Linear Singularities Research Articles

Diffractive charm jet production at hadron colliders in the two-gluon exchange model

We present a calculation of diffractive charm jet production at hadron colliders in perturbative QCD based on the two-gluon exchange model. Differing from the previous calculations, we abandon the use of the effective color-singlet virtual gluon simplification, and use the real gluon in the calculations for the partonic process. We find the final result is free of the linear singularities due to the small transverse momenta of the exchanged two gluons. In the leading logarithmic approximation in QCD, this process is related to the off-diagonal gluon density in the proton. As a result, this process may provide a wide window for testing the two-gluon exchange model, and may be particularly useful in studying the small-$x$ physics. In comparison, the diffractive bottom jet production is also discussed, and is found to be important only for the large transverse momentum of the jet.

Vortices with fractional circulation quantum in superfluid 3HeA 2

Due to the specific discrete symmetry of the superfluid 3HeA 2 order parameter, linear singularities can exist which are characterized by a quarter-integer quantum of superflow velocity circulation. Some consequences of this observation are analyzed.

The stressed state near a microflaw cluster point

The stressed state near cluster point z = 0 for microflaws (MiFs) in the form of cracks or thin linear sharply-angled inclusions in an elastic plane located along a line on one side or other of the cluster point and satisfy certain conditions is investigated. This is preceded by the analytic solution of the first and second fundamental problems of the theory of elasticity for a plane with an infinite set of collinear linear singularities clustering at a finite point. Cases are considered in which the flaws are such that their images under the mapping ζ = 1/ z are situated periodically along an entire line or only along a ray. Stability to fracture, both in the neighbourhood of an MiF cluster point and globally for an MiF system, are investigated using force and energy fracture criteria. Examples describing the fracture mechanism are given. An analytic solution of the problem of the interaction of a macroflaw (MaF) with an infinite series of MiFs collinear with it and clustering at the vertex of the MaF is obtained. The investigation is based on a conformal mapping and the results of [1–4], in which solutions are obtained in closed form of the first and second fundamental problems of the theory of elasticity for a plane with a denumerable set of cuts with a cluster point at infinity.

Structural ledges at precipitate/matrix interfaces in a (Ni, Co) superalloy: atomic structures and elastic fields

The broad faces of plate-like DO 19 precipitates of a (Ni, Co) base superalloy are decorated with triangular networks of linear singularities (LS's) accomodating the 2.5% isotropic length misfit in the atomically dense planes (111) fcc∥(0001) DO19. High-resolution electron microscopy images depict the detailed atomic cores of two of these LS's and show that they are associated with ledges of two (111) spacings in height. The elastic fields surrounding the LS's are analyzed by using both multislice computations and the Somigliana dislocation model in anisotropic elasticity theory. As a result, the Burgers-vector content of the observed ledges is found to be 1 6 〈112〉 vectors.

Asymptotics of solutions of a linear singularity perturbed system with degeneracy

Asymptotic expansions with respect to a small parameter e are constructed for a fundamental system of solutions of a linear singularity perturbed system of equations of the form $$\varepsilon ^h A(t,\varepsilon )\frac{{dx}}{{dt}} = B(t,\varepsilon )x$$ on a finite interval of variation of the independent variable. It is assumed here that the (n×n) -matricesA (t, ɛ) and B(t,ɛ) can be expanded in series in powers of\(A(t,\varepsilon ) = \sum\limits_{k = 0}^\infty {A_k } (t)\varepsilon ^k , B(t,\varepsilon ) = \sum\limits_{k = 0}^\infty {B_k } (t)\varepsilon ^k ,\) where the matrix A0(t)is degenerate on the given interval and the pencil of matrices B∩(t)−ΩA0 (t) has several “finite” and “infinite” elementary divisors of the same multiplicity.

Linear singularities and their motion in improper ferroelectrics

Abstract In improper ferroelectrics with the two-component order parameter (GMO-type) linear topological defects (circulation lines) are possible. They divide the regions of the rotational antiphase boundary with the different sense of rotation or correspond to a juncture of the antiphase boundary with the two polarization boundaries. It is shown that there exists a force applied to these lines due to the Lifshitz invariant induced by the shear strain. It is proposed to use this force for a selective influence on the antiphase boundaries.

