Table of contents

A general simple theory for the interspecific allometric scaling is developed in the d + 1-dimensional space (d biological lengths and a physiological time) of metabolic states of organisms. It is assumed that natural selection shaped the metabolic states in such a way that the mass and energy d + 1-densities are size-invariant quantities (independent of body mass). The different metabolic states (basal and maximum) are described by considering that the biological lengths and the physiological time are related by different transport processes of energy and mass. In the basal metabolism, transportation occurs by ballistic and diffusion processes. In d = 3, the 3/4 law occurs if the ballistic movement is the dominant process, while the 2/3 law appears when both transport processes are equivalent. Accelerated movement during the biological time is related to the maximum aerobic sustained metabolism, which is characterized by the scaling exponent 2d/(2d + 1) (6/7 in d = 3). The results are in good agreement with empirical data and a verifiable empirical prediction about the aorta blood velocity in maximum metabolic rate conditions is made.

In this paper, we examine the mechanics of a nano-scaled gigahertz oscillator comprising a fullerene that is moving within the center of a bundle of carbon nanotubes. Although numerical results specifically for a C₆₀ fullerene are presented, the method is equally valid for any fullerene which can be modeled as a spherical molecule. A general definition of a nanotube bundle is employed which can comprise any number of parallel carbon nanotubes encircling the oscillating fullerene. Results are presented which prescribe the dimension of the bundle for any nanotube radius and the optimal configurations which give rise to the maximum suction energy for the fullerene. Prior results for fullerene single-walled nanotube oscillators are employed, and new results are also derived. These include a calculation of optimum nanotube bundle size to be employed for a C₆₀-nanotube bundle oscillator, as well as new analytical expressions for the force and energy for a semi-infinite nanotube and a fullerene not located on the axis of the cylinder.

We consider the totally asymmetric exclusion process (TASEP) of particles on a one-dimensional lattice that interact with site exclusion and are driven into one direction only. The mean-field approximation of the dynamical equation for the one-particle density of this model is shown to be equivalent to the exact Euler–Lagrange equations for the equilibrium density profiles of a binary mixture. In this mixture particles occupy one (two) lattice sites and correspond to resting (moving) particles in the TASEP. Despite the strict absence of bulk phase transitions in the equilibrium mixture, the influence of density-dependent external potentials is shown to induce abrupt changes in the one-body density that are equivalent to the exact out-of-equilibrium phase transitions between steady states in the TASEP with open boundaries.

We study the time evolution of an atom suddenly coupled to a thermal radiation field. As a simplified model of the atom-electromagnetic field system we use a system composed of a harmonic oscillator linearly coupled to a scalar field in the framework of the recently introduced dressed coordinates and dressed states. We show that the time evolution of the thermal expectation values for the occupation number operators depends exclusively on the probabilities associated with the emission and absorption of field quanta. In particular, the time evolution of the number operator associated with the atom is given in terms of the probability of remaining in the first excited state and the decay probabilities from this state by emission of field quanta of frequencies ω_k. Also, it is shown that independent of the initial state of the atom, it thermalizes with the thermal radiation field in a time scale of the order of the inverse coupling constant.

We elucidate the structure of the hierarchy of the connected operators that commute with the Markov matrix of the totally asymmetric exclusion process. We derive the combinatorial formula for the connected operators that was conjectured in our previous work.

We introduce an exactly-solvable family of one-dimensional driven-diffusive systems defined on a discrete lattice. We find the quadratic algebra of this family which has an infinite-dimensional representation. We discuss the phase diagram of the system in a couple of special cases.

Using cellular automata dynamics, a discrete technique to study stochastic growth equations (SGE) is presented. By analogy to deposition models in which the growth rule depends on height differences between neighbours, we introduce an interface growth process with synchronous updating in which the transition probability for a given site i to receive a particle at a time t is defined as p_i(t) = ρexp [κΓ_i(t)]. ρ and κ are the model parameters and Γ_i(t) is a function which depends on the height of the site i and its neighbours, and its functional form is specified through discretization of the deterministic part of the growth equation associated with a given deposition process. To validate the method, we study its application to two linear SGE—the Edwards–Wilkinson equation and the Mullins–Herring equation, and a nonlinear one—the Kardar–Parisi–Zhang equation. The statistical analysis of the height distributions in simulations recovered the correct values for roughening exponents, confirming that the processes generated are indeed in the universality classes of the original growth equations. We also observed a crossover from random deposition to the correlated regime when the parameter κ is varied in each case studied.

