Phase-Space Metric for Non-Hamiltonian Systems

We consider an invariant skew-symmetric phase-space metric for non-Hamiltonian systems. We say that the metric is an invariant if the metric tensor field is an integral of motion. We derive the time-dependent skew-symmetric phase-space metric that satisfies the Jacobi identity. The example of non-Hamiltonian systems with linear friction term is considered.Comment: 12 page

Nonholonomic Constraints with Fractional Derivatives

We consider the fractional generalization of nonholonomic constraints defined by equations with fractional derivatives and provide some examples. The corresponding equations of motion are derived using variational principle.Comment: 18 page

Dynamics of Viscoplastic Deformation in Amorphous Solids

We propose a dynamical theory of low-temperature shear deformation in amorphous solids. Our analysis is based on molecular-dynamics simulations of a two-dimensional, two-component noncrystalline system. These numerical simulations reveal behavior typical of metallic glasses and other viscoplastic materials, specifically, reversible elastic deformation at small applied stresses, irreversible plastic deformation at larger stresses, a stress threshold above which unbounded plastic flow occurs, and a strong dependence of the state of the system on the history of past deformations. Microscopic observations suggest that a dynamically complete description of the macroscopic state of this deforming body requires specifying, in addition to stress and strain, certain average features of a population of two-state shear transformation zones. Our introduction of these new state variables into the constitutive equations for this system is an extension of earlier models of creep in metallic glasses. In the treatment presented here, we specialize to temperatures far below the glass transition, and postulate that irreversible motions are governed by local entropic fluctuations in the volumes of the transformation zones. In most respects, our theory is in good quantitative agreement with the rich variety of phenomena seen in the simulations.Comment: 16 pages, 9 figure

Capabilities of multi-pinhole SPECT with two stationary detectors for in vivo rat imaging

We aimed to investigate the image quality of the U-SPECT5/CT E-Class a micro single-photon emission computed tomography (SPECT) system with two large stationary detectors for visualization of rat hearts and bones using clinically available Tc-99m-labelled tracers. Sensitivity, spatial resolution, uniformity and contrast-to-noise ratio (CNR) of the small-animal SPECT scanner were investigated in phantom studies using an ultra-high-resolution rat and mouse multi-pinhole collimator (UHR-RM). Point source, hot-rod, and uniform phantoms with Tc-99m-solution were scanned for high-count performance assessment and count levels equal to animal scans, respectively. Reconstruction was performed using the similarity-regulated ordered-subsets expectation maximization (SROSEM) algorithm with Gaussian smoothing. Rats were injected with similar to 100 MBq [Tc-99m]Tc-MIBI or similar to 150 MBq [Tc-99m]Tc-HMDP and received multi-frame micro-SPECT imaging after tracer distribution. Animal scans were reconstructed for three different acquisition times and post-processed with different sized Gaussian filters. Following reconstruction, CNR was calculated and image quality evaluated by three independent readers on a five-point scale from 1="very poor" to 5="very good". Point source sensitivity was 567 cps/MBq and radioactive rods as small as 1.2 mm were resolved with the UHR-RM collimator. Collimator-dependent uniformity was 55.5%. Phantom CNR improved with increasing rod size, filter size and activity concentration. Left ventricle and bone structures were successfully visualized in rat experiments. Image quality was strongly affected by the extent of post-filtering, whereas scan time did not have substantial influence on visual assessment. Good image quality was achieved for resolution range greater than 1.8 mm in bone and 2.8 mm in heart. The recently introduced small animal SPECT system with two stationary detectors and UHR-RM collimator is capable to provide excellent image quality in heart and bone scans in a rat using standardized reconstruction parameters and appropriate post-filtering. However, there are still challenges in achieving maximum system resolution in the sub-millimeter range with in vivo settings under limited injection dose and acquisition time

Estimating the elastic modulus of landfast ice from wave observations

Progress in our understanding of wave–ice interactions is currently hindered by the lack of in situ observations and information of sea-ice properties, including the elastic modulus. Here, we estimate the effective elastic modulus of sea ice using observations of waves in ice through the deployment of three open-source geophone recorders on landfast sea ice. From observations of low-frequency dispersive waves, we obtain an estimate of the effective elastic modulus in the range of 0.4–0.7 GPa. This is lower than the purely elastic modulus of the ice estimated at 1 GPa as derived from in situ beam experiments. Importantly, our experimental observation is significantly lower than the default value currently in use in wave models. While our estimate is not representative for all sea ice, it does indicate that considerably more measurements are required to provide confidence in the development of parameterizations for this complex sea-ice property for wave models

Hidden attractors in fundamental problems and engineering models

Recently a concept of self-excited and hidden attractors was suggested: an attractor is called a self-excited attractor if its basin of attraction overlaps with neighborhood of an equilibrium, otherwise it is called a hidden attractor. For example, hidden attractors are attractors in systems with no equilibria or with only one stable equilibrium (a special case of multistability and coexistence of attractors). While coexisting self-excited attractors can be found using the standard computational procedure, there is no standard way of predicting the existence or coexistence of hidden attractors in a system. In this plenary survey lecture the concept of self-excited and hidden attractors is discussed, and various corresponding examples of self-excited and hidden attractors are considered

Optical Dissection of Neural Circuits Responsible for Drosophila Larval Locomotion with Halorhodopsin

Halorhodopsin (NpHR), a light-driven microbial chloride pump, enables silencing of neuronal function with superb temporal and spatial resolution. Here, we generated a transgenic line of Drosophila that drives expression of NpHR under control of the Gal4/UAS system. Then, we used it to dissect the functional properties of neural circuits that regulate larval peristalsis, a continuous wave of muscular contraction from posterior to anterior segments. We first demonstrate the effectiveness of NpHR by showing that global and continuous NpHR-mediated optical inhibition of motor neurons or sensory feedback neurons induce the same behavioral responses in crawling larvae to those elicited when the function of these neurons are inhibited by Shibirets, namely complete paralyses or slowed locomotion, respectively. We then applied transient and/or focused light stimuli to inhibit the activity of motor neurons in a more temporally and spatially restricted manner and studied the effects of the optical inhibition on peristalsis. When a brief light stimulus (1–10 sec) was applied to a crawling larva, the wave of muscular contraction stopped transiently but resumed from the halted position when the light was turned off. Similarly, when a focused light stimulus was applied to inhibit motor neurons in one or a few segments which were about to be activated in a dissected larva undergoing fictive locomotion, the propagation of muscular constriction paused during the light stimulus but resumed from the halted position when the inhibition (>5 sec) was removed. These results suggest that (1) Firing of motor neurons at the forefront of the wave is required for the wave to proceed to more anterior segments, and (2) The information about the phase of the wave, namely which segment is active at a given time, can be memorized in the neural circuits for several seconds