We propose a new analytic approach to study the phase diagram of random heteropolymers, based on the cavity method. For copolymers we analyze the nature and phenomenology of the glass transition as a function of sequence correlations. Depending on these correlations, we find that two different scenarios for the glass transition can occur. We show that, beside the much studied possibility of an ...

We thoroughly investigate a simple model representative of the recently synthesized Janus particles, i.e., colloidal spherical particles whose surface is divided into two areas of different chemical composition. When the two surfaces are solvophilic and solvophobic, these particles constitute the simplest example of surfactants. The phase diagram includes a colloidal-poor (gas), colloidal-rich ...

Advancements in the synthesis of faceted nanoparticles and colloids have spurred interest in the phase behavior of polyhedral shapes. Regular tetrahedra have attracted particular attention because they prefer local symmetries that are incompatible with periodicity. Two dense phases of regular tetrahedra have been reported recently. The densest known tetrahedron packing is achieved in a crystal ...

We summarize our recent results on the phase diagram of QCD with N f = 2+1 quark flavors, as a function of temperature T and quark chemical potential μ . Using staggered fermions, lattices with temporal extent Nt = 4, and the exact RHMC algorithm, we first determine the critical line in the quark mass plane (mu,d ,ms) where the finite temperature transition at μ = 0 is second order. We confirm ...

In recent years, it has become increasingly important to incorporate explicit dynamics in economic analysis. These two tools that mathematicians have developed, differential equations and optimal control theory, are probably the most basic for economists to analyze dynamic problems. In this paper I will consider the linear differential equations on the plane (phase diagram) and elements of nonl...

Onsager crosses are hard nonconvex bodies formed by rigidly connecting three elongated rods, equally thick but not necessarily equally long, to form perpendicular crosses. We study the phase behavior of systems of such particles, focusing on their ability to form spatially homogeneous orientationally ordered phases with a symmetry lower than that of the standard uniaxial nematic. We treat these...

The aim of this review is to summarize the contemporary understanding of the QCD phase diagram as a function of temperature T and baryo-chemical potential µ B. The focus is on recent theoretical developments due to lattice simulations of the phase diagram.

I use simple thermodynamic reasoning to argue that at temperatures of order a trillion kelvin, QCD, the theory which describes strongly interacting particles such as protons and neutrons under normal conditions, undergoes a phase transition to a plasma of more elementary constituents called quarks and gluons. I review what is known about the plasma phase both from theoretical calculations and f...