Two flavor Nambu-Jona-Lasinio model with N components is studied in curved space time at finite temperature and density in the leading 1/N expansion. In four space time dimension the model exhibits first order phase transition for positive curvature. Whereas in flat space an increase in temperature induces a second order phase transition even at finite density, in curved space the transition be...

We study the low-temperature regime of an atomic liquid on the hyperbolic plane by means of molecular dynamics simulation and we compare the results to a continuum theory of defects in a negatively curved hexagonal background. In agreement with the theory and previous results on positively curved (spherical) surfaces, we find that the atomic configurations consist of isolated defect structures,...

Motivated by interval matrix multiplication we consider (matrix) polytopes A ⊆ R, B ⊆ R, m,n, k ∈ N, and investigate the boundary shape of their pointwise product AB := {AB | A ∈ A, B ∈ B}. We prove that AB cannot have outward curved boundary sections while inward curved sections may exist. This is achieved by a simple local extreme point analysis. Results are proved in a more general abstract ...

In this paper, a plane quadrilateral element with rotational degrees of freedom is developed. Present formulation is based on a hybrid functional with independent boundary displacement and internal optimum strain field. All the optimality constraints, including being rotational invariant, omitting the parasitic shear error and satisfying Fliepa’s pure bending test, are considered. Moreover, the...

In this work we show, that the Lattice Boltzmann method is capable of calculating the drag force on spheres with a sufficient accuracy. The main interest lies on laminar flows around nano particle agglomerates. To give an overview over the simulated force accuracy the results are compared with analytical solutions. Thereby the benefit from curved boundary treatments such as [YD03] and [PL03] is...

We investigate microphase separation patterns on curved surfaces in three-dimensional space by numerically solving a nonlocal Cahn-Hilliard equation for diblock copolymers. In our model, a curved surface is implicitly represented as the zero level set of a signed distance function. We employ a discrete narrow band grid that neighbors the curved surface. Using the closest point method, we apply ...

The problem of determining visibility locations (VLs) on/inside a domain bounded by a planar C1-continuous curve (without vertices), such that entire domain is covered, is discussed in this paper. The curved boundary has been used without being approximated into lines or polygons. Initially, a few observations regarding the VLs for a curved boundary have been made. It is proposed that the set o...

We develop a formalism to calculate the effective action of the strongly coupled conformal field theory (CFT) in curved spacetime. The effective action of the CFT is obtained from AdS/CFT correspondence. The anti de-Sitter (AdS) spacetime has various slicing which give various curved spacetime on its boundary. We show the de Sitter spacetime and the Friedmann-Robertson-Walker (FRW) universe can...

Imperfection sensitivity of large amplitude vibration of curved single-walled carbon nanotubes (SWCNTs) is considered in this study. The SWCNT is modeled as a Timoshenko nano-beam and its curved shape is included as an initial geometric imperfection term in the displacement field. Geometric nonlinearities of von Kármán type and nonlocal elasticity theory of Eringen are employed to derive govern...

The lower bank of the superior temporal sulcus (TEs), part of the inferior temporal cortex, contains neurons selective for disparity-defined three-dimensional (3-D) shape. The large majority of these TEs neurons respond to the spatial variation of disparity, i.e., are higher-order disparity selective. To determine whether curved boundaries or curved surfaces by themselves are sufficient to elic...