scholarly journals Refined bounds of the quantum quadratures within the class of distance-disturbed convex functions in two dimensions

Filomat ◽  
2019 ◽  
Vol 33 (3) ◽  
pp. 825-836
Author(s):  
Gabriela Cristescu ◽  
Muhammad Awan ◽  
Mihail Găianu
Keyword(s):  
Finite Elements ◽  
Convex Functions ◽  
Two Dimensions ◽  
Point Of View ◽  
Two Dimensional ◽  
Convexity Properties

In this paper, we introduce the class of disturbed convex functions defined by means of distance perturbations in two dimensions on co-ordinates. Some quantum trapezoidal estimations are obtained for functions having two dimensional distance-disturbed convexity properties. Refined bounds of the quantum integrals of distance-disturbed convex functions on coordinates are deduced by using the rectangular finite elements technique. These approximations are as best as possible from the sharpness point of view. The sharpness of few results from the literature follows as consequence of the new results in this paper.

LUTTINGER-LIQUID BEHAVIOUR IN 2D: THE VARIATIONAL APPROACH

1993 ◽  
Vol 07 (03) ◽  
pp. 119-141 ◽  
Author(s):  
CLAUDIUS GROS ◽  
ROSER VALENTÍ
Keyword(s):  
Monte Carlo ◽  
Variational Formulation ◽  
Variational Approach ◽  
Order Parameter ◽  
Luttinger Liquid ◽  
Two Dimensions ◽  
Point Of View ◽  
Two Dimensional ◽  
Liquid Type ◽  
D Wave

We study a variational formulation of the Luttinger-liquid concept in two dimensions. We show that a Luttinger-liquid wavefunction with an algebraic singularity at the Fermiedge is given by a Jastrow-Gutzwiller type wavefunction, which we evaluate by variational Monte Carlo for lattices with up to 38 × 38 = 1444 sites. We therefore find that, from a variational point of view, the concept of a Luttinger liquid is well defined even in 2D. We also find that the Luttinger liquid state is energetically favoured by the projected kinetic energy in the context of the 2D t-J model. We study and find coexistence of d-wave superconductivity and Luttinger-liquid behaviour in two-dimensional projected wavefunctions. We then argue that generally, any two-dimensional d-wave superconductor should be unstable against Luttinger-liquid type correlations along the (quasi-1D) nodes of the d-wave order parameter, at temperatures small compared to the gap.

A NEW METHOD FOR CALCULATING CLASSICAL PERIODIC TRAJECTORIES IN TWO DIMENSIONS

1994 ◽  
Vol 04 (02) ◽  
pp. 251-264 ◽  
Author(s):  
K.T.R. DAVIES
Keyword(s):  
Periodic Orbits ◽  
Gaussian Elimination ◽  
Two Dimensions ◽  
Point Of View ◽  
The Other ◽  
New Method ◽  
Two Dimensional ◽  
Many Body ◽  
Periodic Trajectories ◽  
Dimensional Phase Space

Previously, the monodromy method has been widely used for calculating classical periodic trajectories for a two-dimensional Hamiltonian system, or a four-dimensional phase space. In this paper, the problem is formulated from a different point of view, involving Gaussian-elimination algorithms. Thus, we present a new method for calculating classical periodic orbits, in which each of the basic matrices is of dimension two. Two variants are obtained, one assuming that the period of the motion is fixed and the other assuming that the total energy is fixed. We emphasize the importance of calculating the periodic orbits in as small a dimensionality as possible, an advantage which has implications for generalizations of the theory and methods to outstanding many-body problems in nuclear and atomic physics. Comparisons are made between various approaches.

From the natural continuum to the elastic spring cell in three and two dimensions -- a flexibility approach

2019 ◽  
Vol 36 (5) ◽  
pp. 1676-1698 ◽  
Author(s):  
I St Doltsinis
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Lattice Models ◽  
Anisotropic Elasticity ◽  
Two Dimensions ◽  
Point Of View ◽  
Space Structures ◽  
Content Type ◽  
Novel Approach ◽  
Definition Of

