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We consider the problem of path-planning for a point mobile automaton in the presence of unknown obstacles in a two dimensional space. We present an algorithm which has better worst case complexity than that of Lumelsky and Stepanov [4], which is the best known at present.

When a solid grows at the expense of an undercooled melt the liquid-solid interface develops a dendritic shape, characterized by the propagation of a needle-shaped tip advancing at a constant velocity V and the persistent emission of side branches.

A simple and accurate phase-tracking measurement technique for multichannel Bragg cells is presented. The procedure is carried out by illuminating two adjacent channels at a time and then comparing the relative positions of the diffraction fringe patterns in the Fourier plane to obtain the relative phase distribution. The application of this technique is demonstrated using a five-channel Bragg cell.

The definition of several new system functions leads to a more complete characterization of time-varying linear systems. A family of twelve system functions, including the impulse-response K system functions, are used to describe time-varying linear systems. The relationships among the various system functions are clearly illustrated. The K system functions are shown to be convenient for the analysis of cascaded systems. The time-frequency duality concept is discussed with respect to the system functions, and the introduction of physical variables extends the duality concept so that knowing one relationship is equivalent to knowing four relationships. The expansion of system functions in terms of a complete set of functions in two dimensional space or in a sampling series for an appropriately band-limited and/or time- limited system leads to a matrix characterization of time-varying linear systems. Schemes for evaluating the coefficients of the expansions are described.

Semiboundedness of the total Hamiltonian is proved for a selfinteracting Boson field in two dimensional space time. The interaction is given by a Wick polynomial:P(Φ):. The polynomialP is required to have even degree and its leading coefficient must be positive. A space cutoff is introduced in the interaction Hamiltonian.

This work presents an exploration framework which performs data assignment and access scheduling exploration for applications given a multilayer memory architecture. Our framework uses multiobjective criteria during exploration, such as application execution time, energy, bandwidth, and data size. In order to tackle the complexity of the exploration, it is divided into three phases; Pareto diagram composition, data assignment, and access scheduling. The first phase produces multidimensional Pareto points for our application. After this phase, our framework produces distinct data assignments which are represented as Pareto points in a two dimensional space defined by bandwidth requirements and size requirements. Finally, the scheduling phase finds possibly optimal order of the tasks and performs precise scheduling of the tasks. Three feedbacks paths are present which can be used to iteratively improve exploration results. It is possible to trade off the quality of the results and the algorithm runtime. We have evaluated our framework on a medical image processing application. We have shown that our algorithms can perform exploration of the huge design space in an iterative manner and obtains good Pareto diagram coverage.

X-ray diffraction on surface acoustic waves with tunable wavelength provides a way to perform beam scannings. 1D and 2D space scannings of x-ray beams by this method are presented. The feasibility of a purely optical method to perform scanning x-ray imaging without any mechanical movement is discussed.

An efficient implementation of finite element methods for free boundary parabolic problems in general two dimensional space domains is presented. The Stefan problem, the Hele-Shaw problem and the porous medium equation are included. Backward differences or linearization techniques are used for the time discretization of the problem. The performances of these schemes are discussed with several numerical tests.

Let $S = \{ e_1 , \cdots ,e_n \} $ be a collection of n (intersecting) line segments in the plane. Suppose that all segments have their right endpoints lying on the same vertical line, and that one wishes to bound the number of pairs of nonintersecting vertically visible segments that will intersect when extended to the right ($e_i$, $e_j$ are vertically visible if there exists a vertical line segment connecting a point on ei to a point on $e_i$ and not meeting any other segment). It is shown that there are at most $O(n\log ^2 n)$ such pairs, and only $O(n\log n)$ in the case of full rays, where the latter bound can be attained in the worst case. These results are applied to obtain similar upper and lower bounds on the maximum size of the queue in the original implementation of the Bentley–Ottmann algorithm for reporting all intersections between the segments in S, i.e., the implementation where future events are not deleted from the queue. It is also shown that, without the extra conditions on the segmen...

