Damping of Vertically Excited Surface Wave in Weakly Viscous Fluid

In a vertically oscillating circular cylindrical container, singular perturbation theory of two-time scale expansions is developed in weakly viscous fluids to investigate the motion of single free surface standing wave by linearizing the Navier-Stokes equation. The fluid field is divided into an outer potential flow region and an inner boundary layer region. The solutions of both two regions are obtained and a linear amplitude equation incorporating damping term and external excitation is derived. The condition to appear stable surface wave is obtained and the critical curve is determined. In addition, an analytical expression of damping coefficient is determined. Finally, the dispersion relation, which has been derived from the inviscid fluid approximation, is modified by adding linear damping. It is found that the modified results are reasonably closer to experimental results than former theory. Result shows that when forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when forcing frequency is high, the surface tension of the fluid is prominent.

Morphological Stability of Epitaxial Thin Elastic Films by Van Der Waals Force

The morphological stability of epitaxial thin elastic films on a substrate by van der Waals force is discussed. It is found that only van der Waals force with negative Hamaker constant (A < 0) tends to stabilize the film, and the lower bound for the Hamaker constant is also obtained for the stability of thin film. The critical value of the undulation wavelength is found to be a function of both film thickness and external stress. The charateristic time-scale for surface mass diffusion scales to the fourth power to the wavelength of the perturbation.

Recovery of the solitons using a lattice Boltzmann model

We formulate a lattice Boltzmann model which simulates Korteweg-de Vries equation by using a method of higher moments of lattice Boltzmann equation. Using a series of lattice Boltzmann equations in different time scales and the conservation law in time scale to, we obtain equilibrium distribution function. The numerical examples show that the method can be used to simulate soliton.

Molecular Dynamics Simulation of Barnacle Cement

Barnacle cement is an underwater adhesive that is used for permanent settlement. Its main components are insoluble protein complexes that have not been fully studied. In present article, we chose two proteins of barnacle cement for study, 36-KD protein and Mrcp-100K protein. In order to investigate the characteristic of above two proteins, we introduced the method of molecular modeling. And the simulation package GROMACS was used to simulate the behavior of these proteins. In this article, before the simulations, we introduce some theories to predict the time scale for polymer relaxation. During the simulation, we mainly focus on two properties of these two proteins: structural stability and adhesive force to substrate. First, we simulate the structural stability of two proteins in water, and then the stability of 36-KD protein in seawater environment is investigated.We find that the stability varies in the different environments. Next, to study adhesive ability of two proteins, we simulate the process of peeling the two proteins from the substrate (graphite). Then, we analyze the main reasons of these results. We find that hydrogen bonds in proteins play an important role in the protein stability. In the process of the peeling, we use Lennard–Jones 12-6 potential to calculate the van der Waals interactions between proteins and substrate.

Instability in threshold voltage and subthreshold behavior in Hf-In-Zn-O thin film transistors induced by bias-and light-stress

Electrical bias and light stressing followed by natural recovery of amorphous hafnium-indium-zinc-oxide (HIZO) thin film transistors with a silicon oxide/nitride dielectric stack reveals defect density changes, charge trapping and persistent photoconductivity (PPC). In the absence of light, the polarity of bias stress controls the magnitude and direction of the threshold voltage shift (Δ VT), while under light stress, VT consistently shifts negatively. In all cases, there was no significant change in field-effect mobility. Light stress gives rise to a PPC with wavelength-dependent recovery on time scale of days. We observe that the PPC becomes more pronounced at shorter wavelengths. © 2010 American Institute of Physics.

Physical parameters affecting sonoluminescence: A self-consistent hydrodynamic study

We studied the dependence of thermodynamic variables in a sonoluminescing ~SL! bubble on various physical factors, which include viscosity, thermal conductivity, surface tension, the equation of state of the gas inside the bubble, as well as the compressibility of the surrounding liquid. The numerical solutions show that the existence of shock waves in the SL parameter regime is very sensitive to these factors. Furthermore, we show that even without shock waves, the reflection of continuous compressional waves at the bubble center can produce the high temperature and picosecond time scale light pulse of the SL bubble, which implies that SL may not necessarily be due to shock waves.

