9,853 research outputs found
Explicit Non-Abelian Monopoles and Instantons in SU(N) Pure Yang-Mills Theory
It is well known that there are no static non-Abelian monopole solutions in
pure Yang-Mills theory on Minkowski space R^{3,1}. We show that such solutions
exist in SU(N) gauge theory on the spaces R^2\times S^2 and R^1\times S^1\times
S^2 with Minkowski signature (-+++). In the temporal gauge they are solutions
of pure Yang-Mills theory on T^1\times S^2, where T^1 is R^1 or S^1. Namely,
imposing SO(3)-invariance and some reality conditions, we consistently reduce
the Yang-Mills model on the above spaces to a non-Abelian analog of the \phi^4
kink model whose static solutions give SU(N) monopole (-antimonopole)
configurations on the space R^{1,1}\times S^2 via the above-mentioned
correspondence. These solutions can also be considered as instanton
configurations of Yang-Mills theory in 2+1 dimensions. The kink model on
R^1\times S^1 admits also periodic sphaleron-type solutions describing chains
of n kink-antikink pairs spaced around the circle S^1 with arbitrary n>0. They
correspond to chains of n static monopole-antimonopole pairs on the space
R^1\times S^1\times S^2 which can also be interpreted as instanton
configurations in 2+1 dimensional pure Yang-Mills theory at finite temperature
(thermal time circle). We also describe similar solutions in Euclidean SU(N)
gauge theory on S^1\times S^3 interpreted as chains of n
instanton-antiinstanton pairs.Comment: 16 pages; v2: subsection on topological charges added, title
expanded, some coefficients corrected, version to appear in PR
Чисельне розв’язання сингулярного інтегрального рівняння, пов’язаного з динамічною задачею контактної взаємодії
A singular integral equation with a fixed singularity to which the problem of contact interaction of two quarters of spaces in the conditions of harmonic oscillations of longitudinal shear is reduced is considered. A quarters of the space is situated so that the half-space composed of them has a stepped boundary. In the contact area, the conditions for ideal coupled are satisfied. The unknown function in this equation is the contact stresses. For the numerical solution of this equation, a method that takes into account the asymptotic behavior of contact stresses at the edge point is proposed. The basis of this method is the use of special quadrature formulas for singular integrals obtained in the article. When obtaining these formulas, the unknown function was approximated by an interpolation polynomial, in which the roots of the Laguerre polynomials are the points of interpolation. The values of the unknown function at the interpolation points are found by the collocation method, herewith the collocation points of collocationare the roots of the special function. An approximate formula for calculating contact stresses can have practical application. The effectiveness of the proposed method is demonstrated by the numerical example.
Pages of the article in the issue: 93 - 96
Language of the article: UkrainianРозглядається сингулярне інтегральне рівняння з нерухомою особливістю, до якого зводиться задача контактної взаємодії двох чвертей простору в умовах гармонічних коливань повздовжнього зсуву. Чверті простору розміщуються так, що складений з них півпростір має ступінчасту межу. Для чисельного розв’язання цього рівняння запропоновано метод, який враховує справжню асимптотику розв’язку, використовує спеціальні квадратурні формули для сингулярних інтегралів і корені спеціальної функції у якості точок колокації
Non-Abelian Vortices, Super-Yang-Mills Theory and Spin(7)-Instantons
We consider a complex vector bundle E endowed with a connection A over the
eight-dimensional manifold R^2 x G/H, where G/H = SU(3)/U(1)xU(1) is a
homogeneous space provided with a never integrable almost complex structure and
a family of SU(3)-structures. We establish an equivalence between G-invariant
solutions A of the Spin(7)-instanton equations on R^2 x G/H and general
solutions of non-Abelian coupled vortex equations on R^2. These vortices are
BPS solitons in a d=4 gauge theory obtained from N=1 supersymmetric Yang-Mills
theory in ten dimensions compactified on the coset space G/H with an
SU(3)-structure. The novelty of the obtained vortex equations lies in the fact
that Higgs fields, defining morphisms of vector bundles over R^2, are not
holomorphic in the generic case. Finally, we introduce BPS vortex equations in
N=4 super Yang-Mills theory and show that they have the same feature.Comment: 14 pages; v2: typos fixed, published versio
