This paper is concerned with the geometrical shape, wetting length, and contact angle of a microdroplet on a fiber by using the method free energy variation. The governing equation and relevant boundary conditions of the microdroplet were re-derived based on the free energy variation of the droplet/fiber system. The geometrical shape of the droplet was determined as the combination of Legendre’...

We study the free energy of the Parabolic Anderson Model, a time-continuous model of directed polymers in random environment. We prove that in dimension 1 and 2, the free energy is always negative, meaning that very strong disorder always holds. The result for discrete polymers in dimension two, as well as better bounds on the free energy on dimension 1, were first obtained by Hubert Lacoin in ...

We present a parameterized analytical model of alchemical molecular binding. The model describes accurately the free energy profiles of linear single-decoupling alchemical binding free energy calculations. The parameters of the model, which are physically motivated, are obtained by fitting model predictions to numerical simulations. The validity of the model has been assessed on a set of host-g...

We provide a perspective on polymer glass formation, with an emphasis models in which the fluid entropy and collective particle motion dominate theoretical description data analysis. The theory of formation has its origins experimental observations relating to correlations between liquid dynamics going back nearly century ago, it entered new phase recent years. first discuss liquids high-temper...

We introduce a new number–theoretic spin chain and explore its thermodynamics and connections with number theory. The energy of each spin configuration is defined in a translation–invariant manner in terms of the Farey fractions, and is also expressed using Pauli matrices. We prove that the free energy exists and exhibits a unique phase transition at inverse temperature β = 2. The free energy i...

The loop equations for a chain of hermitian random matrices are computed explicitely, including the 1/N2 corrections. To leading order, the master loop equation reduces to an algebraic equation, whose solution can be written in terms of geometric properties of the underlying algebraic curve. In particular we compute the free energy, the resolvents, the 2-loop functions and some mixed one loop f...

A direct calculation of the free energy from the Bethe ansatz equation for the Heisenberg model. Abstract Thermodynamics of the XXX Heisenberg model is studied. The trace of the Boltz-mann weight with respect to the Hilbert space is taken in the thermodynamic limit with the number of up-spins being fixed. The expression of the trace gives an explanation why the correct thermodynamic quantities ...

The strong coupling behavior of finite temperature free energy in N = 4 supersym-metric SU (N) Yang-Mills theory has been recently discussed by Gubser, Klebanov and Tseytlin in the context of AdS-SYM correspondence. In this note, we focus on the weak coupling behavior. As a result of a two-loop computation we obtain, in the large N 't Hooft limit, F (g 2 N → 0) ≈ − π 2 6 N 2 V 3 T 4 (1 − 3 2π 2...

A novel representation —in terms of a Laurent series— for the free energy of string theory at non-zero temperature is constructed. The examples of open bosonic, open supersymmetric and closed bosonic strings are studied in detail. In all these cases the Laurent series representation for the free energy is obtained explicitly. It is shown that the Hagedorn temperature arises in this formalism as...