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Klitgaard Bennetsen posted an update 6 months, 1 week ago
We study generalized Cattaneo (telegrapher’s) equations involving memory effects introduced by smearing the time derivatives. Consistency conditions where the smearing functions obey restrict freedom in their choice but the proposed scheme goes beyond the approach based on using fractional derivatives. We find conditions under which solutions of the equations considered so far can be recognized as probability distributions, i.e., are normalizable and nonnegative on their domains. Nonnegativity of solutions is demonstrated by methods of positive definite and completely monotonic functions with the Bernstein theorem being the cornerstone of the ongoing proofs. Analysis of exactly solvable examples and relevant mean-squared displacements enables us to classify diffusion processes described by such got solutions and to identify them with either ordinary or anomalous diffusion which character may change over time. To complete the present research we compare our results with those obtained using the continuous-time random-walk and the continuous-time persistent random-walk approaches.In the thermodynamics of nanoscopic systems, the relation between classical and quantum mechanical description is of particular importance. To scrutinize this correspondence we study an anharmonic oscillator driven by a periodic external force with slowly varying amplitude both classically and within the framework of quantum mechanics. The energy change of the oscillator induced by the driving is closely related to the probability distribution of work for the system. With the amplitude λ(t) of the drive increasing from zero to a maximum λ_max and then going back to zero again, the initial and final Hamiltonian coincide. Vorinostat The main quantity of interest is then the probability density P(E_f|E_i) for transitions from initial energy E_i to final energy E_f. In the classical case nondiagonal transitions with E_f≠E_i mainly arise due to the mechanism of separatrix crossing. We show that approximate analytical results within the pendulum approximation are in accordance with numerical simulations. In the quantum case numerically exact results are complemented with analytical arguments employing Floquet theory. For both the classical and quantum case we provide an intuitive explanation for the periodic variation of P(E_f|E_i) with the maximal amplitude λ_max of the driving.We develop linear stability analysis (LSA) to quantitatively predict the dynamics of a perturbed plane wave in nonlinear systems. We take a nonintegrable fiber model with purely fourth-order dispersion as an example to demonstrate this method’s effectiveness. For a Gaussian-type initial perturbation with cosine-type modulation on a plane wave, its propagation velocities, periodicity, and localization are predicted successfully, and the range of application is discussed. Importantly, the modulation-instability-induced growth of localized perturbation is proved different from the one of purely periodic perturbation and requires the modification of gain value for more accurate prediction. The method offers a needful supplement and improvement for LSA and paves a way to study the dynamics of a perturbed plane wave in more practical nonlinear systems.A new type of plasma accelerator-a low-power ( less then 30W), miniature (cm-sized), two-stage pulsed magneto-plasma-dynamic thruster-has been proposed. Being magnetized by an axially symmetric dc magnetic field of ∼200 mT, the vacuum arc discharge demonstrates a threshold behavior Parameters such as thrust and the thrust-to-power ratio rapidly jump after a certain dc voltage (∼30 V) is applied on the accelerating electrode. We show that such an effect improves the thrust (from ∼2 to ∼210 µN), efficiency (from ∼1% to 50%), and thrust-to-power ratio (from ∼0.5 to ∼18 µN/W).Vertically aligned carbon nanotube (VA-CNT) arrays were grown on several chromium (Cr)-coated glass substrates using a plasma-enhanced chemical vapor deposition system. The CNTs were 2μm long and had a site density of 2×10^9cm^-2 on the substrates. Two VA-CNT slides on Cr glass substrates were put together to design a homeotropic electro-optic liquid crystal (LC) device. A negative dielectric anisotropic LC was used in the device. The π-π stacking interaction between the LC and the VA-CNTs allows the LC material to align homeotropically in the cell. When an external electric field was applied using the transparent conducting Cr layers, the LC achieves a planar orientation above a threshold field. These results successfully demonstrate the optical, electro-optical operations, and the field-induced dynamic response of a homeotropic LC device employing the VA-CNT arrays as the homeotropic-alignment agent. This study significantly advances the range and understanding of nanostructured surfaces that provide vertical alignment of LCs.We study the mobility of objects embedded in an immersed granular packing and subjected to cyclic loadings. With this aim, we conducted uplift experiments whereby a horizontal plate is embedded in the packing and subjected to a vertical cyclic force oscillating between zero and a maximum amplitude. Tests performed at different cyclic force frequencies and amplitudes evidence the development of three mobility regimes whereby the plate stays virtually immobile, moves up steadily, or slowly creeps upwards. Results show that steady plate uplift can occur at lower force magnitudes when the frequency is increased. We propose an interpretation of this frequency-weakening behavior based on force relaxation experiments and on the analysis of the mobility response of theoretical viscoelastoplastic mechanical analog. These results and analysis point out inherent differences in mobility response between steady and cyclic loadings in immersed granular materials.In a systematic study of shock wave propagating in crystalline polyethylenes using molecular dynamics method and the electron force field (eFF) potential, we show that microscopic structure of shock front is significantly affected by the anisotropy of long carbon chain and the bond breaking and recombination dynamics. However, macroscopic properties measured in Hugoniot experiments, such as compression ratio and shock velocity, are not sensitive to carbon chain anisotropy and bond dynamics. Our work also display that hydrogen molecules are formed when the piston speed is in the region between 10 km/s and 30 km/s. However, carbon-hydrogen pair distribution function does not display an indication of carbon-hydrogen phase segregation.
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