Computations and interaction

We enhance the notion of a computation of the classical theory of computing with the notion of interaction. In this way, we enhance a Turing machine as a model of computation to a Reactive Turing Machine that is an abstract model of a computer as it is used nowadays, always interacting with the user and the world

A new model of a tidally disrupted star

A new semi-analytical model of a star evolving in a tidal field is proposed. The model is a generalization of the so-called 'affine' stellar model. In our model the star is composed of elliptical shells with different parameters and different orientations, depending on time and on the radial Lagrangian coordinate of the shell. The evolution equations of this model are derived from the virial relations under certain assumptions, and the integrals of motion are identified. It is shown that the evolution equations can be deduced from a variational principle. The evolution equations are solved numerically and compared quantitatively with the results of 3D numerical computations of the tidal interaction of a star with a supermassive black hole. The comparison shows very good agreement between the main ``integral'' characteristics describing the tidal interaction event in our model and in the 3D computations. Our model is effectively a one-dimensional Lagrangian model from the point of view of numerical computations, and therefore it can be evolved numerically $10^{2}-10^{3}$ times faster than the 3D approach allows. This makes our model well suited for intensive calculations covering the whole parameter space of the problem.Comment: This version is accepted for publication in ApJ. Stylistic and grammatical changes, new Appendix adde

Numerical computations of swirling recirculating flow

Swirling, recirculating, nonreacting flows were computed using a 2D elliptic program consisting of three tasks. The computations in Task 1 and 2 were made using an independent analysis for the two coaxial swirling flows. The Task 2 computations were made using the measured profiles of the mixing region. In Task 3, a modified 2D elliptic program was employed to include the effects of interaction between the inner and outer streams

A thread calculus with molecular dynamics

We present a theory of threads, interleaving of threads, and interaction between threads and services with features of molecular dynamics, a model of computation that bears on computations in which dynamic data structures are involved. Threads can interact with services of which the states consist of structured data objects and computations take place by means of actions which may change the structure of the data objects. The features introduced include restriction of the scope of names used in threads to refer to data objects. Because that feature makes it troublesome to provide a model based on structural operational semantics and bisimulation, we construct a projective limit model for the theory.Comment: 47 pages; examples and results added, phrasing improved, references replace

A general theory of action languages

We present a general theory of action-based languages as a paradigm, for the description, of those computational systems which include elements of concurrency and networking, and extend this approach to describe dist.ributed systems and also t,o describe the interaction of a system, with an environment. As part of this approach we introduce the Action Language as a common model for the class of nondeterministic concurrent programming languages and define its intensional and interaction semantics in terrors of continuous transformation of environment behavior. This semantics i.s specialized for programs with stores, and extended to describe distributed computations

Casimir interaction between spheres in (D+1)\boldsymbol{(D+1)}-dimensional Minkowski spacetime

We consider the Casimir interaction between two spheres in $(D+1)$-dimensional Minkowski spacetime due to the vacuum fluctuations of scalar fields. We consider combinations of Dirichlet and Neumann boundary conditions. The TGTG formula of the Casimir interaction energy is derived. The computations of the T matrices of the two spheres are straightforward. To compute the two G matrices, known as translation matrices, which relate the hyper-spherical waves in two spherical coordinate frames differ by a translation, we generalize the operator approach employed in [IEEE Trans. Antennas Propag. \textbf{36}, 1078 (1988)]. The result is expressed in terms of an integral over Gegenbauer polynomials. Using our expression for the Casimir interaction energy, we derive the large separation and small separation asymptotic expansions of the Casimir interaction energy. In the large separation regime, we find that the Casimir interaction energy is of order $L^{-2D+3}$, $L^{-2D+1}$ and $L^{-2D-1}$ respectively for Dirichlet-Dirichlet, Dirichlet-Neumann and Neumann-Neumann boundary conditions, where $L$ is the center-to-center distance of the two spheres. In the small separation regime, we confirm that the leading term of the Casimir interaction agrees with the proximity force approximation, which is of order $d^{-\frac{D+1}{2}}$, where $d$ is the distance between the two spheres. Another main result of this work is the analytic computations of the next-to-leading order term in the small separation asymptotic expansion. This term is computed using careful order analysis as well as perturbation method. We find that when $D$ is large, the ratio of the next-to-leading order term to the leading order term is linear in $D$, indicating a larger correction at higher dimensions.Comment: 23 page