Effect of surface tension on the mode selection of vertically excited surface waves in a circular cylindrical vessel

Singular perturbation theory of two-time-scale expansions was developed in inviscid fluids to investigate patternforming, structure of the single surface standing wave, and its evolution with time in a circular cylindrical vessel subject to a vertical oscillation. A nonlinear slowly varying complex amplitude equation, which involves a cubic nonlinear term, an external excitation and the influence of surface tension, was derived from the potential flow equation. Surface tension was introduced by the boundary condition of the free surface in an ideal and incompressible fluid. The results show that when forced frequency is low, the effect of surface tension on the mode selection of surface waves is not important. However, when the forced frequency is high, the surface tension cannot be neglected. This manifests that the function of surface tension is to cause the free surface to return to its equilibrium configuration. In addition, the effect of surface tension seems to make the theoretical results much closer to experimental results.

Vertically forced surface wave in weakly viscous fluids bounded in a circular cylindrical vessel

Two-time scale perturbation expansions were developed in weakly viscous fluids to investigate surface wave motions by linearizing the Navier-Stokes equation in a circular cylindrical vessel which is subject to a vertical oscillation. The fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates a damping term and external excitation, was derived for the weakly viscid fluids. The condition for the appearance of stable surface waves was obtained and the critical curve was determined. In addition, an analytical expression for the damping coefficient was determined and the relationship between damping and other related parameters (such as viscosity, forced amplitude, forced frequency and the depth of fluid, etc.) was presented. Finally, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent.

Sediment incipience in turbulence generated in a square tank by a vertically oscillating grid

The failure of hydraulic structures in many estuaries and coastal regions around the world has been attributed to sediment transport and local scour. The sediment incipience in homogenous turbulence generated by oscillating grid is studied in this paper. The turbulent flow is measured by particle tracer velocimetry (PTV) technique. The integral length scale and time scale of turbulence are obtained. The turbulent flow near the wall is measured by local optical magnification. The sediment incipience is described by static theory. The relationship of probability of sediment incipience and the turbulent kinetic energy were obtained experimentally and theoretically. The distribution of the turbulent kinetic energy near the wall is found to obey the power law and the turbulent energy is further identified as the dynamic mechanism of sediment incipience.

Review of river fisheries valuation in Central and South America

Unlike Africa and Asia, where a large part of the population are heavily dependent upon fishing for their livelihoods, fishing for a living in the interior of Central and South America (CSA) remains a marginal occupation for all but the most isolated of families. As such, the economics and management of fisheries on the continent have received little attention from within the continent and the rest of the world. This study shows that while a number of studies have been carried out on fishing in the region, they tend to be limited in their geographical focus and time scale. Although fishing of freshwater species may appear to be comparatively insignificant in the region, the rivers of CSA are very important. This report attempts to analyze the literature available on CSA river fisheries and attempts to draw out an economic value of these fisheries. It is divided into a number of sections. First, the authors describe the major river basins on the continent, characterize their fisheries, and place freshwater fisheries in CSA into a global context. Second, the authors provide a review of valuation techniques for fisheries and use this analytical framework to review the principal literature on freshwater fisheries in the region. Then they turn their attention to the economic impact of dams and water abstraction schemes, reviewing the available literature to ascertain how/if economic values are computed for the impact on fisheries. Finally, they offer some conclusions and recommendations on the direction for future studies of freshwater fisheries in CSA.

Molecular Dynamics Simulation of Barnacle Cement

Barnacle cement is an underwater adhesive that is used for permanent settlement. Its main components are insoluble protein complexes that have not been fully studied. In present article, we chose two proteins of barnacle cement for study, 36-KD protein and Mrcp-100K protein. In order to investigate the characteristic of above two proteins, we introduced the method of molecular modeling. And the simulation package GROMACS was used to simulate the behavior of these proteins. In this article, before the simulations, we introduce some theories to predict the time scale for polymer relaxation. During the simulation, we mainly focus on two properties of these two proteins: structural stability and adhesive force to substrate. First, we simulate the structural stability of two proteins in water, and then the stability of 36-KD protein in seawater environment is investigated. We find that the stability varies in the different environments. Next, to study adhesive ability of two proteins, we simulate the process of peeling the two proteins from the substrate (graphite). Then, we analyze the main reasons of these results. We find that hydrogen bonds in proteins play an important role in the protein stability. In the process of the peeling, we use Lennard-Jones 12-6 potential to calculate the van der Waals interactions between proteins and substrate.

Viability Conditions for a Compartmentalized Protometabolic System: A Semi-Empirical Approach

In this work we attempt to find out the extent to which realistic prebiotic compartments, such as fatty acid vesicles, would constrain the chemical network dynamics that could have sustained a minimal form of metabolism. We combine experimental and simulation results to establish the conditions under which a reaction network with a catalytically closed organization (more specifically, an (M, R)-system) would overcome the potential problem of self-suffocation that arises from the limited accessibility of nutrients to its internal reaction domain. The relationship between the permeability of the membrane, the lifetime of the key catalysts and their efficiency (reaction rate enhancement) turns out to be critical. In particular, we show how permeability values constrain the characteristic time scale of the bounded protometabolic processes. From this concrete and illustrative example we finally extend the discussion to a wider evolutionary context.