Purpose The employment of spring cell substitutes for the numerical analysis of solids and structures in place of finite elements has occasioned research on the subject with regard to both, the applicability of existing approaches and the advancement of concepts. This paper aims to explore in the context of linear elasticity the substitution of the simplex tetrahedral element in space and the triangle in the plane by corresponding spring cells deduced on a flexibility basis using the natural formalism. Design/methodology/approach The natural formalism is characterized by the homogeneous definition of strain and stress along the lines connecting nodes of the simplex tetrahedron and the triangle. The elastic compliance involves quantities along the prospective spring directions and offers itself for the transition to the spring cell. The diagonal entities are interpreted immediately as spring flexibilities, the off-diagonal terms account for the completeness of the substitution. In addition to the isotropic elastic material, the concept is discussed for anisotropic elasticity in the plane. Findings The natural point of view establishes the spring cell as part of the continuum element. The simplest configuration of pin-joined bars discards all geometrical and physical cross effects. The approach is attracting by its transparent simplicity, revealing deficiencies of the spring cell and identifying directly conditions for the complete substitution of the finite element. Research limitations/implications The spring cell counterparts of the tetrahedral- and the triangular finite elements allow employment in problems in three and two dimensions. However, the deficient nature of the approximation requires attention in the design of the discretization lattice such that the conditions of complete finite element substitution are approached as close as possible. Practical implications Apart from plane geometries, triangular spring cells have been assembled to lattice models of space structures such as membrane shells and similar. Tetrahedral cells have been used, in modelling plates and shell structures exhibiting bending stiffness. Originality/value The natural formalism of simplex finite elements in three and two dimensions is used for defining spring cells on a flexibility basis and exploring their properties. This is a novel approach to spring cells and an original employment of the natural concept in isotropic and anisotropic elasticity.

Superluminal coordinate transformations: the two-dimensional case

1983 ◽  
Vol 61 (2) ◽  
pp. 256-263 ◽  
Author(s):  
Louis Marchildon ◽  
Adel F. Antippa ◽  
Allen E. Everett
Keyword(s):  
Time Reversal ◽  
Discrete Symmetries ◽  
Two Dimensions ◽  
Point Of View ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Coordinate Transformations ◽  
The Relationship

This is the first part of a two-paper series, in which we critically examine the various proposals that have been made for superluminal coordinate transformations. Here we consider the two-dimensional case. Starting from rather general assumptions, we show that the superluminal coordinate transformations in two dimensions are essentially uniquely determined. Different proposals for such transformations are then analyzed from the point of view of those assumptions. The relationship between the superluminal transformations and the discrete symmetries P (parity), T (time reversal), and PT is also discussed.

Finite elements-boundary elements coupling for the movement modeling in two-dimensional structures

1992 ◽  
Vol 2 (11) ◽  
pp. 2035-2044 ◽  
Author(s):  
A. Nicolet ◽  
F. Delincé ◽  
A. Genon ◽  
W. Legros
Keyword(s):  
Finite Elements ◽  
Boundary Elements ◽  
Two Dimensional

Urbanicity, City Delegations, and Two-Dimensional Liberalism

2018 ◽  
Author(s):  
Thomas K. Ogorzalek
Keyword(s):  
National Level ◽  
Two Dimensions ◽  
Political Order ◽  
Two Dimensional ◽  
Local Institutions ◽  
Horizontal Integration ◽  
National Politics ◽  
United Front ◽  
Strategies For Success

This theoretical chapter develops the argument that the conditions of cities—large, densely populated, heterogeneous communities—generate distinctive governance demands supporting (1) market interventions and (2) group pluralism. Together, these positions constitute the two dimensions of progressive liberalism. Because of the nature of federalism, such policies are often best pursued at higher levels of government, which means that cities must present a united front in support of city-friendly politics. Such unity is far from assured on the national level, however, because of deep divisions between and within cities that undermine cohesive representation. Strategies for success are enhanced by local institutions of horizontal integration developed to address the governance demands of urbanicity, the effects of which are felt both locally and nationally in the development of cohesive city delegations and a unified urban political order capable of contending with other interests and geographical constituencies in national politics.

scholarly journals Interface Roughening in Two Dimensions

2021 ◽  
Vol 182 (3) ◽  
Author(s):  
Gernot Münster ◽  
Manuel Cañizares Guerrero
Keyword(s):  
Field Theory ◽  
Monte Carlo ◽  
Capillary Wave ◽  
System Size ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Wave Approximation ◽  
Statistical Field ◽  
Statistical Field Theory ◽  
Interface Roughening

AbstractRoughening of interfaces implies the divergence of the interface width w with the system size L. For two-dimensional systems the divergence of $$w^2$$ w 2 is linear in L. In the framework of a detailed capillary wave approximation and of statistical field theory we derive an expression for the asymptotic behaviour of $$w^2$$ w 2 , which differs from results in the literature. It is confirmed by Monte Carlo simulations.

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