the interplay of the shear gradient with the nonlinear behavior of the hydrodynamic interaction among the spheres causes in a large range of parameters a bifurcation to a surprising oscillatory bead motion. The parameter ranges wherein this bifurcation is either super- or subcritical are determined.

Heat conduction in a one-dimensional non-Markovian damping channel between two heat baths separated by a finite distance is studied numerically. It is found that the Fourier heat law is not obeyed for a finite-size underdamped channel under a Gaussian white noise and the coefficient of heat conductivity is a nonmonotonic function of the channel length in the sub-Ohmic damping case. The key dynamic feature is that the system does not approach the stationary state when it arrives at the cold bath for the former, and the system exhibits different diffusive behaviors from ballistic diffusion to subdiffusion at initial and asymptotic periods of time for the latter. We evaluate a damping-dependent critical separation size between two heat baths above which the heat conductivity becomes independent of the separation.

We investigate the motion of a particle governed by a generalized Langevin equation with fractional derivative, nonlocal dissipative force, and long-time correlation function. We derive general expressions for the variances with a linear external force. We also analyze their asymptotic behaviors for the power-law correlation function without external force.

The original Feynman-Kleinert [Phys. Rev. A 34, 5080 (1986)] variational approach to Euclidean path integrals is improved by introducing a reference harmonic potential whose center is allowed to change with time. The motion of the center of the potential is varied such that the “effective potential” of Feynman and Kleinert is minimized and leads to an equation of motion for the classical path in the reference system that closely reproduces the “exact” average path. The formalism is applied to the double-well potential $V\left(x\right)=-x^2∕2+g{x}^4∕4+1∕4g$. This modification improves the accuracy of the approximate quantum-mechanical distribution function and, to a larger extent, the density matrix.

Free cooling of a gas of inelastically colliding hard spheres represents a central paradigm of kinetic theory of granular gases. At zero gravity the temperature of a freely cooling homogeneous granular gas follows a power law in time. How does gravity, which brings inhomogeneity, affect the cooling? We combine molecular dynamics simulations, a numerical solution of hydrodynamic equations and an analytic theory to show that a granular gas cooling under gravity undergoes thermal collapse: it cools down to zero temperature and condenses on the bottom of the container in a finite time.

For the isobutoxyethanol-water mixture of critical composition acoustical scaling function measurements have been performed at frequencies between $200\mathrm{kHz}$ and $3\mathrm{MHz}$. Using the relaxation rates of concentration fluctuations as resulting from dynamic light scattering and shear viscosity measurements, the acoustical data can be well represented by the Bhattacharjee-Ferrell empirical scaling function. The theoretically predicted scaled half attenuation frequency ${\Omega }_{1∕2}^{BF}=2.1$ follows from the experiments. However, the adiabatic coupling constant, derived from the amplitude of the Bhattacharjee-Ferrell critical term, displays an unreliably strong temperature dependence. It is shown that this dependence upon temperature likely reflects a hidden low-frequency and low amplitude relaxation term in the acoustical spectra of the mixture of critical composition.

We present and discuss the results of pointwise velocity measurements performed on a viscoelastic micellar solution made of cetyltrimethylammonium bromide and sodium salicylate in water, respectively, at the concentrations of 50 and $100\mathrm{mmol}$. The sample is contained in a Couette device and subjected to flow in the strain controlled mode. This particular solution shows shear banding and, in a narrow range of shear rates at the right end of the stress plateau, apparent shear thickening occurs. Time-dependent recordings of the shear stress in this range reveal that the flow has become unstable and that large sustained oscillations of the shear stress and of the first normal stresses difference emerge and grow in the flow. Local pointwise velocity measurements clearly reveal a velocity profile typical of shear banding when the imposed shear rate belongs to the plateau, but also important wall slip in the entire range of velocity gradients investigated. In the oscillations regime, the velocity is recorded as a function of time at a fixed point close to the rotor of the Couette device. The time-dependent velocity profile reveals random fluctuations but, from time to time, sharp decreases much larger than the standard deviation are observed. An attempt is made to correlate these strong variations with the stress oscillations and a correlation coefficient $r$ is computed. However, the small value found for the coefficient $r$ does not allow us to draw a final conclusion as concerns the correlation between stress oscillations and velocity fast decreases.

We present a stochastic model of filament growth driven by the motor-assisted transport of particles along the filament. We show how the growth can be analyzed in terms of a sequence of first passage times for a particle hopping between the two ends of the filament, and use this to calculate the mean and variance of the length as a function of time. We determine how the growth depends on the waiting time density of the underlying hopping process, and highlight differences in the growth generated by normal and anomalous transport, for which the mean waiting time is finite and infinite, respectively. In the case of normal transport, we determine the length at which there is a balance between particle-driven assembly and particle-independent disassembly of the filament. The existence of such a balance point is thought to provide a mechanism for flagellar length control.

We show that a model proposed by Rubin, Rosenau, and Gottlieb [J. Appl. Phys. 77, 4054 (1995)] for dispersion caused by an inherent material characteristic length belongs to the class of simple materials. Therefore, it is possible to generalize the idea of Rubin, Rosenau, and Gottlieb to include a wide range of material models, from nonlinear elasticity to turbulence. Using this insight, we are able to fine-tune nonlinear and dispersive effects in the theory of nonlinear elasticity in order to generate pulse solitary waves and also bulk traveling waves with compact support.

In this paper, we summarize our experimental observations on complex-oscillatory spiral waves that arise in a Belousov-Zhabotinsky (BZ) reaction-diffusion system. The observed wave structures generically bear line defects across which the phase of local oscillation changes by a multiple of $2\pi$. The local oscillation at every spatial point along a line defect of period-2 (P-2) oscillatory media is period-1 (P-1) oscillatory. For the homogeneous BZ reaction can be excitable, simply periodic, complex periodic, or chaotic as the control parameters are tuned, a number of different complex wave states are revealed. A two-dimensional phase diagram, which includes domains of P-2 oscillatory spirals, intermittently breathing spirals, period-3 (P-3) oscillatory spirals, two different types of mixed-mode periodic spirals, and line-defect-mediated turbulence, is constructed. Several different transitions among different dynamic states are described systematically. In all cases, line defects are found to play an important role.

For a system of two phase oscillators coupled with delayed self-feedback we study the impact of pulsatile stimulation administered to both oscillators. This system models the dynamics of two coupled phase-locked loops (PLLs) with a finite internal delay within each loop. The delayed self-feedback leads to a rich variety of dynamical regimes, ranging from phase-locked and periodically modulated synchronized states to chaotic phase synchronization and desynchronization. Remarkably, for large coupling strength the two PLLs are completely desynchronized. We study stimulus-locked responses emerging in the different dynamical regimes. Simple phase resets may be followed by a response clustering, which is intimately connected with long poststimulus resynchronization. Intriguingly, a maximal perturbation (i.e., maximal response clustering and maximal resynchronization time) occurs, if the system gets trapped at a stable manifold of an unstable saddle fixed point due to appropriately calibrated stimulus. Also, single stimuli with suitable parameters can shift the system from a stable synchronized state to a stable desynchronized state or vice versa. Our result show that appropriately calibrated single pulse stimuli may cause pronounced transient and/or long-lasting changes of the oscillators’ dynamics. Pulse stimulation may, hence, constitute an effective approach for the control of coupled oscillators, which might be relevant to both physical and medical applications.