Derivation of SPH equations in a moving referential coordinate system

The conventional SPH method uses kernel interpolation to derive the spatial semi-discretisation of the governing equations. These equations, derived using a straight application of the kernel interpolation method, are not used in practice. Instead the equations, commonly used in SPH codes, are heuristically modified to enforce symmetry and local conservation properties. This paper revisits the process of deriving these semi-discrete SPH equations. It is shown that by using the assumption of a moving referential coordinate system and moving control volume, instead of the fixed referential coordinate system and fixed control volume used in the conventional SPH method, a set of new semi- discrete equations can be rigorously derived. The new forms of semi-discrete equations are similar to the SPH equations used in practice. It is shown through numerical examples that the new rigorously derived equations give similar results to those obtained using the conventional SPH equations

Transport Theorem for Spaces and Subspaces of Arbitrary Dimensions

Copyright © 2020 by the authors. Using the apparatus of traditional differential geometry, the transport theorem is derived for the general case of a M-dimensional domain moving in a N-dimensional space, . The interesting concepts of curvatures and normals are illustrated with well-known examples of lines, surfaces and volumes. The special cases where either the space or the moving subdomain are material are discussed. Then, the transport at hypersurfaces of discontinuity is considered. Finally, the general local balance equations for continuum of arbitrary dimensions with discontinuities are derived

Mesoscopic Phase Fluctuations: General Phenomenon in Condensed Matter

General conditions for the occurrence of mesoscopic phase fluctuations in condensed matter are considered. The description of different thermodynamic phases, which coexist as a mixture of mesoscopically separated regions, is based on the {\it theory of heterophase fluctuations}. The spaces of states, typical of the related phases, are characterized by {\it weighted Hilbert spaces}. Several models illustrate the main features of heterophase condensed matter.Comment: 23 pages, Latex, no figure

Little groups of irreps of O(3), SO(3), and the infinite axial subgroups

Little groups are enumerated for the irreps and their components in any basis of O(3) and SO(3) up to rank 9, and for all irreps of C$_{\infty}$, C$_{\infty h}$, C$_{\infty v}$, D$_{\infty}$ and D$_{\infty h}$. The results are obtained by a new chain criterion, which distinguishes massive (rotationally inequivalent) irrep basis functions and allows for multiple branching paths, and are verified by inspection. These results are relevant to the determination of the symmetry of a material from its linear and nonlinear optical properties and to the choices of order parameters for symmetry breaking in liquid crystals.Comment: 28 pages and 3 figure

Pseudo-boundaries in discontinuous 2-dimensional maps

It is known that Kolmogorov-Arnold-Moser boundaries appear in sufficiently smooth 2-dimensional area-preserving maps. When such boundaries are destroyed, they become pseudo-boundaries. We show that pseudo-boundaries can also be found in discontinuous maps. The origin of these pseudo-boundaries are groups of chains of islands which separate parts of the phase space and need to be crossed in order to move between the different sub-spaces. Trajectories, however, do not easily cross these chains, but tend to propagate along them. This type of behavior is demonstrated using a ``generalized'' Fermi map.Comment: 4 pages, 4 figures, Revtex, epsf, submitted to Physical Review E (as a brief report

Archaeal aminoacyl-tRNA synthetases interact with the ribosome to recycle tRNAs

Aminoacyl-tRNA synthetases (aaRS) are essential enzymes catalyzing the formation of aminoacyl-tRNAs, the immediate precursors for encoded peptides in ribosomal protein synthesis. Previous studies have suggested a link between tRNA aminoacylation and high-molecular-weight cellular complexes such as the cytoskeleton or ribosomes. However, the structural basis of these interactions and potential mechanistic implications are not well understood. To biochemically characterize these interactions we have used a system of two interacting archaeal aaRSs: an atypical methanogenic-type seryl-tRNA synthetase and an archaeal ArgRS. More specifically, we have shown by thermophoresis and surface plasmon resonance that these two aaRSs bind to the large ribosomal subunit with micromolar affinities. We have identified the L7/L12 stalk and the proteins located near the stalk base as the main sites for aaRS binding. Finally, we have performed a bioinformatics analysis of synonymous codons in the Methanothermobacter thermautotrophicus genome that supports a mechanism in which the deacylated tRNAs may be recharged by aaRSs bound to the ribosome and reused at the next occurrence of a codon encoding the same amino acid. These results suggest a mechanism of tRNA recycling in which aaRSs associate with the L7/L12 stalk region to recapture the tRNAs released from the preceding ribosome in polysome

