Biharmonic Attractors of Internal Gravity Waves

Abstract— The hydrodynamic system that admits the development of internal wave attractors under biharmonic forcing is investigated. It is shown that in the case of low amplitude of external forcing the wave pattern consists of two attractors that interact between themselves only slightly: the total energy of the system is equal to the sum of energies of the components with high accuracy. In the nonlinear case the attractors interact in the more complex way which leads to the development of a cascade of triad interactions generating a rich set of time scales. In the case of closely adjacent frequencies of the components of a biharmonic perturbation, the nonlinear “beating” regime develops, namely, the mean energy of the system of coupled attractors performs oscillations at a large time scale that corresponds to the beating period. It is found that the high-frequency energy fluctuations corresponding to the same mean energy can differ by an order of magnitude depending on whether the envelope of the mean value increases or decreases.

On a variant of Newton-Coulomb's law

A variant of the usual formulas for gravitational and electrostatic fields, differing from those by a logarithmic term, is introduced in order to solve some questions connected with a possible atomic contraction phenomenon at large time scale and the so-called hidden mass problem in cosmology. This approach is conceptuallly related to the MOND theory of M. Milgrom but allows a reversal of attracting forces when the distance becomes very small. The asymptotic behavior of solutions of a related dissipative ODE is studied, we obtain that all bounded trajectories converge to a point where the field vanishes.

Coarse-Grained Models of RNA Nanotubes for Large Time Scale Studies in Biomedical Applications

In order to describe the physical properties of large time scale biological systems, coarse-grained models play an increasingly important role. In this paper we develop Coarse-Grained (CG) models for RNA nanotubes and then, by using Molecular Dynamics (MD) simulation, we study their physical properties. Our exemplifications include RNA nanotubes of 40 nm long, equivalent to 10 RNA nanorings connected in series. The developed methodology is based on a coarse-grained representation of RNA nanotubes, where each coarse bead represents a group of atoms. By decreasing computation cost, this allows us to make computations feasible for realistic structures of interest. In particular, for the developed coarse-grained models with three bead approximations, we calculate the histograms for the bond angles and the dihedral angles. From the dihedral angle histograms, we analyze the characteristics of the links used to build the nanotubes. Furthermore, we also calculate the bead distances along the chains of RNA strands in the nanoclusters. The variations in these features with the size of the nanotube are discussed in detail. Finally, we present the results on the calculation of the root mean square deviations for a developed RNA nanotube to demonstrate the equilibration of the systems for drug delivery and other biomedical applications such as medical imaging and tissue engineering.

Gap Junction Dynamics Induces Localized Conductance Bistability in Cardiac Tissue

Connexins are specialized ionic channels that control the action potential propagation between cardiac myocytes. In this paper, we study the connexin dynamics in a one-dimensional model of cardiac tissue. We show that the connexin dynamics may lead to a spatial organization of the gap junction conductance. In the numerical simulations presented in this paper we have found two different regimes for the spatial organization of the conductances: (a) a spatially uniform conductance; (b) a spatially complex pattern of local values of high and low conductances. In addition, we have observed that, locally, the two final states are limit cycles with a period equal to the period associated with the external excitation of the tissue strand. The conductance dispersion usually takes place on a very large time scale, i.e. thousands of heart beats, and on a very short spatial scale. Due to its simplicity, the one-dimensional setting allows a detailed study of the emerging structure and in particular very long simulations. We have studied the transition between the two aforementioned states as a function of the gap junction conductance characteristics. Furthermore, we have studied the effect of initially added noises on the outcome of the system. Finally, using spatial autocorrelation functions we have characterized the spatial dispersion in conductance values.

Phase shift between changes in global temperature and atmospheric Co2 content under the external emissions of greenhouse gases into the atmosphere

The phase shift between changes in the global surface temperature Tg and atmospheric CO2 content has been shown earlier not to characterize causal relationships in the Earth system in the general case. Specifically, the sign of this phase shift under nongreenhouse radiative forcing changes depends on the time scale of this forcing. This paper analyzes the phase shift between changes in the global surface temperature Tg and the atmospheric CO2 content qCO2 under synchronous external emissions of carbon dioxide and methane into the atmosphere on the basis of numerical experiments with the IAP RAS climatic model and a conceptual climate model with carbon cycle. For a sufficiently large time scale of external forcing, the changes in qCO2 lag relative to the corresponding changes in Tg.

Analysis on Variability of Buzau River Monthly Discharges

The purpose of this article is analysing the variability of Buzau river monthly mean discharges, maximum and minimum over time and the impact of Siriu Dam on these discharges. Keeping a stable, moderate variability on the water flow has a significant importance, as this assures normality of life and functionality of the dams. On another hand, the dams are in-built with a range of parameters, decided according to this variability of the discharges. The used data has been collected from Nehoiu and Basca Roziliei hydrometric stations and spans on 55 years, from 1st January 1955 to 31st December 2010. Mid-period, on 30th September 1984, Siriu Dam started operating and the results reveal that its impact on the variability has been moderate on a large time scale. Important changes appear on smaller time scale, as months. The results are supported by graphs drawn in Excel and methods embedded by software.

A Retrospective Analysis of the Evolution of Pratt Trusses in Indiana

A simple method is presented to carry out a retrospective analysis to examine the development of load-bearing structures. The idea is to eliminate the differences coming from technological changes (such as joints, profiles, loads) by using relative numbers to express the relation of the structures to the possible theoretical solutions under the same circumstances. The method is demonstrated by investigating the impact of historical changes focusing on metal Pratt trusses spanning about 100 ft, located in Indiana, U.S., erected between 1870 and 1937. Data of 87 structures was collected and compared to the results of a multi-objective optimisation computed using a genetic algorithm. Using the relative numbers acquired by evaluating the objective functions for the historical structures, a large time-scale optimisation process through history can be visualised. Plotting them on the Pareto-front diagram determined by the genetic algorithm and examining the historical background of the state revealed that the economic and industrial changes, in fact, had a considerable impact on the design trends, which manifests in changes of the weights of the objective functions.