Adiabatic Brownian motor with a stepwise potential perturbed by a dichotomous harmonic sygnal

We obtained an analytical expression for the average motion velocity of an adiabatic Brownian motor (ratchet), which operates due to small dichotomous spatially harmonic fluctuations of a stepwise potential. The symmetry properties of the average velocity as a functional of the stationary and fluctuating components of the nanoparticle potential energy are revealed, and the ranges of values of the system parameters that ensure the rightward and leftward motion of the motor are determined. We showed that the average motor velocity is a non-monotonic function of the stepwise potential height. For a singular (infinitely high and narrow) potential barrier, the average velocity depends non-monotonically on the «power» of this barrier (the barrier width multiplied by the exponent of the ratio of the barrier height to the thermal energy). The article continues the further development of theoretical methods of symmetry analysis by applying the general approaches proposed by the authors to specific motor systems.

Durotaxis of passive nanoparticles on elastic membranes

The transport of macromolecules and nanoscopic particles to a target cellular site is a crucial aspect in many physiological processes. This directional motion is generally controlled via active mechanical and chemical processes. Here we show, by means of molecular dynamics simulations and an analytical theory, that completely passive nanoparticles can exhibit directional motion when embedded in non-uniform mechanical environments. Specifically, we study the motion of a passive nanoparticle adhering to a mechanically non-uniform elastic membrane. We observe a non-monotonic affinity of the particle to the membrane as a function of the membrane's rigidity, which results in the particle transport. This transport can be both up or down the rigidity gradient, depending on the absolute values of the rigidities that the gradient spans across. We conclude that rigidity gradients can be used to direct average motion of passive macromolecules and nanoparticles on deformable membranes, resulting in the preferential accumulation of the macromolecules in regions of certain mechanical properties.

Sparse Optical Flow Computation Using Wave Equation-Based Energy

Identification of motion in videos is a fundamental task for several computer vision problems. One of the main tools for motion identification is optical flow, which estimates the projection of the 3D velocity of the objects onto the plane of the camera. In this work, we propose a differential optical flow method based on the wave equation. The optical flow is computed by minimizing a functional energy composed by two terms: a data term based on brightness constancy and a regularization term based on energy of the wave. Flow is determined by solving a system of linear equations. The decoupling of the pixels in the solution allows solving the system by a direct or iterative approach and makes the method suitable for parallelization. We present the convergence conditions for our method since it does not converge for all the image points. For comparison purposes, we create a global video descriptor based on histograms of optical flow for the problem of action recognition. Despite its sparsity, results show that our method improves the average motion estimation, compared with classical methods. We also evaluate optical flow error measures in image sequences of a classical dataset for method comparison.

Average motion of emerging solar active region polarities

Context. The tilt of solar active regions described by Joy’s law is essential for converting a toroidal field to a poloidal field in Babcock-Leighton dynamo models. In thin flux tube models the Coriolis force causes what we observe as Joy’s law, acting on east-west flows as they rise towards the surface. Aims. Our goal is to measure the evolution of the average tilt angle of hundreds of active regions as they emerge, so that we can constrain the origins of Joy’s law. Methods. We measured the tilt angle of the primary bipoles in 153 emerging active regions (EARs) in the Solar Dynamics Observatory Helioseismic Emerging Active Region survey. We used line-of-sight magnetic field measurements averaged over 6 h to define the polarities and measure the tilt angle up to four days after emergence. Results. We find that at the time of emergence the polarities are on average aligned east-west, and that neither the separation nor the tilt depends on latitude. We do find, however, that EARs at higher latitudes have a faster north-south separation speed than those closer to the equator at the emergence time. After emergence, the tilt angle increases and Joy’s law is evident about two days later. The scatter in the tilt angle is independent of flux until about one day after emergence, when we find that higher-flux regions have a smaller scatter in tilt angle than lower-flux regions. Conclusions. Our finding that active regions emerge with an east-west alignment is consistent with earlier observations, but is still surprising since thin flux tube models predict that tilt angles of rising flux tubes are generated below the surface. Previously reported tilt angle relaxation of deeply anchored flux tubes can be largely explained by the change in east-west separation. We conclude that Joy’s law is caused by an inherent north-south separation speed present when the flux first reaches the surface, and that the scatter in the tilt angle is consistent with buffeting of the polarities by supergranulation.

