Topology Of Solutions Research Articles

Non-collapsing membrane instantons in higher dimensions

We introduce a particular embedding of seven-dimensional self-duality membrane equations in C 3× R which breaks G 2 invariance down to SU(3). The world-volume membrane instantons define SU(3) special lagrangian submanifolds of C 3. We discuss in detail solutions for spherical and toroidal topologies assuming factorization of time. We show that the extra dimensions manifest themselves in the solutions through the appearance of a non-zero conserved charge which prevents the collapse of the membrane. We find non-collapsing rotating membrane instantons which contract from infinite size to a finite one and then they bounce to infinity in finite time. Their motion is periodic. These generalized complex Nahm equations, in the axially symmetric case, lead to extensions of the continuous Toda equation to complex space.

TOPOLOGY OPTIMIZATION OF COMPLIANT MECHANISMS WITH STRENGTH CONSIDERATIONS1*

Multicriteria formulations that have been reported previously in topology design of compliant mechanisms address flexibility and stiffness issues simultaneously and aim to attain an optimal balance between these two conflicting attributes. Such techniques are successful in indirectly controlling the local stress levels by constraining the input displacement. Individual control on the conflicting objectives is often difficult to achieve with these flexibility-stiffness formulations. Resultant topologies may sometimes be overly stiff, and there is no guarantee against failure. Local stresses may exceed the permissible yield strength of the constituting material in such designs. In this article, local failure conditions relating to stress constraints are incorporated in topology optimization algorithms to obtain compliant and strong designs. Quality functions are employed to impose stress constraints on retained material, ignoring nonexisting regions in the design domain. Stress constraints are further relaxed to regularize the design space to help the mathematical programming algorithms based on the Karush-Kuhn-Tucker conditions yield improved solutions. Examples are solved to corroborate the solutions for failure-free compliant topologies that are much improved in comparison to those obtained using flexibility-stiffness multicriteria objectives. *Communicated by S. Azarm.

Optimal Design and Experimental Validation of Compliant Mechanical Amplifiers for Piezoceramic Stack Actuators

An optimization method has been developed for design of compliant mechanical amplifiers for piezoceramic stack actuators. A topology optimization approach is used where the objective is to maximize the stroke amplification, and results show good algorithm convergence and good mechanism performance. The focus of this paper is on using the optimal topology solution to generate a solid model, and on improving the actuator performance through detail design and analysis of the resulting monolithic compliant mechanical amplifiers. A study of the effect of various flexure hinge configurations and other design parameters on the amplification and mechanical advantage of an actuator is performed. Another actuator with a large stroke amplification is designed using a batch of random starting points to the optimization algorithm. Prototype actuators have been fabricated, and the results of experimental validations are presented.

LP-Based Heuristic Algorithms for Interconnecting Token Rings viaSource Routing Bridges

We develop a method to determine the topology of a network that interconnects a number of token rings using source routing bridges. The purpose is to compute a topology that provides low response delays for network users at a minimal cost of bridge installations. We formulate this network design problem as a mixed binary integer linear program. We develop effective heuristic algorithms. The algorithms exploit the topology and routing solutions of the linear programming relaxation in a sophisticated manner which we believe is new in the literature. The model incorporates performance issues, such as network stability, bridge overflow, back pressure effect and broadcast storm, that are specific to the underlying communication technology. By formally incorporating these performance issues, we tighten the model formulation and improve the quality of the LP bound considerably. Computational results are reported for problems with up to 20 token rings and 190 potential bridge locations.

On optimal converter placement in wavelength-routed networks

Wavelength converters increase the traffic-carrying capacity of circuit-switched optical networks by relaxing the wavelength continuity constraints. We consider the problem of optimally placing a given number of wavelength converters on a path to minimize the call-blocking probability. Using a simple performance model, we first prove that uniform spacing of converters is optimal for the end-to-end performance when link loads are uniform and independent. We then show that significant gains are achievable with optimal placement compared to random placement. For nonuniform link loads, we provide a dynamic programming algorithm for the optimal placement and compare the performance with random and uniform placement. Optimal solutions for bus and ring topologies are also presented. Finally, we discuss the effect of the traffic model on the placement decision.

Classical and quantum gravity in 1 + 1 dimensions. II: The universal coverings

A set of simple rules for constructing the maximal (e.g. analytic) extensions for any metric with a Killing field in an (effectively) two-dimensional spacetime is formulated. The application of these rules is extremely straightforward, as is demonstrated by various examples and illustrated with numerous figures. Despite the resulting simplicity we also comment on some subtleties concerning the concept of Penrose diagrams. Most noteworthy among these, perhaps, is that (smooth) spacetimes which have both degenerate and non-degenerate (Killing) horizons do not allow for globally smooth Penrose diagrams. Physically speaking this obstruction corresponds to an infinite relative red/blueshift between observers moving across the two horizons. The present work provides a further step in the classification of all global solutions of the general class of two-dimensional gravity - Yang - Mills systems introduced in part I, comprising, for example, all generalized (linear and nonlinear) dilaton theories. In part I we constructed the local solutions, which were found to always have a Killing field; in this paper we provide all universal covering solutions (the simply connected maximally extended spacetimes). A subsequent part III will treat the diffeomorphism inequivalent solutions for all other spacetime topologies. Part II is entirely self-contained; prior reading of part I is not necessary.

Uniqueness theorems for subharmonic functions in unbounded domains

A theorem of Carlson says that a holomorphic function of exponential growth in the half-plane cannot approach zero exponentially along the boundary unless it vanishes identically. This paper presents a generalization of this result for subharmonic functions in a Greenian domain Ω \Omega , using the Martin boundary, minimal fine topology and PWB solution to the h h -Dirichlet problem. Applications of the general theorem to specific choices of Ω \Omega , such as the half-space and strip, are presented in later sections.

Topology and Static Solitary Solutions of the Modified Sine-Gordon Field

Topology and Static Solitary Solutions of the Modified Sine-Gordon Field