374 research outputs found
Representations of the discrete inhomogeneous Lorentz group and Dirac wave equation on the lattice
We propose the fundamental and two dimensional representation of the Lorentz
groups on a (3+1)-dimensional hypercubic lattice, from which representations of
higher dimensions can be constructed. For the unitary representation of the
discrete translation group we use the kernel of the Fourier transform. From the
Dirac representation of the Lorentz group (including reflections) we derive in
a natural way the wave equation on the lattice for spin 1/2 particles. Finally
the induced representation of the discrete inhomogeneous Lorentz group is
constructed by standard methods and its connection with the continuous case is
discussed.Comment: LaTeX, 20 pages, 1 eps figure, uses iopconf.sty (late submission
Variation in fertilisation abilities between hemiclonal hybrid and sexual parental males of sympatric water frogs (Rana lessonae, R. esculenta, R. ridibunda)
In many species, males and females mate with multiple partners, which gives rise to sperm competition and multiple paternity. The experiments on water frogs presented here demonstrate that such sperm competition can affect the structure and dynamics of mixed species communities. The hybrid frog Rana esculenta (LR) mates with one of its parental species, usually Rana lessonae (LL) although in some areas R. ridibunda (RR), to regain the premeiotically eliminated parental genome ("hybridogenesis"). Mixed LL/LR-populations are stable although hybrid numbers should continuously increase at the expense of parental animals, because of differences in female fecundity and other factors. This would finally lead to the extinction of the sexual host, followed by that of the sexual parasite, unless the reproductive superiority of R. esculenta is reduced by other factors, such as lower hybrid male fertility. Eggs from LL- and LR-females were fertilised in vitro by single- and multi-male sperm suspensions of LL-, LR- and RR-males. In all experiments, the proportion of offspring sired by R. esculenta sperm was significantly lower than that sired by R. lessonae or R. ridibunda sperm. Gonad mass, sperm morphology, sperm swimming velocity, and sperm survival did not explain these differences in fertilisation success, nor did gamete recognition and compatibility. Sperm density was the only trait that paralleled fertilisation success; but it offers no explanation either, because densities were equalised for the in vitro fertilisations. In natural LL/LR populations, the significantly smaller amount, poorer competitive ability and lower long-term survival of R. esculenta compared to R. lessonae sperm will reduce the initial reproductive superiority of hybrids and contribute to the stabilisation of mixed water frog populations. Differences in fertilisation ability are also likely to be relevant for the structure and dynamics of several other systems with encounters between eggs and sperm from different genotypes, ecotypes, ploidy levels and/or species
Cardiac cell modelling: Observations from the heart of the cardiac physiome project
In this manuscript we review the state of cardiac cell modelling in the context of international initiatives such as the IUPS Physiome and Virtual Physiological Human Projects, which aim to integrate computational models across scales and physics. In particular we focus on the relationship between experimental data and model parameterisation across a range of model types and cellular physiological systems. Finally, in the context of parameter identification and model reuse within the Cardiac Physiome, we suggest some future priority areas for this field
Symmetry based determination of space-time functions in nonequilibrium growth processes
We study the space-time correlation and response functions in nonequilibrium
growth processes described by linear stochastic Langevin equations. Exploiting
exclusively the existence of space and time dependent symmetries of the
noiseless part of these equations, we derive expressions for the universal
scaling functions of two-time quantities which are found to agree with the
exact expressions obtained from the stochastic equations of motion. The
usefulness of the space-time functions is illustrated through the investigation
of two atomistic growth models, the Family model and the restricted Family
model, which are shown to belong to a unique universality class in 1+1 and in
2+1 space dimensions. This corrects earlier studies which claimed that in 2+1
dimensions the two models belong to different universality classes.Comment: 18 pages, three figures included, submitted to Phys. Rev.
Group classification of (1+1)-Dimensional Schr\"odinger Equations with Potentials and Power Nonlinearities
We perform the complete group classification in the class of nonlinear
Schr\"odinger equations of the form
where is an arbitrary
complex-valued potential depending on and is a real non-zero
constant. We construct all the possible inequivalent potentials for which these
equations have non-trivial Lie symmetries using a combination of algebraic and
compatibility methods. The proposed approach can be applied to solving group
classification problems for a number of important classes of differential
equations arising in mathematical physics.Comment: 10 page
Supersymmetric version of a hydrodynamic system in Riemann invariants and its solutions
In this paper, a supersymmetric extension of a system of hydrodynamic type
equations involving Riemann invariants is formulated in terms of a superspace
and superfield formalism. The symmetry properties of both the classical and
supersymmetric versions of this hydrodynamical model are analyzed through the
use of group-theoretical methods applied to partial differential equations
involving both bosonic and fermionic variables. More specifically, we compute
the Lie superalgebras of both models and perform classifications of their
respective subalgebras. A systematic use of the subalgebra structures allow us
to construct several classes of invariant solutions, including travelling
waves, centered waves and solutions involving monomials, exponentials and
radicals.Comment: 30 page
Kinetics of phase-separation in the critical spherical model and local scale-invariance
The scaling forms of the space- and time-dependent two-time correlation and
response functions are calculated for the kinetic spherical model with a
conserved order-parameter and quenched to its critical point from a completely
disordered initial state. The stochastic Langevin equation can be split into a
noise part and into a deterministic part which has local scale-transformations
with a dynamical exponent z=4 as a dynamical symmetry. An exact reduction
formula allows to express any physical average in terms of averages calculable
from the deterministic part alone. The exact spherical model results are shown
to agree with these predictions of local scale-invariance. The results also
include kinetic growth with mass conservation as described by the
Mullins-Herring equation.Comment: Latex2e with IOP macros, 28 pp, 2 figures, final for
Galilean Conformal and Superconformal Symmetries
Firstly we discuss briefly three different algebras named as nonrelativistic
(NR) conformal: Schroedinger, Galilean conformal and infinite algebra of local
NR conformal isometries. Further we shall consider in some detail Galilean
conformal algebra (GCA) obtained in the limit c equal to infinity from
relativistic conformal algebra O(d+1,2) (d - number of space dimensions). Two
different contraction limits providing GCA and some recently considered
realizations will be briefly discussed. Finally by considering NR contraction
of D=4 superconformal algebra the Galilei conformal superalgebra (GCSA) is
obtained, in the formulation using complex Weyl supercharges.Comment: 16 pages, LateX; talk presented at XIV International Conference
"Symmetry Methods in Physics", Tsakhkadzor, Armenia, August 16-22, 201
Fiber Organization has Little Effect on Electrical Activation Patterns during Focal Arrhythmias in the Left Atrium
Over the past two decades there has been a steady trend towards the
development of realistic models of cardiac conduction with increasing levels of
detail. However, making models more realistic complicates their personalization
and use in clinical practice due to limited availability of tissue and cellular
scale data. One such limitation is obtaining information about myocardial fiber
organization in the clinical setting. In this study, we investigated a chimeric
model of the left atrium utilizing clinically derived patient-specific atrial
geometry and a realistic, yet foreign for a given patient fiber organization.
We discovered that even significant variability of fiber organization had a
relatively small effect on the spatio-temporal activation pattern during
regular pacing. For a given pacing site, the activation maps were very similar
across all fiber organizations tested
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