Short-time Behavior Research Articles

Transient Superdiffusion and Long-Range Correlations in the Motility Patterns of Trypanosomatid Flagellate Protozoa.

We report on a diffusive analysis of the motion of flagellate protozoa species. These parasites are the etiological agents of neglected tropical diseases: leishmaniasis caused by Leishmania amazonensis and Leishmania braziliensis, African sleeping sickness caused by Trypanosoma brucei, and Chagas disease caused by Trypanosoma cruzi. By tracking the positions of these parasites and evaluating the variance related to the radial positions, we find that their motions are characterized by a short-time transient superdiffusive behavior. Also, the probability distributions of the radial positions are self-similar and can be approximated by a stretched Gaussian distribution. We further investigate the probability distributions of the radial velocities of individual trajectories. Among several candidates, we find that the generalized gamma distribution shows a good agreement with these distributions. The velocity time series have long-range correlations, displaying a strong persistent behavior (Hurst exponents close to one). The prevalence of “universal” patterns across all analyzed species indicates that similar mechanisms may be ruling the motion of these parasites, despite their differences in morphological traits. In addition, further analysis of these patterns could become a useful tool for investigating the activity of new candidate drugs against these and others neglected tropical diseases.

Hypoelliptic Heat Kernels on Nilpotent Lie Groups

The starting point of our analysis is an old idea of writing an eigenfunction expansion for a heat kernel considered in the case of a hypoelliptic heat kernel on a nilpotent Lie group G. One of the ingredients of this approach is the generalized Fourier transform. The formula one gets using this approach is explicit as long as we can find all unitary irreducible representations of G. In the current paper we consider an n-step nilpotent Lie group G n as an illustration of this technique. First we apply Kirillov’s orbit method to describe these representations for G n . This allows us to write the corresponding hypoelliptic heat kernel using an integral formula over a Euclidean space. As an application, we describe a short-time behavior of the hypoelliptic heat kernel in our case.

First passage time distribution in heterogeneity controlled kinetics: going beyond the mean first passage time.

The first passage is a generic concept for quantifying when a random quantity such as the position of a diffusing molecule or the value of a stock crosses a preset threshold (target) for the first time. The last decade saw an enlightening series of new results focusing mostly on the so-called mean and global first passage time (MFPT and GFPT, respectively) of such processes. Here we push the understanding of first passage processes one step further. For a simple heterogeneous system we derive rigorously the complete distribution of first passage times (FPTs). Our results demonstrate that the typical FPT significantly differs from the MFPT, which corresponds to the long time behaviour of the FPT distribution. Conversely, the short time behaviour is shown to correspond to trajectories connecting directly from the initial value to the target. Remarkably, we reveal a previously overlooked third characteristic time scale of the first passage dynamics mirroring brief excursion away from the target.

マルコフパラメータマッチングに基づく離散時間線形システムの多時間分解能制御

In this paper, we propose a synthesis method of multi-time-resolved control systems for discrete-time linear systems. In this method, on the basis of a low-rank model stemming from the Wedderburn rank reduction, we derive a redundant state-space realization of systems that enables a systematic design of a dynamical compensator stabilizing the short-time behavior of systems. Owing to the fact that the low-rank model has the same reachable and observable subspaces as the original system, we can systematically design a multiresolved control system while explicitly considering the short-time and long-time behavior of systems. The efficiency of the multiresolved control is shown through an illustrative example of frequency control of power systems.

A Mathematical Model for the Proliferation, Accumulation and Spread of Pathogenic Proteins Along Neuronal Pathways with Locally Anomalous Trapping

There is growing evidence that many neurodegenerative disease processes involve the proliferation, accumulation and spread of pathogenic proteins. The transport of proteins in the brain is typically hindered on small scales by micro-domain traps and binding sites but it may be enhanced on larger scales by neuronal pathways identified as white matter transport networks. We have introduced a mathematical network model to simulate a pathogenic protein neurodegenerative disease in the brain taking into account the anomalous transport. The proliferation and accumulation of pathogenic proteins is modelled using a set of reaction kinetics equations on the nodes of a network. Transport of the proteins on the network is modelled as a continuous time random walk with power law distributed waiting times on the nodes. This power law waiting time distribution is shown to be consistent with anomalously slowed diffusion on local scales but transport is enhanced on larger scales by the jumps between nodes. The model reveals that the disease spreads as a propagating front throughout the brain. The anomalous behaviour leads to a lessor variation in the concentration of pathogenic proteins. The enhanced transport on the network ensures that the approach to equilibrium is dominated by the short time behaviour of the waiting time density, hence the effects of subdiffusion are not as pronounced as in a spatial continuum.

