Non-hydrodynamic modes in viscoelastic behaviour of simple fluids

ABSTRACT

We discuss the role of non-hydrodynamic processes in viscoelastic transition in pure liquids. In particular, using both analytical results and molecular dynamics simulations, we clarify the effect of the shear stress relaxation on the transverse dynamics. We use as an example the Lennard-Jones fluids. We analyse the frequency dependence of the shear modulus and its connection to the non-hydrodynamic shear relaxation mode. The analysis of the relaxation times of the non-hydrodynamic modes in longitudinal and transverse dynamics makes evidence that the emergence of the non-hydrodynamic transverse excitations outside the propagation gap is not directly connected to the onset of the positive sound dispersion.     

Multistability of twisted states in non-locally coupled Kuramoto-type models

A ring of N identical phase oscillators with interactions between L-nearest neighbors is considered, where L ranges from 1 (local coupling) to N/2 (global coupling). The coupling function is a simple sinusoid, as in the Kuramoto model, but with a minus sign which has a profound influence on its behavior. Without the limitation of the generality, the frequency of the free-running oscillators can be set to zero. The resulting system is of gradient type, and therefore, all its solutions converge to an equilibrium point. All so-called q-twisted states, where the phase difference between neighboring oscillators on the ring is 2πq/N, are equilibrium points, where q is an integer. Their stability in the limit N → ∞ is discussed along the line of Wiley et al. [Chaos 16, 015103 (2006)] In addition, we prove that when a twisted state is asymptotically stable for the infinite system, it is also asymptotically stable for sufficiently large N. Note that for smaller N, the same q-twisted states may become unstable and other q-twisted states may become stable. Finally, the existence of additional equilibrium states, called here multi-twisted states, is shown by numerical simulation. The phase difference between neighboring oscillators is approximately 2πq/N in one sector of the ring, -2πq/N in another sector, and it has intermediate values between the two sectors. Our numerical investigation suggests that the number of different stable multi-twisted states grows exponentially as N → ∞. It is possible to interpret the equilibrium points of the coupled phase oscillator network as trajectories of a discrete-time translational dynamical system where the space-variable (position on the ring) plays the role of time. The q-twisted states are then fixed points, and the multi-twisted states are periodic solutions of period N that are close to a heteroclinic cycle. Due to the apparently exponentially fast growing number of such stable periodic solutions, the system shows spatial chaos as N → ∞.     

Representation of a Monotone Curve by a Contour with Regular Change in Curvature

The problem of modelling a smooth contour with a regular change in curvature representing a monotone curve with specified accuracy is solved in this article. The contour was formed within the area of the possible location of a convex curve, which can interpolate a point series. The assumption that if a sequence of points can be interpolated by a monotone curve, then the reference curve on which these points have been assigned is monotone, provides the opportunity to implement the proposed approach to estimate the interpolation error of a point series of arbitrary configuration. The proposed methods for forming a convex regular contour by arcs of ellipses and B-spline ensure the interpolation of any point series in parts that can be interpolated by a monotone curve. At the same time, the deflection of the contour from the boundaries of the area of the possible location of the monotone curve can be controlled. The possibilities of the developed methods are tested while solving problems of the interpolation of a point series belonging to monotone curves. The problems are solved in the CAD system of SolidWorks with the use of software application created based on the methods developed in the research work.     

Distribution of light alkanes in the reaction of graphite hydrogenation at pressure of 0.1–7.8 GPa and temperatures of 1000–1350°C

ABSTRACT

We studied the effect of pressure and temperature on the hydrocarbon (HC) chain length distribution and total amount of HCs in the reaction of direct graphite hydrogenation at pressures of 0.1–7.8?GPa and temperatures of 1000–1350°C. An increase in pressure was found to lead both to an increase in the absolute yield of HCs due to direct graphite hydrogenation and to chain elongation of HC products. Light alkanes predominate among HCs in the entire studied range of P–T parameters. However, their concentration in quenched fluids increases as pressure is elevated, from less than 10?rel.% at 0.1?GPa to more than 40–50?rel.% at P?≥?3.8?GPa. Methane is actually the only light alkane among reaction products at 0.1?GPa and 1000°C, while it is a minor component at 7.8?GPa and 1350°C. The most stable alkane at pressures above 3.8?GPa is ethane (C₂H₆).     

The Lawson number of a semitopological semilattice

Semigroup Forum - For a Hausdorff topologized semilattice X its Lawson number $$\bar{\Lambda }(X)$$ is the smallest cardinal $$\kappa $$ such that for any distinct points $$x,y\in X$$ there exists...     

Membrane potential is involved in regulation of photosynthetic reactions in the marine diatom Thalassiosira weissflogii

High-intensity Chl fluorescence transients (OJIP transients) and light-induced kinetics of the delayed light emission were measured in diatom microalga Thalassiosira weissflogii in the presence of various uncouplers and photosynthetic inhibitors. The I step in the OJIP transients in T. weissflogii was essentially reduced or completely absent but was restored in the presence of uncouplers valinomycin, FCCP, and nigericin. Moreover, valinomycin enhanced ΔpH-dependent non-photochemical fluorescence quenching following the OJIP rise. In the presence of valinomycin, the transthylakoid membrane potential was significantly inhibited as evaluated by measurements of the delayed light emission. The results suggest a membrane potential control of the fluorescence yield in T. weissflogii. Possible mechanisms underlying the observed effects of uncouplers are discussed.     

Reactions of 4,5‐Dihydro‐1,4‐Benzothiazepin‐3(2H)‐one 1,1‐Dioxide and 1,5‐Dihydro‐4,1‐Benzothiazepin‐2(3H)‐one 4,4‐Dioxide Derivatives with Vilsmeier Reagent and DMFDMA

The regioselectivity of the interaction between isomeric 4,5‐dihydro‐1,4‐benzothiazepin‐3(2H)‐one 1,1‐dioxide and 1,5‐dihydro‐4,1‐benzothiazepin‐2(3H)‐one 4,4‐dioxide derivatives with the Vilsmeier reagent and DMFDMA (N,N‐dimethylformamide dimethylacetal) has been investigated. The structures of synthesized compounds are confirmed by ¹H, ¹³C NMR, elemental analysis, and X‐ray data.