scholarly journals DOMAIN WALL SOLUTION OF THE SKYRME MODEL

2006 ◽  
Vol 21 (28n29) ◽  
pp. 5845-5859
Author(s):  
CHANG-GUANG SHI ◽  
MINORU HIRAYAMA
Keyword(s):  
Energy Density ◽  
Domain Wall ◽  
Skyrme Model ◽  
The Other ◽  
Hyperbolic Function ◽  
Weierstrass Function ◽  
Domain Wall Solution ◽  
Special Limit ◽  
Static Energy

A class of domain-wall-like solutions of the Skyrme model is obtained analytically. They are described by the tangent hyperbolic function, which is a special limit of the Weierstrass ℘ function. The behavior of one of the two terms in the static energy density is like that of a domain wall. The other term in the static energy density does not vanish but becomes constant at the points far apart from the wall.

scholarly journals On the Definition of Energy Flux in One-Dimensional Chains of Particles

Entropy ◽  
2019 ◽  
Vol 21 (11) ◽  
pp. 1036
Author(s):  
Paolo De Gregorio
Keyword(s):  
Energy Density ◽  
Integral Operator ◽  
Energy Flux ◽  
Ad Hoc ◽  
The Other ◽  
Energy Density Distribution ◽  
One Dimensional ◽  
Integral Quantity ◽  
Definition Of ◽  
Local Quantity

We review two well-known definitions present in the literature, which are used to define the heat or energy flux in one dimensional chains. One definition equates the energy variation per particle to a discretized flux difference, which we here show it also corresponds to the flux of energy in the zero wavenumber limit in Fourier space, concurrently providing a general formula valid for all wavelengths. The other relies somewhat elaborately on a definition of the flux, which is a function of every coordinate in the line. We try to shed further light on their significance by introducing a novel integral operator, acting over movable boundaries represented by the neighboring particles’ positions, or some combinations thereof. By specializing to the case of chains with the particles’ order conserved, we show that the first definition corresponds to applying the differential continuity-equation operator after the application of the integral operator. Conversely, the second definition corresponds to applying the introduced integral operator to the energy flux. It is, therefore, an integral quantity and not a local quantity. More worryingly, it does not satisfy in any obvious way an equation of continuity. We show that in stationary states, the first definition is resilient to several formally legitimate modifications of the (models of) energy density distribution, while the second is not. On the other hand, it seems peculiar that this integral definition appears to capture a transport contribution, which may be called of convective nature, which is altogether missed by the former definition. In an attempt to connect the dots, we propose that the locally integrated flux divided by the inter-particle distance is a good measure of the energy flux. We show that the proposition can be explicitly constructed analytically by an ad hoc modification of the chosen model for the energy density.

scholarly journals STATIC CYLINDRICALLY SYMMETRIC INTERIOR SOLUTIONS IN f(R) GRAVITY

2012 ◽  
Vol 27 (25) ◽  
pp. 1250138 ◽  
Author(s):  
M. SHARIF ◽  
SADIA ARIF
Keyword(s):  
Energy Density ◽  
Exact Solutions ◽  
Perfect Fluid ◽  
Functional Form ◽  
Ricci Scalar ◽  
The Other ◽  
New Exact Solutions ◽  
Cylindrically Symmetric ◽  
Theory Of Gravity ◽  
Interior Solutions

We investigate some exact static cylindrically symmetric solutions for a perfect fluid in the metric f(R) theory of gravity. For this purpose, three different families of solutions are explored. We evaluate energy density, pressure, Ricci scalar and functional form of f(R). It is interesting to mention here that two new exact solutions are found from the last approach, one is in particular form and the other is in the general form. The general form gives a complete description of a cylindrical star in f(R) gravity.

ON A MINIMIZING PROPERTY OF THE HOPF SOLITON IN THE FADDEEV–SKYRME MODEL

2008 ◽  
Vol 20 (07) ◽  
pp. 765-786
Author(s):  
TAKESHI ISOBE
Keyword(s):  
Skyrme Model ◽  
The Other

We study local minimizing solutions for the Faddeev–Skyrme problem on the 3-sphere with radius R. We show that for [Formula: see text] the Hopf soliton is a local minimizing solution and all the other local minimizing solutions near the Hopf soliton are obtained as the composition of isometries of S3 with the Hopf soliton.