Non-Markovianity measure using two-time correlation functions

We investigate non-Markovianity measure using two-time correlation functions for open quantum systems. We define non-Markovianity measure as the difference between the exact two-time correlation function and the one obtained in the Markov limit. Such non-Markovianity measure can easily be measured in experiments. We found that the non-Markovianity dynamics in different time scale crucially depends on the system-environment coupling strength and other physical parameters such as the initial temperature of the environment and the initial state of the system. In particular, we obtain the short-time and long-time behaviors of non-Markovianity for different spectral densities. We also find that the thermal fluctuation always reduce the non-Markovian memory effect. Also, the non-Markovianity measure shows non-trivial initial state dependence in different time scales.

Fairness is intuitive

In this paper we provide new evidence showing that fair behavior is intuitive to most people. We find a strong association between a short response time and fair behavior in the dictator game. This association is robust to controls that take account of the fact that response time might be affected by the decision-maker’s cognitive ability and swiftness. The experiment was conducted with a large and heterogeneous sample recruited from the general population in Denmark. We find a striking similarity in the association between response time and fair behavior across groups in the society, which suggests that the predisposition to act fairly is a general human trait.

Fokker-Planck equation of Schramm-Loewner evolution.

In this paper we statistically analyze the Fokker-Planck (FP) equation of Schramm-Loewner evolution (SLE) and its variant SLE(κ,ρc). After exploring the derivation and the properties of the Langevin equation of the tip of the SLE trace, we obtain the long- and short-time behaviors of the chordal SLE traces. We analyze the solutions of the FP and the corresponding Langevin equations and connect it to the conformal field theory (CFT) and present some exact results. We find the perturbative FP equation of the SLE(κ,ρc) traces and show that it is related to the higher-order correlation functions. Using the Langevin equation we find the long-time behaviors in this case. The CFT correspondence of this case is established and some exact results are presented.

Depolarized light scattering from prolate anisotropic particles: The influence of the particle shape on the field autocorrelation function.

We provide a theoretical analysis for the intermediate scattering function typically measured in depolarized dynamic light scattering experiments. We calculate the field autocorrelation function g1(VH)(Q,t) in dependence on the wave vector Q and the time t explicitly in a vertical-horizontal scattering geometry for differently shaped solids of revolution. The shape of prolate cylinders, spherocylinders, spindles, and double cones with variable aspect ratio is expanded in rotational invariants flm(r). By Fourier transform of these expansion coefficients, a formal multipole expansion of the scattering function is obtained, which is used to calculate the weighting coefficients appearing in the depolarized scattering function. In addition to translational and rotational diffusion, especially the translational-rotational coupling of shape-anisotropic objects is considered. From the short-time behavior of the intermediate scattering function, the first cumulants Γ(Q) are calculated. In a depolarized scattering experiment, they deviate from the simple proportionality to Q(2). The coefficients flm(Q) strongly depend on the geometry and aspect ratio of the particles. The time dependence, in addition, is governed by the translational and rotational diffusion tensors, which are calculated by means of bead models for differently shaped particles in dependence on their aspect ratio. Therefore, our analysis shows how details of the particle shape--beyond their aspect ratio--can be determined by a precise scattering experiment. This is of high relevance in understanding smart materials which involve suspensions of anisotropic colloidal particles.

Calibration of optical tweezers with non-spherical probes via high-resolution detection of Brownian motion

