Geometry and Forces in Relativistic and Pre-Relativistic Theories

It has been shown elsewhere that in the case of relativistic theories, there exists a local differential-topological criterion which distinguishes sharply between geometry and forces. This criterion is also epistemologically effective. In this paper, we explain why this local criterion fails in the pre-relativistic context. The principal reason for the difference is that the causal structure is determined by a quadratic function of 3-velocity in the relativistic case and by a linear function of 3-velocity in the pre-relativistic case.     

Fluids with highly directional attractive forces. IV. Equilibrium polymerization

We investigate approximation methods for systems of molecules interacting by core repulsion and highly directional attraction due to several attraction sites. The force model chosen imitates a chemical bond by providing for bond saturation when binding occurs. The dense fluid is an equilibrium mixture ofs-mers with mutual repulsion. We use a previously derived reformulation of statistical thermodynamics, in which the particle species are monomeric units with a specified set of attraction sites bonded. Thermodynamic perturbation theory (TPT) and integral equations of two types are derived. The use of TPT is illustrated by explicit calculation for a molecular model with two attraction sites, capable of forming chain and ring polymers. Successes and defects of TPT are discussed. The integral equations for pair correlations between particles of specified bonding include calculation of self-consistent densities of species. Methods of calculating thermodynamic properties from the solutions of integral equations are given.Supported by the NSF under grant No. CHE-82-11236.     

A Conversation with William A. Fowler – Part I

Nobel laureate William A. Fowler recalls his early education in physics; his part in the history of nuclear physics at the California Institute of Technology in the 1930s; parallel efforts elsewhere, particularly at Berkeley and the Department of Terrestrial Magnetism in Washington,D.C.; his contacts with J. Robert Oppenheimer; and his work with Charles C. Lauritsen and Tommy Lauritsen before and after World War II.John Greenberg received his Ph.D. degree from the University of Wisconsin and was Caltech research fellow in history from 1980–1984. The Editors were saddened to learn that he died while this interview was in press. Requests for reprints may be directed to Judith R. Goodstein, Institute Archives 015A-74, Caltech, Pasadena, CA 91125 USA; e-mail: jrg@caltech.edu.     

The Onsager-Casimir relations revisited

We study the fate of the Onsager-Casimir reciprocity relations for a continuous system when some of its variables are eliminated adiabatically. Just as for discrete systems, deviations appear in correction terms to the reduced evolution equation that are of higher order in the time scale ratio. The deviations are not removed by including correction terms to the coarse-grained thermodynamic potential. However, via a reformulation of the theory, in which the central role of the thermodynamic potential is taken over by an associated Lagrangian-type expression, we arrive at a modified form of the Onsager-Casimir relations that survives the adiabatic elimination procedure. There is a simple relation between the time evolution of the redefined thermodynamic forces and that of the basic thermodynamic variables; this relation also survives the adiabatic elimination. The formalism is illustrated by explicit calculations for the Klein-Kramers equation, which describes the phase space distribution of Brownian particles, and for the corrected Smoluchowski equation derived from it by adiabatic elimination of the velocity variable. The symmetry relation for the latter leads to a simple proof that the reality of the eigenvalues of the simple Smoluchowski equation is not destroyed by the addition of higher order corrections, at least not within the framework of a formal perturbation expansion in the time scale ratio.     

Nucleon-nucleon interaction with tensor forces in the quark compound bag model

A model forN-N interaction proposed earlier by two of us (VSB and VKG), has been extended to incorporate the tensor component of the nuclear force. Based on the quark compound bag model (QCB), the nucleon-nucleon potential has a short range repulsive core which is non-local and has a characteristic energy dependence and is expressed in terms of the parameters relating to the six-quark compound bag. To account for the low energy properties, this repulsive core interaction is supplemented by a phenomenological non-local potential containing both central (S-wave) and tensor components and operates only outside the QCB. Using this model, we analyse and compare the results with the experimental data for the electromagnetic form factors of the deuteron, theD-state observables, such as the quadrupole moment, theD-state probability, and theD/S ratio along with then-p scattering phase shifts up to about 400 MeV.     

