We solve the linearized Poisson-Boltzmann equation analytically, subject to justifiable approximations, for a suspension containing a large number of identical spherical macroions under conditions of constant surface charge and zero added salt, in order to investigate the phase behavior of charge-stabilized colloidal suspensions. Our results for the electrostatic part of the Helmholtz free ener...

We study the effective potential of three-dimensional O(N) models. In statistical physics the effective potential represents the free-energy density as a function of the order parameter (Helmholtz free energy), and, therefore, it is related to the equation of state. In particular, we consider its small-field expansion in the symmetric (high-temperature) phase, whose coefficients are related to ...

In Table S1, the computational estimates are obtained as follows. The reactant and product molecular configurations are first relaxed separately at the PBE+vdW level of theory [1], using the all-electron program package FHI-aims [2]. We used tight settings for the numeric atom centered orbitals basis sets and integration grids, as explained in Ref. [2]. Following relaxation, the complex geometr...

We show that new families of diffraction-free nonparaxial accelerating optical beams can be generated by considering the symmetries of the underlying vectorial Helmholtz equation. Both two-dimensional transverse electric and magnetic accelerating wave fronts are possible, capable of moving along elliptic trajectories. Experimental results corroborate these predictions when these waves are launc...

The free vibration analysis ofhomogeneous isotropic micropolar thermoelastic cylindrical curved plate in circumferential direction has been investigated in the context of generalized themoelasticity III, recently developed by Green and Naghdi. The model has been simplified using Helmholtz decomposition technique and the resulting equations have been solved using separation of variable method. M...

We reformulate the Bekenstein bound as the requirement of positivity of the Helmholtz free energy at the minimum value of the function L = E−S/(2πR), where R is some measure of the size of the system. The minimum of L occurs at the temperature T = 1/(2πR). In the case of n-dimensional anti-de Sitter spacetime, the rather poorly defined size R acquires a precise definition in terms of the AdS ra...

Starting from Newton's equations of motion, we derive a dynamical density functional theory (DDFT) applicable to atomic liquids. The theory has the feature that it requires as input the Helmholtz free energy functional from equilibrium density functional theory. This means that, given a reliable equilibrium free energy functional, the correct equilibrium fluid density profile is guaranteed. We ...

Wavelength plays a distinguished role in classical electromagnetic and acoustic scattering. Most significant features of the far field patterns radiated by a collection of sources or scatterers are related to their sizes and relative distances, measured in wavelengths. These significant features are reflected in the invariance of the Helmholtz equation with respect to translation, and its homog...

The simplest parabolic equation of normal type with periodic boundary condition is considered, and the problem of stabilization to zero of its solution with arbitrary initial condition by starting control supported in a prescribed subset is investigated. This problem is reduced to one inequality for starting control, and the proof of this inequality is given. Introduction. This paper is devoted...

We study DNA denaturation by integrating elasticity - as described by the Gaussian network model - with bond binding energies, distinguishing between different base pairs and stacking energies. We use exact calculation, within the model, of the Helmholtz free-energy of any partial denaturation state, which implies that the entropy of all formed "bubbles" ("loops") is accounted for. Considering ...