Nonlinear oscillations in discrete and continuous systems

The first thesis topic is a perturbation method for resonantly coupled nonlinear oscillators. By successive near-identity transformations of the original equations, one obtains new equations with simple structure that describe the long time evolution of the motion. This technique is related to two-timing in that secular terms are suppressed in the transformation equations. The method has some important advantages. Appropriate time scalings are generated naturally by the method, and don't need to be guessed as in two-timing. Furthermore, by continuing the procedure to higher order, one extends (formally) the time scale of valid approximation. Examples illustrate these claims. Using this method, we investigate resonance in conservative, non-conservative and time dependent problems. Each example is chosen to highlight a certain aspect of the method.

The second thesis topic concerns the coupling of nonlinear chemical oscillators. The first problem is the propagation of chemical waves of an oscillating reaction in a diffusive medium. Using two-timing, we derive a nonlinear equation that determines how spatial variations in the phase of the oscillations evolves in time. This result is the key to understanding the propagation of chemical waves. In particular, we use it to account for certain experimental observations on the Belusov-Zhabotinskii reaction.

Next, we analyse the interaction between a pair of coupled chemical oscillators. This time, we derive an equation for the phase shift, which measures how much the oscillators are out of phase. This result is the key to understanding M. Marek's and I. Stuchl's results on coupled reactor systems. In particular, our model accounts for synchronization and its bifurcation into rhythm splitting.

Finally, we analyse large systems of coupled chemical oscillators. Using a continuum approximation, we demonstrate mechanisms that cause auto-synchronization in such systems.

Some problems in nonlinear elasticity

Two separate problems are discussed: axisymmetric equilibrium configurations of a circular membrane under pressure and subject to thrust along its edge, and the buckling of a circular cylindrical shell.

An ordinary differential equation governing the circular membrane is imbedded in a family of n-dimensional nonlinear equations. Phase plane methods are used to examine the number of solutions corresponding to a parameter which generalizes the thrust, as well as other parameters determining the shape of the nonlinearity and the undeformed shape of the membrane. It is found that in any number of dimensions there exists a value of the generalized thrust for which a countable infinity of solutions exist if some of the remaining parameters are made sufficiently large. Criteria describing the number of solutions in other cases are also given.

Donnell-type equations are used to model a circular cylindrical shell. The static problem of bifurcation of buckled modes from Poisson expansion is analyzed using an iteration scheme and pertubation methods. Analysis shows that although buckling loads are usually simple eigenvalues, they may have arbitrarily large but finite multiplicity when the ratio of the shell's length and circumference is rational. A numerical study of the critical buckling load for simple eigenvalues indicates that the number of waves along the axis of the deformed shell is roughly proportional to the length of the shell, suggesting the possibility of a "characteristic length." Further numerical work indicates that initial post-buckling curves are typically steep, although the load may increase or decrease. It is shown that either a sheet of solutions or two distinct branches bifurcate from a double eigenvalue. Furthermore, a shell may be subject to a uniform torque, even though one is not prescribed at the ends of the shell, through the interaction of two modes with the same number of circumferential waves. Finally, multiple time scale techniques are used to study the dynamic buckling of a rectangular plate as well as a circular cylindrical shell; transition to a new steady state amplitude determined by the nonlinearity is shown. The importance of damping in determining equilibrium configurations independent of initial conditions is illustrated.

Nonlinear dispersive wave problems

The nonlinear partial differential equations for dispersive waves have special solutions representing uniform wavetrains. An expansion procedure is developed for slowly varying wavetrains, in which full nonlinearity is retained but in which the scale of the nonuniformity introduces a small parameter. The first order results agree with the results that Whitham obtained by averaging methods. The perturbation method provides a detailed description and deeper understanding, as well as a consistent development to higher approximations. This method for treating partial differential equations is analogous to the "multiple time scale" methods for ordinary differential equations in nonlinear vibration theory. It may also be regarded as a generalization of geometrical optics to nonlinear problems.

To apply the expansion method to the classical water wave problem, it is crucial to find an appropriate variational principle. It was found in the present investigation that a Lagrangian function equal to the pressure yields the full set of equations of motion for the problem. After this result is derived, the Lagrangian is compared with the more usual expression formed from kinetic minus potential energy. The water wave problem is then examined by means of the expansion procedure.