D3+D6 solution and D4+D6 solution

We make the supergravity solutions describing the branes (D3 branes and D4 branes) localized within the D6 branes in the near core region of D6 brane. From the D=11 solutions (M3 branes and M4 branes with the Z_N identifications in the transverse space) we obtain the D=10 supergravity solutions of D3 branes localized within D6 branes and D4 branes localized within D6 branes by reducing the dimension down to D=10 along a circular direction of S³ part of the transverse space. M3 brane solution leads to D=10 background representing D3 branes localized on D6 branes in the region close to the D6 branes core. M4 branes lead to the D4 branes localized on D6 branes in the region close to the D6 brane core.     

A Class of Kaluza-Klein Solutions Curved in 4D and Flat in 5D

We give a broad class of solutions of the Kaluza-Klein equations that is static, spherically symmetric in 3D, curved in 4D and flat in 5D. These solutions generalize others that have been applied in cosmology and astrophysics.     

The method of fundamental solutions for 2D and 3D Stokes problems

A numerical scheme based on the method of fundamental solutions (MFS) is proposed for the solution of 2D and 3D Stokes equations. The fundamental solutions of the Stokes equations, Stokeslets, are adopted as the sources to obtain flow field solutions. The present method is validated through other numerical schemes for lid-driven flows in a square cavity and a cubic cavity. Test results obtained for a rectangular cavity with wave-shaped bottom indicate that the MFS is computationally efficient than the finite element method (FEM) in dealing with irregular shaped domain. The paper also discusses the effects of number of source points and their locations on the numerical accuracy.     

Global regularity of the 4D restricted Euler equations

We are concerned with the critical threshold phenomena in the restricted Euler (RE) equations. Using the spectral and trace dynamics we identify the critical thresholds for the 3D and 4D restricted Euler equations. It is well known that the 3D RE solutions blow up. Projected on the 3-sphere, the set of initial eigenvalues which give rise to bounded stable solutions is reduced to a single point, which confirms that the 3D RE blowup is generic. In contrast, we identify a surprisingly rich set of the initial spectrum on the 4-sphere which yields global smooth solutions; thus, 4D regularity is generic.     

Abundant solutions of Wick-type stochastic fractional 2D KdV equations

A modified fractional sub-equation method is applied to Wick-type stochastic fractional two-dimensional （2D） KdV equations. With the help of a Hermit transform, we obtain a new set of exact stochastic solutions to Wick-type stochastic fractional 2D KdV equations in the white noise space. These solutions include exponential decay wave solutions, soliton wave solutions, and periodic wave solutions. Two examples are explicitly given to illustrate our approach.     

Absorption and quasinormal modes of classical fields propagating on 3D and 4D de Sitter spacetime

We extensively study the exact solutions of the massless Dirac equation in 3D de Sitter spacetime that we published recently. Using the Newman-Penrose formalism, we find exact solutions of the equations of motion for the massless classical fields of spin s= 12,1,2 and to the massive Dirac equation in 4D de Sitter metric. Employing these solutions, we analyze the absorption by the cosmological horizon and de Sitter quasinormal modes. We also comment on the results given by other authors.     

Exact solutions in 3D new massive gravity

We show that the field equations of new massive gravity (NMG) consist of a massive (tensorial) Klein-Gordon-type equation with a curvature-squared source term and a constraint equation. We also show that, for algebraic type D and N spacetimes, the field equations of topologically massive gravity (TMG) can be thought of as the "square root" of the massive Klein-Gordon-type equation. Using this fact, we establish a simple framework for mapping all types D and N solutions of TMG into NMG. Finally, we present new examples of types D and N solutions to NMG.     

Structural elements and collapse regimes in 3D flows on a slope

The mechanisms and structural elements of an instability whose development results in the collapse of flow fragments have been studied in the scope of the Hamilton version of the “shallow water” 3D model on a slope. The study indicated that the 3D model differs from its 2D analog in a more varied set of collapsing solutions. In particular, the solutions describing anisotropic collapse, during which the area of a collapsing fragment in contact with the slope contracts into a segment rather than a point, exist together with the solutions describing radially symmetric (isotropic) collapse.     