Optical tweezers are commonly used and powerful tools to perform force measurements on the piconewton scale and to detect nanometer-scaled displacements. However, the precision of these instruments relies to a great extent on the accuracy of the calibration method. A well-known calibration procedure is to record the stochastic motion of the trapped particle and compare its statistical behavior with the theory of the Brownian motion in a harmonic potential. Here we present an interactive calibration software which allows for the simultaneous fitting of three different statistical observables (power spectral density, mean square displacement and velocity autocorrelation function) calculated from the trajectory of the probe to enhance fitting accuracy. The fitted theory involves the hydrodynamic interactions experimentally observable at high sampling rates. Furthermore, a qualitative extension is included in our model to handle the thermal fluctuations in the orientation of optically trapped asymmetric objects. The presented calibration methodology requires no prior knowledge of the bead size and can be applied to non-spherical probes as well. The software was validated on synthetic and experimental data. Program summaryProgram title: PFMCalCatalogue identifier: AEXH_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEXH_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 206,399No. of bytes in distributed program, including test data, etc.: 10,319,465Distribution format: tar.gzProgramming language: MatLab 2011a (MathWorks Inc.).Computer: General computer running MatLab (MathWorks Inc.), using Statistics Toolbox.Operating system: Any which supports Matlab using Statistics Toolbox.RAM: 10 MBClassification: 3, 4.9, 18, 23.Nature of problem: Calibration of optical tweezers by measuring the Brownian motion of the trapped object. The voltage-to-displacement ratio of the detection system (the inverse of the sensitivity), the stiffness of the trap and the size of the bead are obtained via the simultaneous fitting of the power spectral density (PSD), mean square displacement (MSD) and velocity autocorrelation (VAF) functions calculated from the trajectory. The calibration can be performed for non-spherical probes as well.Solution method: Initialization points for all parameters are inferred from characteristic features of the statistical observables (PSD, MSD and VAF) based on the method developed by Grimm et al. in [1]. Theoretical functions for the PSD, the MSD and the VAF are calculated from the model of Brownian motion confined by a harmonic potential taking hydrodynamic interactions into consideration [2–4]. This calibration methodology has been successfully used in actual experiments with micro-spheres [5, 6]. Calculated functions are fitted to the measurement data via the Levenberg–Marquardt least square fitting routine available in the MatLab Optimalization Toolbox, using the nlinfit function. If the error to the measured data has been estimated, the corresponding data values can be weighted by the inverse of the standard error squared in order to eliminate bias introduced by heteroscedasticity. In order to increase robustness and avoid convergence to local minima, minimum search from multiple initial values in the vicinity of the first guess is possible.Additional comments: Input of the program is the experimental PSDexp, MSDexp, and VAFexp data points calculated from the measured x,y and z projections of the trajectory of the particle. The data may best be blocked and may optionally contain an error for each data point for better results. The data should be formatted into three columns: 1. independent variables (time or frequency array), 2. function values, 3. optionally, error values (e.g. standard error calculated from the binning) to improve fitting efficiency. In case error values were not estimated, the third column should be filled with zeros. The first row is reserved for a header, data is read from the second row. Data size should not be larger than a few hundreds of rows, otherwise, using larger blocks for binning is advised. In order to observe the short time behavior of the Brownian motion, influenced by hydrodynamic effects, the sampling rate should be typically higher than 100 kHz. Total sampling time is typically tens of seconds, to achieve a good resolution in the frequency range. The optical axis of the laser, the microscope and the detector system should be co-aligned to exclude artificial crosstalk between the x,y and z channels of the position detector.Running time: Seconds

Linear stability of Taylor–Couette flow of shear-thinning fluids: modal and non-modal approaches

In this paper, the response of circular Couette flow of shear-thinning fluids between two infinitely long coaxial cylinders to weak disturbances is addressed. It is highlighted by transient growth analysis. Both power-law and Carreau models are used to describe the rheological behaviour of the fluid. The first part of the paper deals with the asymptotic long-time behaviour of three-dimensional infinitesimal perturbations. Using the normal-mode approach, an eigenvalue problem is derived and solved by means of the spectral collocation method. An extensive description and the classification of eigenspectra are presented. The influence of shear-thinning effects on the critical Reynolds numbers as well as on the critical azimuthal and axial wavenumbers is analysed. It is shown that with a reference viscosity defined with the characteristic scales$\hat{{\it\mu}}_{ref}=\hat{K}(\hat{R}_{1}\hat{{\it\Omega}}_{1}/\hat{d})^{(n-1)}$for a power-law fluid and$\hat{{\it\mu}}_{ref}=\hat{{\it\mu}}_{0}$for a Carreau fluid, the shear-thinning character is destabilizing for counter-rotating cylinders. Moreover, the axial wavenumber increases with$\mathit{Re}_{2}$and with shear-thinning effects. The second part investigates the short-time behaviour of the disturbance using the non-modal approach. For the same inner and outer Reynolds numbers, the amplification of the kinetic energy perturbation becomes much more important with increasing shear-thinning effects. Two different mechanisms are used to explain the transient growth, depending on whether or not there is a stratification of the angular momentum. On the Rayleigh line and for Newtonian fluids, the optimal perturbation is in the form of azimuthal streaks, which transform into Taylor vortices through the anti-lift-up mechanism. In the other cases, the optimal perturbation is initially oriented against the base flow, then it tilts to align with the base flow at optimal time. The scaling laws for the optimal energy amplification proposed in the literature for Newtonian fluids are extended to shear-thinning fluids.

