Periodic solutions of a many-rotator problem in the plane. II. Analysis of various motions

Various solutions are displayed and analyzed (both analytically and numerically) of arecently-introduced many-body problem in the plane which includes both integrable and nonintegrable cases (depending on the values of the coupling constants); in particular the origin of certain periodic behaviors is explained. The light thereby shone on the connection among \textit{integrability} and \textit{analyticity} in (complex) time, as well as on the emergence of a \textit{chaotic} behavior (in the guise of a sensitive dependance on the initial data) not associated with any local exponential divergence of trajectories in phase space, might illuminate interesting phenomena of more general validity than for the particular model considered herein.Comment: Published by JNMP at http://www.sm.luth.se/math/JNMP

Exact real-time dynamics of the quantum Rabi model

We use the analytical solution of the quantum Rabi model to obtain absolutely convergent series expressions of the exact eigenstates and their scalar products with Fock states. This enables us to calculate the numerically exact time evolution of and for all regimes of the coupling strength, without truncation of the Hilbert space. We find a qualitatively different behavior of both observables which can be related to their representations in the invariant parity subspaces.Comment: 8 pages, 7 figures, published versio

Lagrangian Formalism for nonlinear second-order Riccati Systems: one-dimensional Integrability and two-dimensional Superintegrability

The existence of a Lagrangian description for the second-order Riccati equation is analyzed and the results are applied to the study of two different nonlinear systems both related with the generalized Riccati equation. The Lagrangians are nonnatural and the forces are not derivable from a potential. The constant value $E$ of a preserved energy function can be used as an appropriate parameter for characterizing the behaviour of the solutions of these two systems. In the second part the existence of two--dimensional versions endowed with superintegrability is proved. The explicit expressions of the additional integrals are obtained in both cases. Finally it is proved that the orbits of the second system, that represents a nonlinear oscillator, can be considered as nonlinear Lissajous figuresComment: 25 pages, 7 figure

Extension of Nikiforov-Uvarov Method for the Solution of Heun Equation

We report an alternative method to solve second order differential equations which have at most four singular points. This method is developed by changing the degrees of the polynomials in the basic equation of Nikiforov-Uvarov (NU) method. This is called extended NU method for this paper. The eigenvalue solutions of Heun equation and confluent Heun equation are obtained via extended NU method. Some quantum mechanical problems such as Coulomb problem on a 3-sphere, two Coulombically repelling electrons on a sphere and hyperbolic double-well potential are investigated by this method

Unique positive solution for an alternative discrete Painlevé I equation

We show that the alternative discrete Painleve I equation has a unique solution which remains positive for all n >0. Furthermore, we identify this positive solution in terms of a special solution of the second Painleve equation involving the Airy function Ai(t). The special-function solutions of the second Painleve equation involving only the Airy function Ai(t) therefore have the property that they remain positive for all n>0 and all t>0, which is a new characterization of these special solutions of the second Painlevé equation and the alternative discrete Painlevé I equation

Transformations of Heun's equation and its integral relations

We find transformations of variables which preserve the form of the equation for the kernels of integral relations among solutions of the Heun equation. These transformations lead to new kernels for the Heun equation, given by single hypergeometric functions (Lambe-Ward-type kernels) and by products of two hypergeometric functions (Erd\'elyi-type). Such kernels, by a limiting process, also afford new kernels for the confluent Heun equation.Comment: This version was published in J. Phys. A: Math. Theor. 44 (2011) 07520

Mean-field analysis of the majority-vote model broken-ergodicity steady state

We study analytically a variant of the one-dimensional majority-vote model in which the individual retains its opinion in case there is a tie among the neighbors' opinions. The individuals are fixed in the sites of a ring of size $L$ and can interact with their nearest neighbors only. The interesting feature of this model is that it exhibits an infinity of spatially heterogeneous absorbing configurations for $L \to \infty$ whose statistical properties we probe analytically using a mean-field framework based on the decomposition of the $L$-site joint probability distribution into the $n$-contiguous-site joint distributions, the so-called $n$-site approximation. To describe the broken-ergodicity steady state of the model we solve analytically the mean-field dynamic equations for arbitrary time $t$ in the cases n=3 and 4. The asymptotic limit $t \to \infty$ reveals the mapping between the statistical properties of the random initial configurations and those of the final absorbing configurations. For the pair approximation ($n=2$) we derive that mapping using a trick that avoids solving the full dynamics. Most remarkably, we find that the predictions of the 4-site approximation reduce to those of the 3-site in the case of expectations involving three contiguous sites. In addition, those expectations fit the Monte Carlo data perfectly and so we conjecture that they are in fact the exact expectations for the one-dimensional majority-vote model

Dual dopamine D2 receptor and β2-adrenoceptor agonists for the treatment of chronic obstructive pulmonary disease: the pre-clinical rationale

AbstractThis paper describes the rationale for the development of dual dopamine D2-receptor and β2-adrenoceptor agonists as potential treatments for the symptoms of chronic obstructive pulmonary disease (COPD). The putative involvement of pulmonary sensory afferent nerves in mediating the key COPD symptoms of breathlessness, cough and excess sputum production is outlined and the hypothesis that activation of D2-receptors on such nerves would modulate their activity is developed. This premise was tested, in a range of animal models, using the first of a novel class of dual dopamine D2-receptor and β2-adrenoceptor agonists, sibenadet HCI (Viozan™, AR-C68397AA). In the course of these studies it was demonstrated that sibenadet, through activation of D2-receptors, inhibited discharge of rapidly adapting receptors and was effective in reducing reflex-induced tachypnoea, mucus production and cough in the dog. Sibenadet, through its activation of β2-adrenoceptors, was also shown to be an effective bronchodilator with a prolonged duration of action following topical administration to the lungs. These studies also indicated that sibenadet had a wide therapeutic ratio with respect to expected undesirable side-effects such as emesis and cardiovascular disturbances. These results provided a compelling rationale for the initiation of a clinical development programme with sibenadet for the treatment of COPD

Bench-to-bedside review: Sepsis is a disease of the microcirculation

Microcirculatory perfusion is disturbed in sepsis. Recent research has shown that maintaining systemic blood pressure is associated with inadequate perfusion of the microcirculation in sepsis. Microcirculatory perfusion is regulated by an intricate interplay of many neuroendocrine and paracrine pathways, which makes blood flow though this microvascular network a heterogeneous process. Owing to an increased microcirculatory resistance, a maldistribution of blood flow occurs with a decreased systemic vascular resistance due to shunting phenomena. Therapy in shock is aimed at the optimization of cardiac function, arterial hemoglobin saturation and tissue perfusion. This will mean the correction of hypovolemia and the restoration of an evenly distributed microcirculatory flow and adequate oxygen transport. A practical clinical score for the definition of shock is proposed and a novel technique for bedside visualization of the capillary network is discussed, including its possible implications for the treatment of septic shock patients with vasodilators to open the microcirculation

Quasi-doubly periodic solutions to a generalized Lame equation

We consider the algebraic form of a generalized Lame equation with five free parameters. By introducing a generalization of Jacobi's elliptic functions we transform this equation to a 1-dim time-independent Schroedinger equation with (quasi-doubly) periodic potential. We show that only for a finite set of integral values for the five parameters quasi-doubly periodic eigenfunctions expressible in terms of generalized Jacobi functions exist. For this purpose we also establish a relation to the generalized Ince equation.Comment: 15 pages,1 table, accepted for publication in Journal of Physics