167 research outputs found
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
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 and thickness formed from such a
membrane in water. In a grand canonical approach we find that the leading
contribution to the Casimir energy behaves like which gives
rise to an attractive force which tends to contract the tube radius. We find
that 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
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
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
Viscous regularization and r-adaptive remeshing for finite element analysis of lipid membrane mechanics
As two-dimensional fluid shells, lipid bilayer membranes resist bending and
stretching but are unable to sustain shear stresses. This property gives
membranes the ability to adopt dramatic shape changes. In this paper, a finite
element model is developed to study static equilibrium mechanics of membranes.
In particular, a viscous regularization method is proposed to stabilize
tangential mesh deformations and improve the convergence rate of nonlinear
solvers. The Augmented Lagrangian method is used to enforce global constraints
on area and volume during membrane deformations. As a validation of the method,
equilibrium shapes for a shape-phase diagram of lipid bilayer vesicle are
calculated. These numerical techniques are also shown to be useful for
simulations of three-dimensional large-deformation problems: the formation of
tethers (long tube-like exetensions); and Ginzburg-Landau phase separation of a
two-lipid-component vesicle. To deal with the large mesh distortions of the
two-phase model, modification of vicous regularization is explored to achieve
r-adaptive mesh optimization
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
Management approaches and aquaculture of sturgeons in the Lower Danube region countries
Summary This paper presents the status and trends in management of sturgeon species and the development of sturgeon aquaculture in the Lower Danube countries: Romania, Bulgaria, Serbia, Ukraine and Moldova. Sturgeon fishery moratoria and aquaculture development represent first steps in the Lower Danube countries to combat extirpation. Supportive stocking was used as a compensation for the impact of sturgeon fishery and dam construction, but these efforts unfortunately lacked adequate cooperation and coordination between and among region countries. Unsolved problems remain, such as the presence of illegal sturgeon fishery, water pollution, habitat destruction and fragmentation. Construction of fish passes and habitat restoration project developments are two key issues that have yet to be tackled in the Lower Danube region
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