Disentangling turbulent and non-diffusive fluxes in the boundary layer

<p>Arithmetic averaging procedures are traditionally used in many applications in the field of micrometeorology, but these neglect Osborne Reynolds's specification of turbulence, and thus, strictly speaking, violate the momentum conservation law. Recently, it has been shown  that applying linear momentum conservation to surface exchanges defines an average motion in the surface-normal direction (i.e., a Stefan flow), and thereby describes a non-diffusive transport that is distinct from turbulent transport. Here we examine data from a nearly ideal micrometeorological field site (extensive, flat, and mono specific-reed wetland) to show that traditional flux-tower calculations, including but not limited to the Webb corrections,  generally provide an inadequate approximation of turbulent  fluxes and yet still adequately characterize the net fluxes in most traditional cases. The importance of such conflation of diffusive and non-diffusive transport is greatest for situations with relatively large non-diffusive fluxes, as occurs during particular times of day in general and particularly when considering fluxes in the stream-wise direction. An examination of fluxes calculated using the traditional arithmetic averaging procedure, versus the proposed, more theoretically appropriate calculations that fully obey conservation law, illustrates important implications for the characterization of gas-exchange processes and more generally the discipline of micrometeorology. These implications may become particularly critical in near future as gas flux measurements enter an era of automated operation on massive network scales, including automated gas flux calculations. At the same time, such measurements strive to adequately represent gas exchange of newer species with extremely low fluxes (vs traditionally measured larger fluxes of H2O and CO2). Multiple assumptions, and neglected terms and processes historically deployed for evaluating larger fluxes, may no longer work well when much smaller fluxes are considered, especially when measured by a non-expert using a fully automated flux station. These no-longer-negligible aspects include fundamentals of adequately handling the diffusive and non-diffusive transport mechanisms addressed in this presentation.</p>

Light Control of the Diffusion Coefficient of Active Fluids

Active fluids refer to the fluids that contain self-propelled particles such as bacteria or microalgae, whose properties differ fundamentally from the passive fluids. Such particles often exhibit an intermittent motion, with high-motility “run” periods broken by low-motility “tumble” periods. The average motion can be modified with external stresses, such as nutrient or light gradients, leading to a directed movement called chemotaxis and phototaxis, respectively. Using cyanobacterium Synechocystis sp. PCC 6803, a model microorganism to study photosynthesis, we track the bacterial response to light stimuli, under isotropic and nonisotropic (directional) conditions. In particular, we investigate how the intermittent motility is influenced by illumination. We find that just after a rise in light intensity, the probability to be in the run state increases. This feature vanishes after a typical characteristic time of about 1 h, when initial probability is recovered. Our results are well described by a mathematical model based on the linear response theory. When the perturbation is anisotropic, we observe a collective motion toward the light source (phototaxis). We show that the bias emerges due to more frequent runs in the direction of the light, whereas the run durations are longer whatever the direction.

Stimulus reliability automatically biases temporal integration of discrete perceptual targets

Many decisions, from crossing a busy street to choosing a profession, require integration of discrete sensory events. Previous studies have shown that integrative decision-making favours more reliable stimuli, mimicking statistically optimal integration. It remains unclear, however, whether reliability biases are automatic or strategic. To address this issue, we asked observers to reproduce the average motion direction of two suprathreshold coherent motion signals, presented successively and varying in reliability. Although unbiased responses were both optimal and possible by virtue of task rules and suprathreshold motion coherence, we found robust behavioural biases favouring the more reliable stimulus. Using population-tuning modelling of brain activity recorded using electroencephalography, we characterised tuning to the average motion direction. In keeping with the behavioural biases, the tuning profiles also exhibited reliability biases. Taken together, our findings reveal that temporal integration of discrete sensory events is automatically and sub-optimally weighted according to stimulus reliability.

