A PROCEDURE FOR THE ALLOCATION OF TWO-DIMENSIONAL RESOURCES IN A MULTIAGENT SYSTEM

2009 ◽  
Vol 18 (03n04) ◽  
pp. 381-422 ◽  
Author(s):  
KARTHIK IYER ◽  
MICHAEL N. HUHNS
Keyword(s):  
Resource Allocation ◽  
Multiagent System ◽  
Two Dimensional ◽  
Existence Of A Solution ◽  
One Dimensional ◽  
Classic Problem ◽  
Allocation Procedure ◽  
Sufficiency Condition ◽  
Higher Dimensional ◽  
Partial Overlap

This paper presents a constructive solution to the classic problem of land division. It is the first solution that enables the allocation of higher-dimensional resources without degenerating them first into a series of one-dimensional resource allocation problems. We base our allocation procedure on the topology of overlaps among the regions of interest of different agents. Our result is an algorithm suitable for computer implementation, unlike earlier ones that were only existential in nature. It uses the notion of degree of partial overlap to create a sufficiency condition for the existence of a solution, and proposes a procedure to find the overlaps in such a case. The proposed solution is fair, strategy-proof, non-existential, and does not explicitly need the resource to be measurable. The agents do not have to reveal their private utility functions. We extend our earlier result for one-dimensional resource allocation to this two-dimensional one and explain the distinctive issues involved.

A Graphical Exposition of the Ising Problem

1971 ◽  
Vol 12 (3) ◽  
pp. 365-377 ◽  
Author(s):  
Frank Harary
Keyword(s):  
Dimensional Case ◽  
Two Dimensional ◽  
One Dimensional ◽  
Higher Dimensional ◽  
The One

Ising [1] proposed the problem which now bears his name and solved it for the one-dimensional case only, leaving the higher dimensional cases as unsolved problems. The first solution to the two dimensional Ising problem was obtained by Onsager [6]. Onsager's method was subsequently explained more clearly by Kaufman [3]. More recently, Kac and Ward [2] discovered a simpler procedure involving determinants which is not logically complete.

scholarly journals QUASI-ONE DIMENSIONAL FLUIDS THAT EXHIBIT HIGHER DIMENSIONAL BEHAVIOR

2010 ◽  
Vol 24 (25n26) ◽  
pp. 5051-5059 ◽  
Author(s):  
SILVINA M. GATICA ◽  
M. MERCEDES CALBI ◽  
GEORGE STAN ◽  
R. ANDREEA TRASCA ◽  
MILTON W. COLE
Keyword(s):  
Carbon Nanotubes ◽  
Phase Transitions ◽  
Finite Temperature ◽  
Review Paper ◽  
Two Dimensional ◽  
Reduced Dimensionality ◽  
Narrow Channels ◽  
One Dimensional ◽  
Higher Dimensional ◽  
Effective Dimensionality

Fluids confined within narrow channels exhibit a variety of phases and phase transitions associated with their reduced dimensionality. In this review paper, we illustrate the crossover from quasi-one dimensional to higher effective dimensionality behavior of fluids adsorbed within different carbon nanotubes geometries. In the single nanotube geometry, no phase transitions can occur at finite temperature. Instead, we identify a crossover from a quasi-one dimensional to a two dimensional behavior of the adsorbate. In bundles of nanotubes, phase transitions at finite temperature arise from the transverse coupling of interactions between channels.

One-dimensional Systems

2020 ◽  
pp. 48-105
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Ising Model ◽  
Potts Model ◽  
Statistical Models ◽  
Model Systems ◽  
Recursive Method ◽  
Two Dimensional ◽  
Matrix Approach ◽  
One Dimensional ◽  
Higher Dimensional ◽  
Transfer Matrix Approach

Chapter 2 discusses one-dimensional statistical models, for example, the Ising model and its generalizations (Potts model, systems with O(n) or Zn-symmetry, etc.). It discusses several methods of solution and covers the recursive method, the transfer matrix approach, and series expansion techniques. General properties of these methods, which are valid on higher-dimensional lattices, are also covered. The contents of this chapter are quite simple and pedagogical but extremely useful for understanding the following sections of the book. One of the appendices at the end of the chapter is devoted to a famous problem of topology, i.e. the four-colour problem, and its relation with the two-dimensional Potts model.

