Related papers: Optimization of the branching pattern in coherent …
We study the phase diagram of a class of models in which a generalized cluster interaction can be quenched by Ising exchange interaction and external magnetic field. We characterize the various phases through winding numbers. They may be…
We explore the possibilities and limitations of using a coherent second phase to engineer the thermo-mechanical properties of a martensitic alloy by modifying the underlying free energy landscape that controls the transformation. We use…
A mathematical framework is proposed to predict the features of the (5 5 7) lath transformation in low-carbon steels based on energy minimisation. This theory generates a one-parameter family of possible habit planes and a selection…
According to Richardson's cascade description of turbulence, large vortices break up to form smaller ones, thereby transferring kinetic energy towards smaller scales. Energy dissipation occurs at the smallest scales due to viscosity. We…
In this paper, we study the form over the minimum spanning tree problem (MST) from which we will derive an intuitively generalized model and new methods with the upper bound of runtimes of logarithm. The new pattern we made has taken…
We use protein folding energy landscape concepts such as golf-course and funnel to study re-equilibration in athermal martensite parameter regime of triangle-to-centered rectangle, square-to-oblique, and triangle-to-oblique transitions…
Computer simulations of coarse-grained molecular models for amphiphilic systems can provide insight into the the structure of amphiphiles at interfaces. They can help to identify the factors that determine the phase behavior, and they can…
To study martensitic phase transformation we use a micromechanical model based on statistical mechanics. Employing lattice Monte-Carlo simulations and realistic material properties for shape-memory alloys (SMA), we investigate the combined…
This paper investigates the conditions necessary for the elimination of transition layers at interfaces involving compound domains, extending the classical framework of cofactor conditions. Although cofactor conditions enable stress-free…
The topological transitions that occur to the grain boundary network during grain growth in a material with uniform grain boundary energies are believed to be known. The same is not true for more realistic materials, since more general…
Progresses in additive manufacturing technologies allow the realization of finely graded microstructured materials with tunable mechanical properties. This paves the way to a wealth of innovative applications, calling for the combined…
The organization of interactions in complex systems can be described by networks connecting different units. These graphs are useful representations of the local and global complexity of the underlying systems. The origin of their…
{}From a finite-size scaling (FSS) theory of cumulants of the order parameter at phase coexistence points, we reconstruct the scaling of the moments. Assuming that the cumulants allow a reconstruction of the free energy density no better…
Ultrametric structure of the energy cascade process in a dynamical model of turbulence is studied. The tree model we use can be viewed as an approximated one-dimensional truncation of the wavelets resolved Navier-Stokes dynamics. Varying…
Atomically thin 2-dimensional heterostructures are a promising, novel class of materials with groundbreaking properties. The possiblity of choosing the many constituent components and their proportions allows optimizing these materials to…
We derive a model for the optimization of the bending and torsional rigidities of non-homogeneous elastic rods. This is achieved by studying a sharp interface shape optimization problem with perimeter penalization, that treats both…
Inertial fluid flow deformation around pillars in a microchannel is a new method for controlling fluid flow. Sequences of pillars have been shown to produce a rich phase space with a wide variety of flow transformations. Previous work has…
Branching architecture characterizes numerous systems, ranging from synthetic (hyper)branched polymers and biomolecules such as lignin, amylopectin, and nucleic acids to tracheal and neuronal networks. Its ubiquity reflects the many…
We extend the phase field crystal method for nonequilibrium patterning to stochastic systems with external source where transient dynamics is essential. It was shown that at short time scales the system manifests pattern selection…
We study pattern formation within the $J_1$-$J_3$ - spin model on a two-dimensional square lattice in the case of incompatible (ferromagnetic) boundary conditions on the spin field. We derive the discrete-to-continuum $\Gamma$-limit at the…