The field theory of symmetrical layered electrolytic systems and the thermal Casimir effect

We present a general extension of a field-theoretic approach developed in earlier papers to the calculation of the free energy of symmetrically layered electrolytic systems which is based on the Sine-Gordon field theory for the Coulomb gas. The method is to construct the partition function in terms of the Feynman evolution kernel in the Euclidean time variable associated with the coordinate normal to the surfaces defining the layered structure. The theory is applicable to cylindrical systems and its development is motivated by the possibility that a static van der Waals or thermal Casimir force could provide an attractive force stabilising a dielectric tube formed from a lipid bilayer, an example of which are t-tubules occurring in certain muscle cells. In this context, we apply the theory to the calculation of the thermal Casimir effect for a dielectric tube of radius $R$ and thickness $\delta$ formed from such a membrane in water. In a grand canonical approach we find that the leading contribution to the Casimir energy behaves like $-k_BTL\kappa_C/R$ which gives rise to an attractive force which tends to contract the tube radius. We find that $\kappa_C \sim 0.3$ for the case of typical lipid membrane t-tubules. We conclude that except in the case of a very soft membrane this force is insufficient to stabilise such tubes against the bending stress which tend to increase the radius. We briefly discuss the role of lipid membrane reservoir implicit in the approach and whether its nature in biological systems may possibly lead to a stabilising mechanism for such lipid tubes.Comment: 28 pages, 2 figures, LaTe

Droplet Fluctuations in the Morphology and Kinetics of Martensites

We derive a coarse grained, free-energy functional which describes droplet configurations arising on nucleation of a product crystal within a parent. This involves a new `slow' vacancy mode that lives at the parent-product interface. A mode-coupling theory suggests that a {\it slow} quench from the parent phase produces an equilibrium product, while a {\it fast} quench produces a metastable martensite. In two dimensions, the martensite nuclei grow as `lens-shaped' strips having alternating twin domains, with well-defined front velocities. Several empirically known structural and kinetic relations drop out naturally from our theory.Comment: 4 pages, REVTEX, and 3 .eps figures, compressed and uuencoded, Submitted to Phys. Rev. Let

A mathematical modelling study of an athlete's sprint time when towing a weighted sled

This is the author's accepted manuscript. The final publication is available at Springer via http://dx.doi.org/10.1007/s12283-013-0114-2.This study used a mathematical model to examine the effects of the sled, the running surface, and the athlete on sprint time when towing a weighted sled. Simulations showed that ratio scaling is an appropriate method of normalising the weight of the sled for athletes of different body size. The relationship between sprint time and the weight of the sled was almost linear, as long as the sled was not excessively heavy. The athlete’s sprint time and rate of increase in sprint time were greater on running surfaces with a greater coefficient of friction, and on any given running surface an athlete with a greater power-to-weight ratio had a lower rate of increase in sprint time. The angle of the tow cord did not have a substantial effect on an athlete’s sprint time. This greater understanding should help coaches set the training intensity experienced by an athlete when performing a sled-towing exercise

The Effect of Body Size on Countermovement Jump Kinetics in Children aged 7 to 11 years

The purpose this study was to examine the effect of body size oncountermovement jump (CMJ)kinetics in children.Participants(n = 160) aged 7-11 years, divided equally by sex and into primary school year groups(years 3, 4, 5 and 6), each performedone CMJ on aforce platform. The variables bodyweight(BW), peak force (Fmax), in-jump minimum force (IMF), in-jump vertical force range (IFR) and basic rate of force development (BRFD)wereattained from the force-time history and then subsequently scaled to account for body size. A significant age, sex and interaction effect werefound for theabsolutevariables BW, IMF, Fmaxand IFR (P 0.05). No significant age or sex differences were observed for normalised or allometrically scaled values(P > 0.05). The results indicate thatgirls and boys can be grouped together but that body size must be accounted for to enable accurate conclusions to be drawn independent of growth.Bodysizesignificantlyeffects the representation of CMJ kinetic results and therefore, future studies should report both absolute and scaled values.Future research should developan age-appropriate criterion method for children in order to determine processed CMJ variables to further investigate neuromuscular performance of children