Effects of Sequence Disorder on DNA Looping and Cyclization
Effects of sequence disorder on looping and cyclization of the
double-stranded DNA are studied theoretically. Both random intrinsic curvature
and inhomogeneous bending rigidity are found to result in a remarkably wide
distribution of cyclization probabilities. For short DNA segments, the range of
the distribution reaches several orders of magnitude for even completely random
sequences. The ensemble averaged values of the cyclization probability are also
calculated, and the connection to the recent experiments is discussed.Comment: 8 pages, 4 figures, LaTeX; accepted to Physical Review E; v2: a
substantially revised version; v3: references added, conclusions expanded,
minor editorial corrections to the text; v4: a substantially revised and
expanded version (total number of pages doubled); v5: new Figure 4, captions
expanded, minor editorial improvements to the tex
Bounces/Dyons in the Plane Wave Matrix Model and SU(N) Yang-Mills Theory
We consider SU(N) Yang-Mills theory on the space R^1\times S^3 with Minkowski
signature (-+++). The condition of SO(4)-invariance imposed on gauge fields
yields a bosonic matrix model which is a consistent truncation of the plane
wave matrix model. For matrices parametrized by a scalar \phi, the Yang-Mills
equations are reduced to the equation of a particle moving in the double-well
potential. The classical solution is a bounce, i.e. a particle which begins at
the saddle point \phi=0 of the potential, bounces off the potential wall and
returns to \phi=0. The gauge field tensor components parametrized by \phi are
smooth and for finite time both electric and magnetic fields are nonvanishing.
The energy density of this non-Abelian dyon configuration does not depend on
coordinates of R^1\times S^3 and the total energy is proportional to the
inverse radius of S^3. We also describe similar bounce dyon solutions in SU(N)
Yang-Mills theory on the space R^1\times S^2 with signature (-++). Their energy
is proportional to the square of the inverse radius of S^2. From the viewpoint
of Yang-Mills theory on R^{1,1}\times S^2 these solutions describe non-Abelian
(dyonic) flux tubes extended along the x^3-axis.Comment: 11 pages; v2: one formula added, some coefficients correcte
Effect of hydrogen on the structure of quenched orthorhombic titanium aluminide-based alloy and phase transformations during subsequent heating
The effect of hydrogen on structure formation and changes in the volume fractions of phases in an alloy based on orthorhombic titanium aluminide (O phase) alloy upon its quenching is studied. X-ray diffraction analysis is used to determine the lattice parameters of phases. It has been shown that hydrogen is dissolved mainly in the β0 phase. Differential thermal analysis is used to determine stages and temperature ranges of phase transformations during heating; it was found that introduced hydrogen shifts the β0 → O and reverse O → β0 transformations into the low-temperature range; the enthalpies of transformation are calculated. © 2013 Pleiades Publishing, Ltd
On Explicit Point Multi-Monopoles in SU(2) Gauge Theory
It is well known that the Dirac monopole solution with the U(1) gauge group
embedded into the group SU(2) is equivalent to the SU(2) Wu-Yang point monopole
solution having no Dirac string singularity. We consider a multi-center
configuration of m Dirac monopoles and n anti-monopoles and its embedding into
SU(2) gauge theory. Using geometric methods, we construct an explicit solution
of the SU(2) Yang-Mills equations which generalizes the Wu-Yang solution to the
case of m monopoles and n anti-monopoles located at arbitrary points in R^3.Comment: 1+7 pages, LaTe
Progress on the journey to put field electron emission onto a better scientific basis
This paper forms part of a long-term project to put field electron emission
(FE) onto a better scientific basis, by seeking reliable quantitative agreement
between theory and experiment, especially as regards emission-current values.
The main paper aims are: (1) to respond to remarks made in recent papers; (2)
to restate the thinking behind our 2022 methodology for choosing between
different FE models using experiments; (3) to assess progress; and (4) to make
further suggestions about improved approaches.Comment: 3 pages, 6 tables, 1 figure. Conference paper for IVNC2023 in Boston,
Mass., July 2023. To be published electronically by IEEE Explor
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