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Molecular motors are cellular machines that drive the spatial organization of the cells by transporting cargos along intracellular filaments. Although the mechanical properties of single molecular motors are relatively well characterized, it remains elusive how the geometry of a load imposed on a motor affects its processivity, i.e., the average distance that a motor moves per interaction with a filament. Here, we theoretically explore this question for a single-kinesin molecular motor by analyzing the load dependence of the stepping and detachment processes. We find that the processivity of the kinesin increases with lowering the load angle between the kinesin and the microtubule filament, due to the deceleration of the detachment rate. When the load angle is large, the processivity is predicted to enhance with accelerating the stepping rate through an optimal distribution of the load over the kinetic transition rates underlying a mechanical step of the motor. These results provide new insights into understanding of the design of potential synthetic biomolecular machines that can travel long distances with high velocities.We present experimental and numerical results for the parametric fluctuation properties in the spectra of classically chaotic quantum graphs with unitary or symplectic symmetry. A level dynamics is realized by changing the lengths of a few bonds parametrically. The long-range correlations in the spectra reveal at a fixed parameter value deviations from those expected for generic chaotic systems with corresponding universality class. They originate from modes which are confined to individual bonds or explore only a fraction of the quantum graph. Similarly, discrepancies are observed in the avoided-crossing distribution, velocity correlation function, and the curvature distribution of the level dynamics which also may be attributed to such localized modes. We demonstrate that these may be easily identified by inspecting the level dynamics and consequently their nonuniversal contributions to the parametric spectral properties may be diminished considerably. This is corroborated by numerical studies.To study the effects of chunk mixing, the implosion experiments using capsules filled with deuterated foam (CDF capsule) were carried out on the Shenguang laser facility. Three types of the CDF capsules, namely the capsules without Au dopant, with micrometer Au dopant, and with atomic Au dopant, were used in the experiments. The neutron yields, the size, and the emission intensity of the hotspots were measured. The CDF capsules without Au dopant produced the highest neutron yield and the largest hotspot size at the time of peak emission. this website The capsules with micrometer or atomic Au dopant showed similar reduced neutron yield and hotspot size. The time-resolved hotspot emissions showed different behaviors between different capsules. One-dimensional simulations were carried out to understand the implosion dynamics of the CDF capsule without Au dopant, and to provide the thermodynamic conditions that the Au dopant would experience during the implosion. The effects of Au dopant were then discussed qualitatively.We experimentally study the viscous fingering problem of viscoplastic fluids in channels of rectangular cross section. We find that a yield stress-dependent capillary number (Ca^*) and an aspect ratio-dependent Bond number (Bo^*) can classify the finger shape into ramified and unified fingering patterns, and the finger flow regime into yield stress, viscosity, and aspect ratio-buoyancy-dominated regimes. For these regimes, we provide the transition boundaries using Ca^* and Bo^* and propose simple relations to predict the finger width, for a wide range of flow parameters, versus the capillary number, the channel aspect ratio, and the rheology of the viscoplastic fluid.Using the properties of random Möbius transformations, we investigate the statistical properties of the reflection coefficient in a random chain of lossy scatterers. We explicitly determine the support of the distribution and the condition for coherent perfect absorption to be possible. We show that at its boundaries the distribution has Lifshits-like tails, which we evaluate. We also obtain the extent of penetration of incoming waves into the medium via the Lyapunov exponent. Our results agree well when compared to numerical simulations in a specific random system.We study the first-passage time, the distribution of the maximum, and the absorption probability of fractional Brownian motion of Hurst parameter H with both a linear and a nonlinear drift. The latter appears naturally when applying nonlinear variable transformations. Via a perturbative expansion in ɛ=H-1/2, we give the first-order corrections to the classical result for Brownian motion analytically. Using a recently introduced adaptive-bisection algorithm, which is much more efficient than the standard Davies-Harte algorithm, we test our predictions for the first-passage time on grids of effective sizes up to N_eff=2^28≈2.7×10^8 points. The agreement between theory and simulations is excellent, and by far exceeds in precision what can be obtained by scaling alone.The homogenization approach to wave propagation through saturated porous media is extended in order to include the compressibility of the interstitial fluid and the existence of several connected pore components which may or not percolate. The necessary theoretical developments are summarized and the Christoffel equation whose solutions provide the wave velocities is presented. Some analytical developments are proposed for isotropic media. Finally, a systematic application to a synthetic porous medium illustrates the methodology and its results.The diffuse-interface model (DIM) is a widely used tool for modeling fluid phenomena involving interfaces, such as sessile drops (liquid drops on a solid substrate, surrounded by saturated vapor) and liquid ridges (two-dimensional sessile drops). In this work, it is proved that, surprisingly, the DIM does not admit solutions describing static liquid ridges. If, however, the vapor-to-liquid density ratio is small-for example, for water at room temperature-the ridges can still be observed as quasistatic states, as their evolution is too slow to be distinguishable from evaporation. Interestingly, the nonexistence theorem cannot be extended to axisymmetric sessile drops and ridges near a vertical wall, which are not ruled out.
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