Gating ratchet for cold atoms

We demonstrate experimentally a gating ratchet with cold rubidium atoms in a driven near-resonant optical lattice. A single-harmonic periodic modulation of the optical potential depth is applied, together with a single-harmonic rocking force. Directed motion is observed as a result of the breaking of the symmetries of the system.

Patch coalescence as a mechanism for eukaryotic directional sensing

Eukaryotic cells possess a sensible chemical compass allowing them to orient toward sources of soluble chemicals. The extracellular chemical signal triggers separation of the cell membrane into two domains populated by different phospholipid molecules and oriented along the signal anisotropy. We propose a theory of this polarization process, which is articulated into subsequent stages of germ nucleation, patch coarsening, and merging into a single domain. We find that the polarization time, t{epsilon}, depends on the anisotropy degree through the power law t{epsilon} infinity epsilon{-2}, and that in a cell of radius R there should exist a threshold value epsilon{th} infinity R{-1} for the smallest detectable anisotropy.

Dynamics of energy condensation in two-dimensional turbulence

We report a numerical study, supplemented by phenomenological explanations, of "energy condensation" in forced 2D turbulence in a biperiodic box. Condensation is a finite size effect which occurs after the standard inverse cascade reaches the size of the system. It leads to the emergence of a coherent vortex dipole. We show that the time growth of the dipole is self-similar, and it contains most of the injected energy, thus resulting in an energy spectrum which is markedly steeper than the standard k{-5/3} one. Once the coherent component is subtracted, however, the remaining fluctuations have a spectrum close to k{-1}. The fluctuations decay slowly as the coherent part grows.

Effects of surface tension on immiscible Rayleigh-Taylor turbulence

We present phenomenology describing the internal structure of a turbulent zone, produced as the result of the push of a heavy fluid into a light one, for the case of immiscible fluids. One finds that the Kolmogorov cascade is realized within a range that grows with time, viz., scales between the mixing zone width, L proportional variant t(2), and the viscous scale, eta proportional variant t(-1/4). Surface-tension effects lead to formation of an emulsionlike state. Density fluctuations on scales larger than the typical drop size, l, are governed by the Obukhov-Corrsin cascade. If l >> eta, a wave energy cascade, related to capillary waves propagating along the surfaces of drops, is formed at scales below l, l proportional variant t(-2/5).

Probability of anomalously large bit-error rate in long haul optical transmission

We consider a linear model of optical transmission through a fiber with birefringent disorder in the presence of amplifier noise. Both disorder and noise are assumed to be weak, i.e., the average bit-error rate (BER) is small. The probability distribution function (PDF) of rare violent events leading to the values of BER much larger than its typical value is estimated. We show that the PDF has a long algebraic-like tail.

Boundary effects on chaotic advection-diffusion chemical reactions

A theory of a fast binary chemical reaction, A+B-->C, in a statistically stationary bounded chaotic flow at large Peclet number Pe and large Damköhler number Da is described. The first stage correspondent to formation of the developed lamellar structure in the bulk part of the flow is terminated by an exponential decay, proportional, variant exp((-lambdat) (where lambda is the Lyapunov exponent of the flow), of the chemicals in the bulk. The second and the third stages are due to the chemicals remaining in the boundary region. During the second stage, the amounts of A and B decay proportional, variant 1/sqrt[t], whereas the decay law during the third stage is exponential, proportional, variant exp((-gammat), where gamma approximately lambda/sqrt[Pe].

Shedding and interaction of solitons in weakly disordered optical fibers

The propagation of the soliton pattern through optical fiber with weakly disordered dispersion coefficient is considered. Solitons perturbed by this disorder radiate and, as a consequence, decay. The average radiation profile is found. Emergence of a long-range intrachannel interaction between the solitons (mediated by this radiation) is reported. We show that soliton in a multisoliton pattern experiences a random jitter: intersoliton separation is zero mean Gaussian random field. Fluctuations of this separation are estimated by deltay approximately Dz(2)square root mu, where D measures the disorder strength, z is the propagation distance, and mu stands for the transmission rate (number of solitons per unit length of the fiber). Direct numerical simulations are used to validate theoretical predictions for single soliton decay and two-soliton interaction. Relevance of these results to fiber optics communication technology is discussed.