COMPOSITE SPHALERONS IN THE O(3) NONLINEAR σ-MODEL

1991 ◽  
Vol 06 (26) ◽  
pp. 2371-2377
Author(s):  
T. HUANG ◽  
X. ZHANG
Keyword(s):  
Energy Density ◽  
Static Energy

It is shown that there are a series of composite solutions in the O(3) nonlinear σ-model. Their static energy is given by E(n)=nEsph and the energy density spreads out as n increases.

scholarly journals Domain Walls from M-Branes

1997 ◽  
Vol 12 (15) ◽  
pp. 1087-1094 ◽  
Author(s):  
H. Lü ◽  
C. N. Pope
Keyword(s):  
Domain Wall ◽  
Dimensional Reduction ◽  
Domain Walls ◽  
Additional Term ◽  
Cosmological Term ◽  
Domain Wall Solution ◽  
Toroidal Compactifications ◽  
Four Manifolds ◽  
M Theory ◽  
Kaluza Klein

We discuss the vertical dimensional reduction of M-sbranes to domain walls in D=7 and D=4, by dimensional reduction on Ricci-flat four-manifolds and seven-manifolds. In order to interpret the vertically-reduced five-brane as a domain wall solution of a dimensionally-reduced theory in D=7, it is necessary to generalize the usual Kaluza–Klein ansatz, so that the three-form potential in D=11 has an additional term that can generate the necessary cosmological term in D=7. We show how this can be done for general four-manifolds, extending previous results for toroidal compactifications. By contrast, no generalization of the Kaluza–Klein ansatz is necessary for the compactification of M-theory to a D=4 theory that admits the domain-wall solution coming from the membrane in D=11.

A stealth defect of spacetime

2018 ◽  
Vol 33 (22) ◽  
pp. 1850127 ◽  
Author(s):  
F. R. Klinkhamer ◽  
J. M. Queiruga
Keyword(s):  
Energy Density ◽  
Long Range ◽  
Mass Term ◽  
Matter Field ◽  
Skyrme Model ◽  
Gravitational Mass ◽  
Positive Energy ◽  
Type Solution ◽  
Matter Fields

We discuss a special type of Skyrmion spacetime-defect solution, which has a positive energy density of the matter fields but a vanishing asymptotic gravitational mass. With a mass term for the matter field added to the action (corresponding to massive “pions” in the Skyrme model), this particular soliton-type solution has no long-range fields and can appropriately be called a “stealth defect”.

scholarly journals Valley-polarized domain wall magnons in 2D ferromagnetic bilayers

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Doried Ghader
Keyword(s):  
Domain Wall ◽  
Domain Walls ◽  
Ballistic Transport ◽  
The Other ◽  
Polarized Electrons ◽  
Technological Field ◽  
Electrostatic Doping ◽  
Layer Stacking ◽  
Theoretical Results ◽  
Moriya Interaction

Abstract Valleytronics is a pioneering technological field relying on the valley degree of freedom to achieve novel electronic functionalities. Topological valley-polarized electrons confined to domain walls in bilayer graphene were extensively studied in view of their potentials in valleytronics. Here, we study the magnonic version of domain wall excitations in 2D honeycomb ferromagnetic bilayers (FBL) with collinear order. In particular, we explore the implications of Dzyaloshinskii-Moriya interaction (DMI) and electrostatic doping (ED) on the existence and characteristics of 1D magnons confined to layer stacking domain walls in FBL. The coexistence of DMI and ED is found to enrich the topology in FBL, yet the corresponding domain wall magnons do not carry a well-defined valley index. On the other hand, we show that layer stacking domain walls in DMI-free FBL constitute 1D channels for ballistic transport of topological valley-polarized magnons. Our theoretical results raise hope towards magnon valleytronic devices based on atomically thin topological magnetic materials.

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