Short-term creep properties of Ti-6Al-4V alloy subjected to surface plasma carburizing process

The aim of this study was to investigate the short-time creep behavior of Ti-6Al-4V by plasma carburizing, which was performed at 725°C for 6h in a 50% Ar – 45% H2 – 5% CH4 gas mixture. Nano and microhardness testing, optical microscopy, TEM, X-ray diffraction and optical profilometry were used to characterize the samples. Furthermore, short-term creep tests were performed under a constant tensile load in air at 600°C using a dead-weight-creep-rupture machine. The carburizing treatment resulted in a compound layer measuring approximately 1.7μm in thickness with a hardness of 815HV and a composition of TiC0.66. The creep properties of the “Widmanstätten+carburized” specimens were improved relative to those of untreated specimens. TEM and fracture analysis indicated creep deformation process attributed mainly to α phase deformation and fracture by intergranular decohesion.

Improvement of TiN nanoparticles EPD inducing steric stabilization in non-aqueous suspensions

In this work, the process parameters involved in the electrophoretic deposition (EPD) to obtain thin TiN films was studied and optimised. The stability of commercial TiN nanopowder in isopropyl alcohol adding a cationic polymer (polyethylenimine) as dispersant, with different molecular weights, was investigated to determine the kinetics of the deposition and to reach the most efficient EPD process. Cathodic EPD was performed over electro-polished stainless steel substrates. It was found that the provided dispersion when the PEI with the highest molecular weight was added to the suspension, leads to the best deposition behaviour for short times. New flocculation phenomena were described which affect to the sticking factor, and thus to the evolution of the EPD kinetics. As a result of the designed stabilization system, a reliable and versatile EPD method to produce well consolidated nano-TiN coatings at 1200°C in vacuum atmosphere was described.

Persistent-random-walk approach to anomalous transport of self-propelled particles.

The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's displacement. It is shown that the interplay of step length and turning angle distributions and self-propulsion produces various signs of anomalous diffusion at short time scales and asymptotically a normal diffusion behavior with a broad range of diffusion coefficients. The crossover from the anomalous short-time behavior to the asymptotic diffusion regime is studied and the parameter dependencies of the crossover time are discussed. Higher moments of the displacement distribution are calculated and analytical expressions for the time evolution of the skewness and the kurtosis of the distribution are presented.

Short-term creep behavior of a biodegradable polymer reinforced with wood-fibers

The short-time creep behavior at tensile and single cantilever mode of deformation for a series of biodegradable composites was thoroughly studied. The composites were based on a biodegradable polymer matrix consisted a blend of poly(butylene adipate-terephthalate) (PBAT) copolyester, produced by non-renewable resources, and Polylactic acid (PLA). The matrix was reinforced with three different wood fiber types, at 20 and 30 wt%. The experimental data were analyzed in terms of Findley's and Burger's viscoelastic models. The effect of stress and temperature and wood fiber type on the material's creep response was analytically studied, while the Burger's model parameters were related to the composites morphology. In all cases, the wood fibers improved the creep resistance of the composites.

Wave propagation for the compressible Navier–Stokes equations

We establish the pointwise description of solutions to the isentropic Navier–Stokes equations for compressible fluids in three spatial dimensions. First, we give an explicit construction of the Green function for the linearized system. The Green function consists of singular waves, which dominate the short-time behavior, while the low frequency waves, the dissipative Huygens, diffusion and Riesz waves representing the large-time behavior. The nonlinear terms are treated by a suitable combination of energy estimates and pointwise estimates using the Duhamel's principle for the Green function.

Steady quantum coherence in non-equilibrium environment

We study the steady state of a three-level system in contact with a non-equilibrium environment, which is composed of two independent heat baths at different temperatures. We derive a master equation to describe the non-equilibrium process of the system. For the three level systems with two dipole transitions, i.e., the Λ-type and V-type, we find that the interferences of two transitions in a non-equilibrium environment can give rise to non-vanishing steady quantum coherence, namely, there exist non-zero off-diagonal terms in the steady state density matrix (in the energy representation). Moreover, the non-vanishing off-diagonal terms increase with the temperature difference of the two heat baths. Such interferences of the transitions were usually omitted by secular approximation, for it was usually believed that they only take effect in short time behavior and do not affect the steady state. Here we show that, in non-equilibrium systems, such omission would lead to the neglect of the steady quantum coherence.

