Related papers: Conformal Mapping on Rough Boundaries II: Applicat…
The effect of bias voltages on the statistical properties of rough surfaces has been studied using atomic force microscopy technique and its stochastic analysis. We have characterized the complexity of the height fluctuation of a rough…
We decrease the $rms$ mean curvature and area of a variable surface with a fixed boundary by iterating a few times through a curvature-based variational algorithm. For a boundary with a known minimal surface, starting with a deliberately…
In this paper we provide an estimate from above for the value of the relaxed area functional for a map defined on a bounded domain of the plane with values in the plane and discontinuous on a regular simple curve with two endpoints. We show…
This paper presents a density-based topology optimization approach to design structures under self-weight load. Such loads change their magnitude and/or location as the topology optimization advances and pose several unique challenges,…
Equilibrium crystal surfaces, constrained to equilibrate by means of dissociative dimer deposition and evaporation, have anomalous global surface roughness. We generalize earlier results for one dimensional interfaces to two dimensions. The…
The conjugate function method is an algorithm for numerical computation of conformal mappings for simply and multiply connected domains on surfaces. In this paper the conjugate function method, earlier used for simply connected domains, is…
A new Hardy space Hardy space approach of Dirichlet type problem based on Tikhonov regularization and Reproducing Hilbert kernel space is discussed in this paper, which turns out to be a typical extremal problem located on the upper…
We study Euclidean Wilson loops at strong coupling using the AdS/CFT correspondence, where the problem is mapped to finding the area of minimal surfaces in Hyperbolic space. We use a formalism introduced recently by Kruczenski to…
In this note we complete the analysis carried on in \cite{CGSV} about the topological synchronisation of unimodal maps of the interval coupled in a master-slave configuration, by answering to the questions raised in that paper. Namely, we…
The optimization of porous infill structures via local volume constraints has become a popular approach in topology optimization. In some design settings, however, the iterative optimization process converges only slowly, or not at all even…
We apply analytical and numerical methods to study the linear stability of stripe patterns in two generalizations of the two-dimensional Swift-Hohenberg equation that include coupling to a mean flow. A projection operator is included in our…
In boundary conformal field theories, global symmetries can be broken by boundary conditions, generating a homogeneous conformal manifold. We investigate these geometries, showing they have a coset structure, and give fully worked out…
We relate the existence problem of harmonic maps into $S^2$ to the convex geometry of $S^2$. On one hand, this allows us to construct new examples of harmonic maps of degree 0 from compact surfaces of arbitrary genus into $S^2$. On the…
Turbulent flows above a solid surface are characterised by a hydrodynamic roughness that represents, for the far velocity field, the typical length scale at which momentum mixing occurs close to the surface. Here, we are theoretically…
The influence of surface roughness on transition to turbulence in a Mach 4.5 boundary layer is studied using direct numerical simulations. Transition is initiated by the nonlinearly most dangerous inflow disturbance, which causes the…
When semi-infinite phononic crystals (PCs) are in contact, localized modes may exist at their boundary. The central question is generally to predict their existence and to determine their stability. With the rapid expansion of the field of…
This paper investigates the geometric consequences of equality in area-charge inequalities for spherical minimal surfaces and, more generally, for marginally outer trapped surfaces (MOTS), within the framework of the Einstein-Maxwell…
We study a class of fourth-order geometric problems modelling Willmore surfaces, conformally constrained Willmore surfaces, isoperimetrically constrained Willmore surfaces, bi-harmonic surfaces in the sense of Chen, among others. We prove…
A common problem in the optimization of structures is the handling of uncertainties in the parameters. If the parameters appear in the constraints, the uncertainties can lead to an infinite number of constraints. Usually the constraints…
In this paper we describe a 1-dimensional variational approach to the analytical construction of equivariant biharmonic maps. Our goal is to provide a direct method which enables analysts to compute directly the analytical conditions which…