Complementary energy principle for large elastic deformation

Using the “base forces” as the fundamental unknowns to determine the state of an elastic system, the complementary energy principle for large elastic deformation is constructed for the conjugate quantities being displacement gradients, which possesses exactly the same form as that of classical linear elasticity. It is revealed that the complementary energy contains deformation part and rotation part.     

Entropy Generation for Negative Frictional Pressure Drop in Vertical Slug and Churn Flows

It is widely accepted that the frictional pressure drop is impossible to be negative for pipe flow. However, the negative frictional pressure drops were observed for some cases of two-phase slug and churn flows in pipes, challenging the general sense of thermodynamic irreversibility. In order to solve this puzzling problem, theoretical investigations were performed for the entropy generation in slug and churn flows. It is found that the frictional pressure drop along with a buoyancy-like term contributes to the entropy generation due to mechanical energy loss for steady, incompressible slug and churn flows in vertical and inclined pipes. Experiments were conducted in a vertical pipe with diameter as 0.04 m for slug and churn flows. Most of the experimental data obtained for frictional pressure drop are negative at high gas–liquid ratios from 100 to 10,000. Entropy generation rates were calculated from experimental data. The results show that the buoyancy-like term is positive and responsible for a major part of entropy generation rate while the frictional pressure drop is responsible for a little part of entropy generation rate, because of which the overall entropy generation due to mechanical energy loss is still positive even if the frictional pressure drop is negative in vertical slug and churn flows. It is clear that the negative frictional pressure drops observed in slug and churn flows are not against the thermodynamics irreversibility.     

DLPNO‐CCSD(T) scaled methods for the accurate treatment of large supramolecular complexes

In this work, we present scaled variants of the DLPNO‐CCSD(T) method, dubbed as (LS)DLPNO‐CCSD(T) and (NS)DLPNO‐CCSD(T), to obtain accurate interaction energies in supramolecular complexes governed by noncovalent interactions. The novel scaled schemes are based on the linear combination of the DLPNO‐CCSD(T) correlation energies calculated with the standard (LoosePNO and NormalPNO) and modified (Loose2PNO and Normal2PNO) DLPNO‐CCSD(T) accuracy levels. The scaled DLPNO‐CCSD(T) variants provide nearly TightPNO accuracy, which is essential for the quantification of weak noncovalent interactions, with a noticeable saving in computational cost. Importantly, the accuracy of the proposed schemes is preserved irrespective of the nature and strength of the supramolecular interaction. The (LS)DLPNO‐CCSD(T) and (NS)DLPNO‐CCSD(T) protocols have been used to study in depth the role of the CH–π versus π–π interactions in the supramolecular complex formed by the electron‐donor truxene‐tetrathiafulvalene (truxTTF) and the electron‐acceptor hemifullerene (C₃₀H₁₂). (NS)DLPNO‐CCSD(T)/CBS calculations clearly reveal the higher stability of staggered (dominated by CH–π interactions) versus bowl‐in‐bowl (dominated by π–π interactions) arrangements in the truxTTF•C₃₀H₁₂ heterodimer. Hemifullerene and similar carbon‐based buckybowls are therefore expected to self‐assemble with donor compounds in a richer way other than the typical concave–convex π–π arrangement found in fullerene‐based aggregates. © 2017 Wiley Periodicals, Inc.     

Efficient Evaluation of the Elastic Forces and the Jacobian in the Absolute Nodal Coordinate Formulation

This paper develops a new procedure for evaluating the elastic forces, the elastic energy and the jacobian of the elastic forces in the absolute nodal coordinate formulation. For this procedure, it is fundamental to use some invariant sparse matrices that are integrated in advance and have the property of transforming the evaluation of the elastic forces in a matrix multiplication process. The use of the invariant matrices avoids the integration over the volume of the element for every evaluation of the elastic forces. Great advantages can be achieved from these invariant matrices when evaluating the elastic energy and calculating the jacobian of the elastic forces as well. The exact expression of the jacobian of the differential system of equations of motion is obtained, and some advantages of using the absolute nodal coordinate formulation are pointed out. Numerical results show that there is important time saving as a result of the use of the invariant matrices.