Reaction rate in an evanescent random walkers system

Diffusion mediated reaction models are particularly ubiquitous in the description of physical, chemical or biological processes. The random walk schema is a useful tool for formulating these models. Recently, evanescent random walk models have received attention in order to include finite lifetime processes. For instance, activated chemical reactions, such as laser photolysis, exhibit a different asymptotic limit when compared with immortal walker models. A diffusion limited reaction model based on a one dimensional continuous time random walk on a lattice with evanescent walkers is presented here. The absorption probability density and the reaction rate are analytically calculated in the Laplace domain. A finite absorption rate is considered, a model usually referred to as imperfect trapping. Short and long time behaviors are analyzed.Received: 20 Novembre 2014, Accepted: 20 March 2015; Edited by: C. A. Condat, G. J. Sibona; DOI: http://dx.doi.org/10.4279/PIP.070003Cite as: M A Re, N C Bustos, Papers in Physics 7, 070003 (2015)This paper, by Miguel A. Re, Natalia C. Bustos , is licensed under the Creative Commons Attribution License 3.0.

Experimental study on the bolt–cable combined supporting technology for the extraction roadways in weakly cemented strata

Aiming at the characteristics of the poor steady ability, the short stable time and severe deformation behavior of weakly cemented soft surrounding rock around extraction roadway, a bolt–cable combined supporting technology was proposed. Numerical simulation was performed by using FLAC3D software to study the effects of different supporting systems. The simulation result proves that those supporting systems have good practical values. Based on real-time monitoring and analysis of the deformation of surrounding rock and the stress of supporting structure, real time information of deformation of surrounding rock and stress state of supporting structure of extraction roadway within weakly cemented strata was obtained. Monitoring results show that large deformation and failure of surrounding rock of extraction roadway within weakly cemented strata can be effectively controlled by the bolt–cable combined supporting technology, which ensures the long-term stability and safety of surrounding rock and supporting structure.

Assembly of a basket-like {Sr ⊂ P6Mo18O73} cage from 0D dimmer to 2D network and its photo-/electro-catalytic properties.

A series of basket-like heteropoly blues, formulated as (H4bth)[{Cu(H2O)}2{Sr ⊂ P6MoV2MoVI16O73}]·4H2O (1), {H2bih}3[{FeII(H2O)2}{Sr ⊂ P6MoV2MoVI16O73}]·2H2O (2), (H2bih)3[{CoII(H2O)2}{Sr ⊂ P6MoV2MoVI16O73}]·2H2O (3), (H2bih)3[{NiII(H2O)2}{Sr ⊂ P6MoV2MoVI16O73}]·2H2O (4), (H2bih)2(H2bip)[{Zn (H2O)0.5}{Sr ⊂ P6MoV2MoVI16O73}]·5.5H2O (5), (bth = 1,6-bis(triazole)hexane; bih = 1,6-bis(imidazol)hexane; bip = 1,5-bis(imidazol)pentane) have been synthesized hydrothermally and fully characterized. The structural analysis shows that all the compounds contain two electron reduced polyanions [Sr ⊂ P6MoV2MoVI16O73]8− (abbreviated as {P6Mo18O73}), which consists of a tetra vacant γ-Dawson-type{P2Mo14} unit and a “handle”-shaped {P4Mo4} segment encapsulating a Sr2+ cation in the central cavity. Compound 1 is a 6-connected two-dimensional (2D) layer, which represents the first 2D assembly of basket-type polyoxometalates. Compounds 2–4 are isostructural one-dimensional zigzag chains linked by an M(H2O)2 linker (M = iron for 2, cobalt for 3, and nickel for 4). Compound 5 is a dimeric cluster supported by a binuclear {Zn2(H2O)} unit. The optical band gaps of 1–5 reveal their semiconductive natures. The compounds if used as photocatalysts exhibit a universal high efficiency degradation ability for dyes such as methylene blue, Rhodamine B, and Azon phloxine. The lifetime and reaction mechanism of the catalysts were investigated with a series of experiments. The compounds also show good bifunctional electrocatalytic behavior for the oxidation of ascorbic acid (AA) and reduction of nitrite ions.