33,973 research outputs found
Infrared Consistency of NSVZ and DRED Supersymmetric Gluodynamics
Pade approximant methods are applied to known terms of the DRED beta-
function for N = 1 supersymmetric SU(3) Yang-Mills theory. Each of the [N|M]
approximants with N + M less than or equal to 4 (M not equal to zero)
constructed from this series exhibits a positive pole which precedes any zeros
of the approximant, consistent with the same infrared-attractor pole behaviour
known to characterise the exact NSVZ beta-function. A similar Pade-approximant
analysis of truncations of the NSVZ series is shown consistently to reproduce
the geometric-series pole of the exact NSVZ beta function.Comment: LaTeX, 15 page
Condensation of N interacting bosons: Hybrid approach to condensate fluctuations
We present a new method of calculating the distribution function and
fluctuations for a Bose-Einstein condensate (BEC) of N interacting atoms. The
present formulation combines our previous master equation and canonical
ensemble quasiparticle techniques. It is applicable both for ideal and
interacting Bogoliubov BEC and yields remarkable accuracy at all temperatures.
For the interacting gas of 200 bosons in a box we plot the temperature
dependence of the first four central moments of the condensate particle number
and compare the results with the ideal gas. For the interacting mesoscopic BEC,
as with the ideal gas, we find a smooth transition for the condensate particle
number as we pass through the critical temperature.Comment: 6 pages, 4 figures, to appear in Phys. Rev. Let
The influence of receptor-mediated interactions on reaction-diffusion mechanisms of cellular self-organisation
Understanding the mechanisms governing and regulating self-organisation in the developing embryo is a key challenge that has puzzled and fascinated scientists for decades. Since its conception in 1952 the Turing model has been a paradigm for pattern formation, motivating numerous theoretical and experimental studies, though its verification at the molecular level in biological systems has remained elusive. In this work, we consider the influence of receptor-mediated dynamics within the framework of Turing models, showing how non-diffusing species impact the conditions for the emergence of self-organisation. We illustrate our results within the framework of hair follicle pre-patterning, showing how receptor interaction structures can be constrained by the requirement for patterning, without the need for detailed knowledge of the network dynamics. Finally, in the light of our results, we discuss the ability of such systems to pattern outside the classical limits of the Turing model, and the inherent dangers involved in model reduction
Collision of Viscoelastic Spheres: Compact Expressions for the Coefficient of Normal Restitution
The coefficient of restitution of colliding viscoelastic spheres is
analytically known as a complete series expansion in terms of the impact
velocity where all (infinitely many) coefficients are known. While beeing
analytically exact, this result is not suitable for applications in efficient
event-driven Molecular Dynamics (eMD) or Monte Carlo (MC) simulations. Based on
the analytic result, here we derive expressions for the coefficient of
restitution which allow for an application in efficient eMD and MC simulations
of granular Systems.Comment: 4 pages, 4 figure
Thermodynamics of localized magnetic moments in a Dirac conductor
We show that the magnetic susceptibility of a dilute ensemble of magnetic
impurities in a conductor with a relativistic electronic spectrum is
non-analytic in the inverse tempertature at . We derive a general
theory of this effect and construct the high-temperature expansion for the
disorder averaged susceptibility to any order, convergent at all tempertaures
down to a possible ordering transition. When applied to Ising impurities on a
surface of a topological insulator, the proposed general theory agrees with
Monte Carlo simulations, and it allows us to find the critical temperature of
the ferromagnetic phase transition.Comment: 5 pages, 1 figure, 2 tables, RevTe
Identities for hyperelliptic P-functions of genus one, two and three in covariant form
We give a covariant treatment of the quadratic differential identities
satisfied by the P-functions on the Jacobian of smooth hyperelliptic curves of
genera 1, 2 and 3
A study of the temperature dependence of bienzyme systems and enzymatic chains
It is known that most enzyme-facilitated reactions are highly temperature dependent processes. In general, the temperature coefficient, Q10, of a simple reaction reaches 2.0-3.0. Nevertheless, some enzyme-controlled processes have much lower Q10 (about 1.0), which implies that the process is almost temperature independent, even if individual reactions involved in the process are themselves highly temperature dependent. In this work, we investigate a possible mechanism for this apparent temperature compensation: simple mathematical models are used to study how varying types of enzyme reactions are affected by temperature. We show that some bienzyme-controlled processes may be almost temperature independent if the modules involved in the reaction have similar temperature dependencies, even if individually, these modules are strongly temperature dependent. Further, we show that in non-reversible enzyme chains the stationary concentrations of metabolites are dependent only on the relationship between the temperature dependencies of the first and last modules, whilst in reversible reactions, there is a dependence on every module. Our findings suggest a mechanism by which the metabolic processes taking place within living organisms may be regulated, despite strong variation in temperature
Exact solutions for a class of integrable Henon-Heiles-type systems
We study the exact solutions of a class of integrable Henon-Heiles-type
systems (according to the analysis of Bountis et al. (1982)). These solutions
are expressed in terms of two-dimensional Kleinian functions. Special periodic
solutions are expressed in terms of the well-known Weierstrass function. We
extend some of our results to a generalized Henon-Heiles-type system with n+1
degrees of freedom.Comment: RevTeX4-1, 13 pages, Submitted to J. Math. Phy
Deriving bases for Abelian functions
We present a new method to explicitly define Abelian functions associated
with algebraic curves, for the purpose of finding bases for the relevant vector
spaces of such functions. We demonstrate the procedure with the functions
associated with a trigonal curve of genus four. The main motivation for the
construction of such bases is that it allows systematic methods for the
derivation of the addition formulae and differential equations satisfied by the
functions. We present a new 3-term 2-variable addition formulae and a complete
set of differential equations to generalise the classic Weierstrass identities
for the case of the trigonal curve of genus four.Comment: 35page
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