Isotropic forces

For the rotovibrational spectra of molecules interacting through purely isotropic forces, the Hamiltonian may be written as the sum of two independent terms. One term describes the rotational motion of the molecules, the other the translational motion of the pair. The total energy of the system is then equal to the sum of the rotovibrational and the translational energies. At the same time, the supermolecular wavefunctions are products of rotovibrational and translational functions. Let r designate the set of the rotovibrational quantum numbers and t the set of translational quantum numbers, the equation for yo may be written [314]... 

Turning to the two-dimensional oscillator, with isotropic force constants, one has then for Jf levels singly occupied and for filled shells ... 

Van der Linden, E. and Sagis, L. M. C. 2001. Isotropic force percolation in protein gels. Langmuir 17 5821-5824. 

It appears that a lower critical point is not to be observed with mixtures of spherical molecules with isotropic force fields. The phenomenon seems to be related mainly to modification of the rotational degrees of freedom of the molecules. 

In this work we explore using only properties derived from the gradient vector field of the charge density, using the theory of atoms in molecules (AIM) In this way we demonstrate the usefulness of the charge density to understand such properties as metallicity when ice is in such extreme conditions (> 100 GPa, since above this pressure the tunneling effect of the proton ceases). The pressure is applied via an external isotropic force of compression. 

The large resistance of the membrane to area dilation has been characterized in micromechanical experiments. The changes in surface area that can be produced in the membrane are small, and so they can be characterized in terms of a simple Hookean elastic relationship between the isotropic force resultant N and the fractional change in surface area a = A/Ao — 1 ... 

Area expansivity modulus A measure of the resistance of a membrane to area dilation. It is the proportionality between the isotropic force resultant in the membrane and the corresponding fractional change in membrane area. (Units 1 mN/m = 1 dyn/cm)... 

Competition between two different local particle arrangements, arising from either directional or core-softened isotropic forces, is usually deemed to be responsible for anomalous thermodynamic behavior. However, our results show that the same behaviors may also occur for isotropic interactions characterized by a repulsion that is only marginally softened and yields a single structure at a local level. Such potentials can be relevant in the realm of soft matter, where engineering interparticle forces is possible, and also for hard matter under extreme conditions, where pressure-triggered rearrangements of the crystal structure induce a partial... 

Suppose that the circular film patch to be pressurized extends over 0 < r < a. It is assumed from the outset that the state of stress in the film is an equi-biaxial membrane tension with isotropic force-per-unit-length stress resultant = tg = t. For linear elastic material response, the stress resultant t is related to the equi-biaxial strain of magnitude e. = eg = e according to... 

To make a general moment tensor easier to understand, it helps to decompose it into simpler force systems. First, we express the moment tensor in its principal axis coordinate system. Three values (the Euler angles, for example) are needed to specify the orientation of this system, and three other values specify the moments of three orthogonal dipoles oriented parallel to the coordinate axes. Writing these three principal moments as a column vector, we first decompose the moment tensor into an isotropic force system and a deviatoric remainder. 

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