Decay of scalar turbulence revisited

We demonstrate that at long times the rate of passive scalar decay in a turbulent, or simply chaotic, flow is dominated by regions where mixing is less efficient. We examine two situations. The first is of a spatially homogeneous stationary turbulent flow with both viscous and inertial scales present. It is shown that at large times scalar fluctuations decay algebraically in time at all spatial scales. The second example explains chaotic stationary flow in a disk/pipe. The boundary region of the flow controls the long-time decay, which is algebraic at some transient times, but becomes exponential, with the decay rate dependent on the scalar diffusion coefficient, at longer times.

Turbulence of polymer solutions

We investigate high-Reynolds-number turbulence in dilute polymer solutions. We show the existence of a critical value of the Reynolds number, which separates two different regimes. In the first regime, below the transition, the influence of the polymer molecules on the flow is negligible, so they can be regarded as passively embedded in the flow. This case admits a detailed investigation of the statistics of the polymer elongations. The second state is realized when the Reynolds number is larger than the critical value. This regime is characterized by the strong back reaction of polymers on the flow. We establish some properties of the statistics of the stress and velocity in this regime and discuss its relation to the drag reduction phenomenon.

Statistics of soliton-bearing systems with additive noise

We present a consistent method to calculate the probability distribution of soliton parameters in systems with additive noise. Even though the noise is weak, we are interested in probabilities of large fluctuations (generally non-Gaussian) which are beyond perturbation theory. Our method is a development of the instanton formalism (method of optimal fluctuation) based on a saddle-point approximation in the path integral. We first solve a fundamental problem of soliton statistics governed by a noisy nonlinear Schrödinger equation. We then apply our method to optical soliton transmission systems using signal control elements (filters and amplitude and phase modulators).

Turbulent dynamics of polymer solutions

We study properties of dilute polymer solutions. The probability density function (PDF) of polymer end-to-end extensions R in turbulent flows is examined. We show that if the value of the Lyapunov exponent lambda is smaller than the inverse molecular relaxation time 1/tau then the PDF has a strong peak at the equilibrium size R0 and a power tail at R>>R0. This confirms and extends the results of J. L. Lumley [Symp. Math. 9, 315 (1972)]. There is no essential influence of polymers on the flow in this regime. At lambdatau>1 the majority of molecules is stretched to the linear size R(op)>>R0, which can be much smaller than the maximal length of the molecules due to their back reaction.

Early diagnosis of coxarthrosis (in-shoe plantar pressure measurements)

INTRODUCTION:: Plantar pressure measurement during walking adds dynamic functional data to evaluation of gait disorders of teenagers with coxarthrosis. The duration of the complete gait cycle, its phases (stance and swing phase for right and left feet, double support) and phases of roll-over process are found useful in many clinical applications. METHODS:: In-shoe measurements were completed with Pedar system (99 element capacitive insoles from Novel, Munich, Germany) for 38 teenagers from military school (controls) and 29 teenagers with coxarthrosis. The data from 3 - 5 trials for each subject were collected. The distance was about 10 m, no requirements to the speed and step length were established. Special software was developed. RESULTS:: Time parameters for the complete gait cycle, its phases, phases of roll-over-process were calculated both for the controls and the teenagers with coxarthrosis It was found that stance phase and heel contact phase are decreased for the teenagers with coxarthrosis. DISCUSSION:: Decrease of stance phase, insufficient loading of the heel and decrease of heel contact time are a result of attempts to compensate the painfulness in the hip joint during walking. CONCLUSION:: Time parameters of the complete gait cycle and its phases may be useful in early diagnosis of coxarthrosis and evaluation of efficiency of the treatment.