The recursive algorithm for the optimal static output feedback control problem of linear singularity perturbed systems

A recursive algorithm is developed for solving the algebraic equations comprising the solution of the optimal static output feedback control problem of singularly perturbed linear systems. The algorithm is very efficient from the numerical point of view, since only low-order systems are involved in algebraic calculations and the required solution can be easily obtained up to an arbitrary order of accuracy, that is O( epsilon /sup k/) where epsilon is a small perturbation parameter. The real-world example demonstrates the failure of O( epsilon ) theory used so far in the study of this problem and the necessity for the existence of O( epsilon /sup k/) theory. >

Magnetic defects generated by crystal defects

Linear magnetic defects (LMDs), i.e. linear singularities of the fields of magnetic order parameters in ferromagnets (FMs) and antiferromagnets (AFMs) are investigated. It is shown that disclinations in collinear AFM and in cubic FM generate LMDs. These and similar crystallomagnetic singularities are considered from the point of view of the topological theory of defects in ordered media.

Inverse Design of Composite Turbine Blade Circular Coolant Flow Passages

An inverse design and optimization method is developed to determine the proper size and location of the circular holes (coolant flow passages) in a composite turbine blade. The temperature distributions specified on the outer blade surface and on the surfaces of the inner holes can be prescribed a priori. In addition, heat flux distribution on the outer blade surface can be prescribed and iteratively enforced using optimization procedures. The prescribed heat flux distribution on the outer surface is iteratively approached by using the Sequential Unconstrained Minimization Technique (SUMT) to adjust the sizes and locations of the initially guessed circular holes. During each optimization iteration, a two-dimensional heat conduction equation is solved using direct Boundary Element Method (BEM) with linear temperature singularity distribution. For manufacturing purposes the additional constraints are enforced assuring the minimal prescribed blade wall thickness and spacing between the walls of two neighboring holes. The method is applicable to both single material (homogeneous) and coated (composite) turbine blades. Three different cases were tested to prove the feasibility and the accuracy of the method.

Configurational forces in the mechanics of a solid deformable body

A configurational force /1 –3/, which always originates in a deformable solid whenever the stress source moves, represents physically the contribution of the external strain and stress fields to the dissipation of energy, taker, per unit path length of the source. When the stress source (singularity) is internal, the configurational force is the fundamental. parameter controlling the process of motion and it can be called a driving force. Linear singularities of the type of crack and dislocation contours, point singularities of the type of small cavities and inclusions, etc. are examples of each cases. If the singularity is generated directly by external forces, the configurational force plays an auxiliary role and such cases will be examined below. This is the problem of the motion of a small solid body over the surface of a half-space, and different schemes of wedge motion in an unbounded elasto-plastic space.

Gauge model of disordered magnets

A model of disordered magnets with their ground state degenerate in energy is proposed. It is shown that the presence of singularities in the field of an order parameter leads to the appearance of additional degrees of freedom described by the gauge field of the rotation group. The gauge fields arise as coefficients of the connection of some non-trivial fibre bundle. The lagrangian of disordered magnets with linear singularities (disclinations) in the field of the order parameter is constructed, and the spectrum of hydrodynamic modes is found.

Statistics of flexible rings with excluded volume

A grand partition function of a system of closed self-avoiding lines on a lattice is studied. The examples of such lines are closed linear singularities: dislocations, vortex lines, etc. The partition function is expressed in the form of an integral over fictitious fields so that the behaviour of the whole system and a single ring in the system may be qualitatively described. A length distribution of rings, a mean radius of a ring of length L in the system and an effective interaction of the points of a probe ring, arising from the interaction of the probe ring with other rings, have been derived. An impact of broken rings is discussed.

Linear singularities and structures in superfluid3He-A

Making use of a technique developed by Hu, Kumar, and Maki, we calculate the energies associated with linear singularities, such as vortex lines and disgyrations, and linear structures, such as the Mermin-Ho (MH) and Anderson-Toulouse (AT) structures in superfluid3He-A. The results are used to analyze the most favorable textures in the spherical geometry and in a rotating system.

Linear force and dislocation multipoles in anisotropic elasticity

The displacement field of a linear singularity in an anisotropic medium is developed by superimposing the displacement of a distribution of simple singularities. The result can be expressed in terms of the moments of the distribution. This approach provides a means of comparing atomic displacements obtained by computer simulations of dislocations with analytical results to obtain numerical values for the moments of the effective distribution. Distributions of linear force dipoles can also be used to construct models of solute segregation to dislocations.