We investigate the existence and location of the surface phase known as the 'surface-attached globule' (SAG) conjectured previously to exist in lattice models of three-dimensional polymers when they are attached to a wall that has a short-range potential. The bulk phase, where the attractive intra-polymer interactions are strong enough to cause a collapse of the polymer into a liquid-like globule and the wall either has weak attractive or repulsive interactions, is usually denoted desorbed-collapsed or DC. Recently, this DC phase was conjectured to harbour two surface phases separated by a boundary where the bulk free energy is analytic while the surface free energy is singular. The surface phase for more attractive values of the wall interaction is the SAG phase. We discuss in more detail the properties of this proposed surface phase and provide Monte Carlo evidence for self-avoiding walks up to a length 256 that this surface phase most likely does exist. Importantly, we discuss alternatives for the surface phase boundary. In particular, we conclude that this boundary may lie along the zero wall interaction line and the bulk phase boundaries rather than any new phase boundary curve.

We show, both analytically and numerically, that for a nonlinear system making a transition from one equilibrium state to another under the action of an external time dependent force, the work probability distribution is in general asymmetric, even if the evolution dynamics has a symmetry.

We introduce a general random pseudofractal network model by assigning fitness to each edge. In this model, continuous growth and attachment, determined by their fitness of already existing edges, are the two ingredients. We obtain the analytical results that our model exhibits a power-law degree distribution with exponent γ = 2 + m(1 + αm)⁻¹, where m and α are tunable parameters. We also show that a general random pseudofractal network has a large clustering coefficient and a small average distance leading to a small-world effect. These theoretical results agree well with numerical simulations.

An embedding of chaotic data into a suitable phase space creates a diffeomorphism of the original attractor with the reconstructed attractor. Although diffeomorphic, the original and reconstructed attractors may not be topologically equivalent. In a previous work, we showed how the original and reconstructed attractors can differ when the original is three-dimensional and of genus-one type. In the present work, we extend this result to three-dimensional attractors of arbitrary genus. This result describes symmetries exhibited by the Lorenz attractor and its reconstructions.

For the long-distance communication and manufacturing problems in optical fibers, the propagation of subpicosecond or femtosecond optical pulses can be governed by the variable-coefficient nonlinear Schrödinger equation with higher order effects, such as the third-order dispersion, self-steepening and self-frequency shift. In this paper, we firstly determine the general conditions for this equation to be integrable by employing the Painlevé analysis. Based on the obtained 3 × 3 Lax pair, we construct the Darboux transformation for such a model under the corresponding constraints, and then derive the nth-iterated potential transformation formula by the iterative process of Darboux transformation. Through the one- and two-soliton-like solutions, we graphically discuss the features of femtosecond solitons in inhomogeneous optical fibers.

Jacobi–Nijenhuis algebroids are defined as a natural generalization of Poisson–Nijenhuis algebroids, in the case where there exists a Nijenhuis operator on a Jacobi algebroid which is compatible with it. We study modular classes of Jacobi and Jacobi–Nijenhuis algebroids.

In Pronko and Stroganov (1977 Zh. Eksp. Teor. Fiz.72 2048, 1997 Sov. Phys.—JETP45 1072) the superintegrable system which describes the magnetic dipole with spin (neutron) in the field of linear current was considered. Here we present its generalization for any spin which preserves superintegrability. The dynamical symmetry stays the same as it is for spin .

We construct integrable cases of generalized classical and quantum Gaudin spin chains in an external magnetic field. For this purpose, we generalize the 'shift of argument method' onto the case of classical and quantum integrable systems governed by an arbitrary -valued, non-dynamical classical r-matrix with spectral parameters. We consider several examples of the obtained construction for the cases of skew-symmetric, 'twisted' non-skew-symmetric and 'anisotropic' non-skew-symmetric classical r-matrices. We show, in particular, that in a general case in order for the Gaudin system in a magnetic field to be integrable, the corresponding magnetic field should be non-homogeneous.

We consider lattice equations on which are autonomous, affine linear and possess the symmetries of the square. Some basic properties of equations of this type are derived, as well as a sufficient linearization condition and a conservation law. A systematic analysis of the Lie point and the generalized three- and five-point symmetries is presented. It leads to the generic form of the symmetry generators of all the equations in this class, which satisfy a certain non-degeneracy condition. Finally, symmetry reductions of certain lattice equations to discrete analogs of the Painlevé equations are considered.

The pfaffian solution of a semi-discrete BKP-type equation is obtained at first, then utilizing the source generation procedure, this equation with self-consistent sources (BKPESCS) is presented and its pfaffian solutions are derived. Finally, a bilinear Bäcklund transformation for the semi-discrete BKPESCS is given.

