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Many statistical models are algebraic in that they are defined by polynomial constraints or by parameterizations that are polynomial or rational maps. This opens the door for tools from computational algebraic geometry. These tools can be…
A graph drawing in the plane is called an almost embedding if the images of any two non-adjacent simplices (i.e. vertices or edges) are disjoint. Almost embeddings (more precisely, their higher-dimensional analogues) naturally appear in…
Particle azimuthal anisotropies inside jets, defined within the momentum plane perpendicular to the jet axis, carry the information of the QCD cascade process for jet formation. In this work, we propose to measure the medium-induced…
We compute the thermodynamic properties of the glass phase in a binary mixture of soft spheres. Our approach is a generalization to mixtures of the replica strategy, recently proposed by Mezard and Parisi, providing a first principle…
We fully generalize a previously-developed computational geometry tool [1] to perform large-scale simulations of arbitrary two-dimensional faceted surfaces $z = h(x,y)$. Our method uses a three-component facet/edge/junction storage model,…
Single particle models are sufficient for many topics in introductory physics courses, but become misleading when applied to situations involving changes in internal energy. This paper merges two parallel attempts to reform the teaching of…
In this paper, we extend the method developed in [17, 18] to curves in the Minkowski plane. The method proposes a way to study deformations of plane curves taking into consideration their geometry as well as their singularities. We deal in…
We provide a geometric perspective on the kinetic interaction of matter and radiation, based on a pair bracket approach. We discuss the interaction of kinetic theories via dissipative brackets, with our fundamental example being the…
When electrons flow as a viscous fluid in anisotropic metals, the reduced symmetry can lead to exotic viscosity tensors with many additional, nonstandard components. We present a viscometry technique that can, in principle, measure the…
We study the interaction of two scattering channels for a simple geometric model consisting in a double covering of the plane with two branch points, equipped with the Euclidean metric. We show that the scattering channels are open in the…
The notion of geometric construction is introduced. This notion allows to compare incidence configurations in the algebraic and tropical plane. We provide an algorithm such that, given a tropical instance of a geometric construction, it…
A simplified polycrystalline model (the so-called RL model) is proposed to simulate the anisotropic viscoplastic behavior of metallic materials. A generic method is presented that makes it possible to build a simplified anisotropic material…
In this work, we study the two-particle correlations regarding a peripheral tube model. From our perspective, the main characteristics of the observed two-particle correlations are attributed to the multiplicity fluctuations and the locally…
In two nearby atoms, the dipole-dipole interaction can couple transitions with orthogonal dipole moments. This orthogonal coupling accounts for a number of interesting effects, but strongly depends on the geometry of the setup. Here, we…
Azimuthal anisotropies in heavy-ion collisions are conventionally interpreted as signatures of hydrodynamic flow. We demonstrate that in peripheral collisions, a significant $\cos 2\phi$ asymmetry in the decay leptons of coherently…
We show how the Eulcidean algorithm for polynomials can be used to find the intersection points, with multiplicities, of two plane algebraic curves.
In this paper we present a generalization of a simple solid-on-solid epitaxial model of thin films growth, when surface morphology anisotropy is provoked by anisotropy in model control parameters: binding energy and/or diffusion barrier.…
In the rapidly emerging field of nanotechnology, as well as in biology where chemical reaction phenomena take place in systems with characteristic length scales ranging from micrometer to the nanometer range, understanding of chemical…
In this article, we briefly describe various tools and approaches that algebraic geometry has to offer to straighten bent objects. Throughout this article we will consider a specific example of a bent or curved piece of paper which in our…
In this paper a new theory is developed for the self - assembly of associating molecules confined to a single spatial dimension, but allowed to explore all orientation angles. The interplay of the anisotropy of the pair potential and the…