Stochastic Modelling for Dynamics of Interacting Populations

The paper deals with a mathematical model for two interacting populations. Under the assumption of fast stochastic contacting of populations, we derive stochastic Poisson-type differential equations with a small parameter and propose an approximative algorithm for quantitative analysis of population dynamics that consists of two steps. First, we derive an ordinary differential equation for mean value of each population growth and analyse the average asymptotic population behaviour. Then, applying diffusion approximation procedure, we derive a stochastic Ito differential equation for small random deviations on the average motion in a form of a linear non-homogeneous Ito stochastic differential equation and analyse the probabilistic characteristics of the Gaussian process given by this equation.

Phototactic Behaviour of Active Fluids: Effects of Light Perturbation on Diffusion Coefficient of Bacterial Suspensions

Active fluids refer to the fluids that contain self-propelled particles such as bacteria or micro-algae, whose properties differ fundamentally from the passive fluids. Such particles often exhibit an intermittent motion; with high-motility “run” periods separated by low-motility “tumble” periods. The average motion can be modified with external stresses, such as nutrient or light gradient, leading to a directed movement called chemotaxis and phototaxis, respectively. Using cyanobacterium Synechocystis sp.PCC 6803, a model micro-organism to study photosynthesis, we track the bacterial response to light stimuli, under isotropic and non-isotropic conditions. In particular, we investigate how the intermittent motility is influenced by illumination. We find that just after a rise in light intensity, the probability to be in the run state increases. This feature vanishes after a typical time of about 1 hour, when initial probability is recovered. Our results are well described by a model based on the linear response theory. When the perturbation is anisotropic, the characteristic time of runs is longer whatever the direction, similar to what is observed with isotropic conditions. Yet we observe a collective motion toward the light source (phototaxis) and show that the bias emerges because of more frequent runs towards the light.

Physiological motion of the optic chiasm and its impact on stereotactic radiosurgery dose

Objective: Avoidance of radiation-induced optic neuropathy (RION) from stereotactic radiosurgery (SRS) requires precise anatomical localization; however, no prior studies have characterized the physiologic motion of the optic chiasm. We measured the extent of chiasm motion and its impact on SRS dose. Methods: In this cross-sectional study, serial MRI was performed in multiple planes in 11 human subjects without optic pathway abnormalities to determine chiasm motion across time. Subsequently, the measured displacement was applied to the hypothetical chiasm dose received in 11 patients treated with SRS to a perichiasmatic lesion. Results: On sagittal images, the average anteroposterior chiasm displacement was 0.51 mm [95% confidence interval (CI) 0.27 – 0.75 mm], and the average superior-inferior displacement was 0.48 mm (95% CI 0.22 – 0.74 mm). On coronal images, the average superior–inferior displacement was 0.42 mm (95% CI 0.13 – 0.71 mm), and the average lateral displacement was 0.75 mm (95% CI 0.42 – 1.08 mm). In 11 patients who underwent SRS to a perichiasmatic lesion, the average displacements increased the maximum chiasm dose (Dmax) by a mean of 14 % (range 6–23 %; p < 0.001). Conclusion: Average motion of the optic chiasm was approximately 0.50–0.75 mm, which increased chiasm Dmax by a mean of 14%. In the occasional patient with higher-than-average chiasm motion in a region of steep dose gradient, the increase in chiasm Dmax and risk of RION could be even larger. Similarly, previously reported chiasm dose constraints may underestimate the true dose received during radiosurgery. Advances in knowledge: To limit the risk of RION, clinicians may consider adding a 0.50–0.75 mm expansion to the chiasm avoidance structure.