Flows mixing grains and fluid, called immersed granular flows , are of huge interests in a lot of industrial domains. There exists many ways to simulate such flows and in most of the cases the physical and numerical models depend on the scale at which the fluid has to be represented [1]. This submission is devoted to an hybrid multiscale model to represent immersed granular flows. On one hand, the fluid flow between the grains is deduced from Navier-Stokes equations for incompressible flows taking into account the porosity of the mix and computed using the finite element method at a greater scale than the grains scale . On the other hand, the grains are considered as discrete elements in a Lagrangian way. All the contacts happening during a time step are solved by a nonsmooth discrete elements method and the resolution of the trajectories is based on Newton dynamics. The interaction force between grains and fluid is used as a closure relation for the model and are applied on the fluid as ponctual forces. This kind of model is able to represent highly inhomogeneous immersed granular flows going from pure fluid to porous media. Furthermore, it is able to represent the interactions between grains and complex geometries accuratly thanks to the discrete elements method that are of huge interest for extrusion processes for example. Then, we obtain accurate results for fluid and grains dynamics with a reduced computational time due to the representation of the fluid at a large scale. First results are promising. We have simulated in two dimensions the behaviour of a drop made up of grains falling in a viscous fluid and compared the results with experiments found in [2]. The viscous effects force the drop to exhibit particular shapes during the fall. At each step, we have compared the macroscopic behaviour of the drop and found that it corresponds to a vertical slice of the experiments. At the beginning of the fall some particles leak at the rear of the motion forming a tail. Later, for a sufficiently high number of grains forming the drop, a circulating velocity field splits it when there is no longer enough grains in its centre. This process is recurent for each of the new droplets until there is no longer enough grains forming the droplets. The method used for these simulations will be analysed to prove the convergence and other results involving free surfaces flows will be shown. We will focus on the transport of sediments during a dam burst. Imposing a inflow upstream, we will observe the discharge of the fluid mixing sediments composing of grains with different sizes and shapes to study their influence on the leakage rate. Simulations of such a situation are of huge interests to evaluate the possible damages on cities in the near region of a dam.

Fivefold and sevenfold symmetry operations are, of course, incompatible with repetition by a lattice but, with the appearance of structures involving curved sheets, they and other non-crystallographic operations must now be taken into consideration as possibilities of non-Euclidean crystallography develop. Here are described the symmetry groups which might be called 732 and 73m and which may be found in two-dimensional manifolds.

In this note, a novel, but simple system is described which gives both continuous time resolution and limited two‐dimensional spatial resolution. This system uses multiple, displaced pinholes in conjunction with a streak camera. As an example of this technique, the thermalization of a plasma focus has been studied.

This paper is principally concerned with the enumerations of the partitions of numbers in two-dimensional space. Such partitions are such that the parts are placed at the points or nodes of a lattice, rectangular in shape, and . . . . . . . . . . . . having given numbers of nodes in the sides, and the parts of the numbers partitioned are placed at the nodes in such wise that descending order of magnitude in each row of parts is from left to right and in each column of parts from top to bottom. If the nodes in the sides be m, n, respectively, and the part magnitude be restricted so as to be not greater than l , the generating function which gives by the coefficients of x w in the ascending expansion the number of such partitions of the number w has been long conjectured by the author to have the expression ( l + 1) ( l + 2 ) . . . ( l + m ) ( l + 2) . . . (l + m + 1) . . . . . . ( l + n ) . . . (l + m + n - 1)/(1) (2) . . . ( m ) (2) . . . ( m + 1) . . . . . . ( n ) . . . ( m + n - 1) where ( s ) denotes 1— x s ; but previous attempts to establish this had, except in certain particular cases, resulted in failure.

The conditions that a one-parameter manifold of rays must fulfill in order that a refractive-index distribution will exist for which the manifold is possible are analyzed. A method for calculating the refractive-index distribution is given for several cases. The problem is solved easily when the trajectories of the rays of the manifold do not cross, but it becomes more difficult when the rays are permitted to cross. Example are given of manifolds in which no more than two rays may cross at a given point. The Welford–Winston edge-ray principle, used in the design of nonimaging concentrators, is proved under several assumptions. The connection that exists between the problem treated in this paper and the synthesis of gradient-index two-dimensional nonimaging concentrators is discussed.

Binary images usually are produced by clipping band-limited images generated through physical systems. We examine the conditions under which a prescribed image can be formed by this process. Obviously, when the desired image has infinitely sharp isolated corners, it cannot be formed by clipping a band-limited image. We show, however, that any desired binary image can be approximated arbitrarily closely. To make this approximation one must find a band-limited function that has approximately the desired level crossings, i.e., contours where the function is equal to the threshold value of the clipping operation. This can be done by defining a band-limited function in terms of a product of functions that define the function’s zero-crossing contours. In a finite region, these zero crossings are defined strictly in terms of the zeros of a two-dimensional polynomial.

A simplified model for interregional planning in agriculture appears to offer a method for solving linear programming problems of a given structure (each variable being represented in one constraint and in another constraint which includes all variables). This structure enables us to represent the model in a two dimensional space and to construct "potentiality curves," which constitute a first selection of the variables. The resolution with the remaining variables is easy. Thus, even large programmes can be solved by graphical representations and hand computations. The method proposed is, in fact, an application of a well-known algorithm, the primal-dual method of Dantzig, Ford, and Fulkerson.