A NEW ALGORITHM FOR COMPUTING ONE-DIMENSIONAL STABLE AND UNSTABLE MANIFOLDS OF MAPS

2012 ◽  
Vol 22 (01) ◽  
pp. 1250018 ◽  
Author(s):  
HUIMIN LI ◽  
YANGYU FAN ◽  
JING ZHANG
Keyword(s):  
Bisection Method ◽  
Two Dimensional ◽  
Stable And Unstable Manifolds ◽  
Numerical Examples ◽  
One Dimensional ◽  
Higher Dimensional ◽  
Correction Scheme ◽  
Accuracy Criterion ◽  
Tangent Component ◽  
Unstable Manifolds

A new algorithm is presented to compute one-dimensional stable and unstable manifolds of fixed points for both two-dimensional and higher dimensional diffeomorphism maps. When computing the stable manifold, the algorithm does not require the explicit expression of the inverse map. The global manifold is grown from a local manifold and one point is added at each step. The new point is located with a "prediction and correction" scheme, which avoids searching the computed part of the manifold with a bisection method and accelerates the searching process. By using the fact that the Jacobian transports derivatives along the orbit of the manifold, the tangent component of the manifold is determined and a new accuracy criterion is proposed to check whether the new point that defines the manifold is acceptable. The performance of the algorithm is demonstrated with several numerical examples.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

State-of-the-Art of Modeling Surface Water Impoundments

1982 ◽  
Vol 14 (1-2) ◽  
pp. 241-261 ◽  
Author(s):  
P A Krenkel ◽  
R H French
Keyword(s):  
Water Quality ◽  
Surface Water ◽  
State Of The Art ◽  
Rate Coefficients ◽  
Two Dimensional ◽  
One Dimensional ◽  
Integral Energy ◽  
Range Of Values ◽  
Dimensional Integral ◽  
Water Impoundment

The state-of-the-art of surface water impoundment modeling is examined from the viewpoints of both hydrodynamics and water quality. In the area of hydrodynamics current one dimensional integral energy and two dimensional models are discussed. In the area of water quality, the formulations used for various parameters are presented with a range of values for the associated rate coefficients.

The formation of gas hydrates under shock wave impact on the bubble media (two-dimensional case)

2010 ◽  
Vol 7 ◽  
pp. 90-97
Author(s):  
M.N. Galimzianov ◽  
I.A. Chiglintsev ◽  
U.O. Agisheva ◽  
V.A. Buzina
Keyword(s):  
Shock Wave ◽  
Gas Hydrates ◽  
Hydrate Formation ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Wave Impact ◽  
Bubble Liquid ◽  
One Dimensional ◽  
Bubble Media ◽  
Main Factors

Formation of gas hydrates under shock wave impact on bubble media (two-dimensional case) The dynamics of plane one-dimensional shock waves applied to the available experimental data for the water–freon media is studied on the base of the theoretical model of the bubble liquid improved with taking into account possible hydrate formation. The scheme of accounting of the bubble crushing in a shock wave that is one of the main factors in the hydrate formation intensification with increasing shock wave amplitude is proposed.

Modifications of the Godunov method for computing disturbance propagation in an elastic body

2016 ◽  
Vol 11 (1) ◽  
pp. 119-126 ◽  
Author(s):  
A.A. Aganin ◽  
N.A. Khismatullina
Keyword(s):  
Elastic Body ◽  
Godunov Method ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Order Accuracy ◽  
One Dimensional ◽  
Disturbance Propagation ◽  
Linear Waves ◽  
Longitudinal And Shear Waves ◽  
Contact Discontinuities

Numerical investigation of efficiency of UNO- and TVD-modifications of the Godunov method of the second order accuracy for computation of linear waves in an elastic body in comparison with the classical Godunov method is carried out. To this end, one-dimensional cylindrical Riemann problems are considered. It is shown that the both modifications are considerably more accurate in describing radially converging as well as diverging longitudinal and shear waves and contact discontinuities both in one- and two-dimensional problem statements. At that the UNO-modification is more preferable than the TVD-modification because exact implementation of the TVD property in the TVD-modification is reached at the expense of “cutting” solution extrema.

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