Global stability of large solutions to the 3D Navier-Stokes equations

We prove the stability of mildly decaying global strong solutions to the Navier-Stokes equations in three space dimensions. Combined with previous results on the global existence of large solutions with various symmetries, this gives the first global existence theorem for large solutions with approximately symmetric initial data. The stability of unforced 2D flow under 3D perturbations is also obtained.     

Dispersive estimates for the 2D wave equation

We obtain a dispersive long-time decay with respect to weighted energy norms for solutions of the 2D wave equation with generic potential. The decay extends results obtained by Murata for the 2D Schrödinger equation.     

Structure and Properties of Self-Organized 2D and 3D Antimony/Carbon Composites

The conditions of synthesis of antimony/carbon composites by interlayer self-assembly from colloidal solutions and melts are discussed. The morphology and the structure of these composites are examined. The potential to produce composites of 2D and 3D morphologies is demonstrated. The 2D composite has a multilayer graphene structure with submicron antimony inclusions, while the 3D composite has a spheroidal shell structure with a deformed film-shell with carbon nanoinclusions. The difference in properties of these composites is demonstrated: the 2D composite is conductive, while the 3D composite has a nonlinear current–voltage characteristic that indicates the emergence of novel functional properties of the spheroidal antimony/carbon composite. A model of exfoliation of the layered precursor with covalent interlayer coupling is proposed. This model provides an explanation for the experimentally observed nonlinear hydrodynamic processes in the colloidal antimony solution.     

S-duality in 3D gravity with torsion

The deformation of the connection in three spacetime dimensions by the kinematically equivalent coframe is shown to induce a duality between the (Lorentz-) rotational and translational field momenta, for which the coupling to the deformation parameter is inverted. This new kind of strong/weak duality, pertinent to 3D, is instrumental for studying exact solutions of the 3D Poincaré gauge field equations and the particle content of propagating modes on a background of constant curvature. For a topological Chern-Simons model of gravity, the propagating modes ‘living’ on an Anti-de Sitter (AdS) background correspond to real massive particles. Yang-Mills type generalizations and new cubic Lagrangians are found and completely classified in 3D. AdS or black hole type solutions with constant axial torsion emerge, also for these higher-order Lagrangians with new ‘exotic’ torsion-curvature couplings. Their pattern complies with our S-duality, with new repercussions for the field redefinition of the metric in 3D quantum gravity and the cosmological constant problem.     

New Types of Solutions for the Classic 3D SU (2) Yang–Mills Equations

Doklady Physics - New types of 3D solutions for the classic Yang–Mills equations in the Faddeev–Niemi reformulation are found. In a particular case, these solutions describe 3D vortices.     

A new class of nodal stationary states in a 2D Heisenberg Ferromagnet

A new class of nodal topological excitations in a 2D Heisenberg model is studied. The solutions correspond to a nodal singular point of the gradient field of the azimuthal angle. An analytical solution is found for the isotropic case. The effect of in-plane exchange anisotropy is studied numerically. This results in solutions which are analogues of the conventional out-of-plane solitons in 2D magnets.     

Anisotropic solutions in the 5D space-time-mass theory

In this paper we present anisotropic families of cosmological solutions in the 5-dimensional space-time-mass theory of gravity. In particular, the 5D analogue of the Kasner solution of General Relativity is obtained. Some comments are given on the solutions.     

Rainich theory for type D aligned Einstein–Maxwell solutions

The original Rainich theory for the non-null Einstein–Maxwell solutions consists of a set of algebraic conditions and the Rainich (differential) equation. We show here that the subclass of type D aligned solutions can be characterized just by algebraic restrictions.     

Brane gravitational interactions from 6D supergravity

We investigate the massive graviton contributions to 4D gravity in a 6D brane world scenario, whose bulk field content can include that of 6D chiral gauged supergravity. We consider a general class of solutions having 3-branes, 4D Poincaré symmetry and axisymmetry in the internal space. We show that these contributions, which we compute analytically, can be independent of the brane vacuum energy as a consequence of geometrical and topological properties of the above-mentioned codimension two brane world. These results support the idea that in such models the gravitational interactions may be decoupled from the brane vacuum energy.