We calculate the photon-emission rate from a general atomic system in the mass-proportional continuous spontaneous localization (CSL) model. For an isolated charged particle emitting kilovolt gamma rays, our results agree with those obtained by Fu. For a neutral atomic system, photon emission is strongly suppressed for photon wavelengths much larger than the atomic radius. However, for kilovolt gamma rays, Fu's result is modified by a structure factor that is of order unity, giving no rate suppression. Our calculation is readily generalized to the case of non-white noise, noise couplings that are not mass-proportional, and general (non-Gaussian) spatial correlation functions, and corresponding results are given. We briefly discuss the implications of our calculation for upper bounds on the CSL model parameters.

A comparison is made of various searching procedures, based upon different entanglement measures or entanglement indicators, for highly entangled multiqubits states. In particular, our present results are compared with those recently reported by Brown et al (J. Phys. A: Math. Gen. 2005 38 1119). The statistical distribution of entanglement values for the aforementioned multiqubit systems is also explored.

The charge-symmetric pseudo nucleus pdμ can be formed in the cascade process in the muon catalyzed fusion. The nuclear fusion of the pdμ molecular ion can be considered in the photon field. For the spin states of the pdμ system (L = 0), the radiative fusion rates are calculated employing a new spatial wavefunction. The method takes into account the Coulomb interactions for the calculation of the molecular wavefunction. The related pd astrophysical factors are used, essentially extracted from experimental determinations.

If a single particle obeys non-relativistic QM in R^d and has the Hamiltonian H = −Δ + f(r), where , then the eigenvalues E = E^(d)_nℓ(λ) are given approximately by the semi-classical expression . It is proved that this formula yields a lower bound if P_i = P^(d)_nℓ(q₁), an upper bound if P_i = P^(d)_nℓ(q_k) and a general approximation formula if P_i = P^(d)_nℓ(q_i). For the quantum anharmonic oscillator f(r) = r² + λr^2m, m = 2, 3, ... in d dimension, for example, E = E^(d)_nℓ(λ) is determined by the algebraic expression , where and α, β are constants. An improved lower bound to the lowest eigenvalue in each angular-momentum subspace is also provided. A comparison with the recent results of Bhattacharya et al (1998 Phys. Lett. A 244 9) and Dasgupta et al (2007 J. Phys. A: Math. Theor.40 773) is discussed.

Starting with the Dirac equation in the extreme Kerr metric we derive an integral representation for the propagator of solutions of the Cauchy problem with initial data in the class of smooth compactly supported functions.

Using the plasma model for the metal dielectric function we have calculated the electromagnetic-fluctuation-induced forces on a free standing metallic film in vacuum as a function of the film size and the plasma frequency. The force for unit area is attractive and for a given film thickness it shows an intensity maximum at a specific plasma value, which cannot be predicted on the basis of a non-retarded description of the electromagnetic interaction. If the film is deposited on a substrate or interacts with a plate, both the sign and the value of the force are modified. It is shown that the force can change the sign from attraction to repulsion upon changing the substrate plasma frequency. A detailed comparison between the force on the film boundaries and the force between film and substrate indicates that, for 50–100 nm thick films, they are comparable when film–substrate distance is of the order of the film thickness.

A tensorial approach to Galilean invariance is utilized, together with Lie symmetries of differential equations, in order to derive equations of Fokker–Planck type containing a logarithmic diffusion tensor and drift term. The formalism is based on the projection from an extended (by one space-like dimension) Minkowski manifold to the usual Newtonian spacetime, so that non-relativistic models are described by manifestly covariant Lagrangians. In this paper, we obtain the Fokker–Planck equations from the Euler–Lagrange equations with the extended manifold by using a specific choice of the gauge condition. We work in (1 + 1) spacetime and carry out the analysis for both Abelian and non-Abelian symmetries.

Some years ago, it was shown how fermion self-interacting terms of the Thirring-type impact the usual structure of massless two-dimensional gauge theories [1]. In that work only the cases of pure vector and pure chiral gauge couplings have been considered and the corresponding Thirring term was also pure vector and pure chiral respectively, such that the vector (or chiral) Schwinger model should not lose its chirality structure due to the addition of the quartic interaction term. Here we extend this analysis to a generalized vector and axial coupling both for the gauge interaction and the quartic fermionic interactions. The idea is to perform quantization without losing the original structure of the gauge coupling. In order to do that we make use of an arbitrariness in the definition of the Thirring-like interaction.

The physical reasons why the Drude dielectric function is not compatible with the Lifshitz formula, as opposed to the generalized plasma-like permittivity, are presented. Essentially, the problem is connected with the finite size of metal plates. It is shown that the Lifshitz theory combined with the generalized plasma-like permittivity is thermodynamically consistent.

A careful calculation of radiation from atomic systems in the CSL model (Adler S L and Ramazanoglu F M 2007 J. Phys. A: Math. Theor. at press (preprint 0707.3134)) has reinstated the bound obtained by Fu as the best upper bound on λ, with significant implications for CSL model phenomenology.