Transformation and average as handy tools for pressure measurement data analysis

INTRODUCTION:: Pressure measurement data underneath[Table: see text] the foot represent usually a large number of data files which is equal to double product of the number of the subjects in study and of the number of the trials for each foot. Besides, 'normal' parameters are necessary to compare the results for the controls and for the subjects in study. Statistical parameters (mean values and standard deviations) are not very convenient when it is required to establish cartographical and geometrical parameters or peak pressures, maximum forces, contact areas, contact time and others for foot typing or as a standard. Sometimes it is reasonable to obtain average pressure data as a base for further data analysis. But taking into account that pressure distribution pattern may differ by its length, width and angle of the inclination of the foot axis to the horizontal it was necessary to solve a problem of transformation of any pressure picture to the given length and width (for vertical location of the foot axis). METHODS:: The transformed coordinates X(*) and Y(*) are defined from the following system of equations: X = Y(*) x width/width(*) x sina + X(*) x length/length(*) x cosa + X(o) Y = Y(*) x width/width(*) x cosa - X(*) x length/length(*) x sina + Y(o) where X(o), Y(o) -- the coordinates of the origin; width, length, a -- parameters of the initial pressure picture; width(*), length(*) -- parameters of the transformed pressure picture. X, Y -- are real values but the values of pressure are defined only in the integer coordinates. One of the main parts of average is a reduction of the time process to any number of frames. If N(max) is a maximum number of frames in one of the data files than all other data files must be transformed with accordance to the following formulas: for j-th frame the value of pressure for sensor with coordinates x, y is: P(*1)(xy) (j) = P(1)(xy) (i) x ki + P(1)(xy) (i+1) x k(i+1), where P(1)(xy) (i) -- pressure for sensor with coordinates x, y of the 1-th initial time process; j = 0, ellipsis, N(max) -1; j-th frame corresponds to i-th frame in the initial time process as i = integer(j) x (N -1)/(N(max) -1), N -- a number of frames in initial time process; coefficients k(i) and k(i+1) are equal to k(i) = j x (N -1)/(N(max) -1) -- I, k(i+1) = 1 - ki. Then the values of pressure are averaged: P(*)(xy) (j) = 1 / L x S P(1)(xy) (j), where L is a number of data files. Corresponding software was developed. RESULTS AND DISCUSSION:: 38 files of pressure measurement data of the teenagers from military school were chosen for transformation and average. Statistical errors of transformation and average were calculated for each data file (for peak pressure, force and area) and for all parameters from two software packages: Novel-win v.95.121 and Novel-ortho v.95.121. The maximum errors are for peak pressures (about 7%-10%) and contact areas (about 6%). CONCLUSION:: Transformation and average programs can be successfully used for data analysis additionally to traditional statistical software: groupmask evaluation program.

Velocity of the cop as a reliable parameter for early diagnosis of coxarthrosis

INTRODUCTION:: The first symptoms of the degenerative disease of hip joint appear very early when people are about 14 years old. But clinical and X-ray characters manifest themselves insufficiently: temporary slight pains in hip joints on loading, insignificant painfulness along posterior surface of the joint during palpation, slight lameness on the diseased side. The purpose of this study was to try to involve gait analysis in the clinical research of the teenagers with coxarthrosis and to define the parameters which may be used for early diagnosis of coxarthrosis. METHODS:: 38 male military school teen-agers which have no history in the foot disorders and 20 male and 9 female with coxarthrosis were used for study. Plantar pressure distribution measurements were performed with the mini-emed system (Novel, Munich, Germany). Five dynamic records of each foot were made on the pressure platform (28 x 60 sensors, resolution -- 3 sensors/cm(2), sampling frequency -- 16 Hz). Three trials of gait were accomplished by each subject with inserted insoles (99 sensors in each insole) at the distance about 10 m. Novel-win v.95.121 and Novel-ortho v.95.121 packages were used for data analysis. RESULTS:: For the teenagers with coxarthrosis the loading of heel area is significantly less (< = 15 N/cm(2)), maximum force is generally less. Contact time (in percent of roll-over-process) in the forefoot and toes is increased and is equal to 100% very often. The most interesting results are obtained for the curves of the velocity of the centres of pressure versus time. For the controls this curve has one or two maxima (during 50%-70% of roll-over-process when heel, midfoot and sometimes forefoot are loaded), then a short period of insignificant changes of the velocity (up to 88%-94% of roll-over-process when only forefoot and toes are loaded) and last a very short period of its increase (toe-off phase). For the most part of the teenagers with coxarthrosis this curve seems to be monotonous, oscillating near its mean value line. DISCUSSION:: These disturbances may be explained by valgus deviation of the neck of femur and insufficient function of the muscles of buttocks as a consequence of its lever web decrease. The muscle forces (particularly abducted muscles) are decreased (about 10%-15%). These data are consistent with previous reported findings. CONCLUSION:: To compensate for the painfulness in the diseased hip joint the teenagers load rearfoot and forefoot less than in the 'normal' foot, increasing contact time in the forefoot. As a consequence of disturbances in hip joint a pathway of the centre of pressure is longer than in 'norm' and its velocity changes oscillating near the mean value when for 'normal' teenagers three definite intervals of its change are viewed. Therefore the first symptoms of displastic coxarthrosis of teenagers may be revealed from plantar pressure measurements by analysing the character of time dependence the velocity of the centres of pressure and loading of different areas of the foot (force and contact time). Additionally, functional state of hip joint muscles, X-ray and clinical symptoms, heat radiation and laser biophotometry data give an opportunity to define the character of locomotor function disorders.