Hydrodynamic and hydromagnetic stability

We present an extensive molecular‐dynamics simulation for a bead spring model of a melt of linear polymers. The number of monomers N covers the range from N=5 to N=400. Since the entanglement length Ne is found to be approximately 35, our chains cover the crossover from the nonentangled to the entangled regime. The Rouse model provides an excellent description for short chains N<Ne, while the dynamics of the long chains can be described by the reptation model. By mapping the model chains onto chemical species we give estimates of the times and distances of onset of the slowing down in motion due to reptation. Comparison to neutron spin‐echo data confirm our mapping procedure, resolving a discrepancy between various experiments. By considering the primitive chain we are able to directly visualize the confinement to a tube. Analyzing the Rouse mode relaxation allows us to exclude the generalized Rouse models, while the original reptation prediction gives a good description of the data.

Dynamics of entangled linear polymer melts: A molecular‐dynamics simulation

Preface Acknowledgements Notation Part I. Overview and Background Topics: 1. Introduction 2. Overview 3. Theoretical background 4. Periodic solids and electron bands 5. Uniform electron gas and simple metals Part II. Density Functional Theory: 6. Density functional theory: foundations 7. The Kohn-Sham ansatz 8. Functionals for exchange and correlation 9. Solving the Kohn-Sham equations Part III. Important Preliminaries on Atoms: 10. Electronic structure of atoms 11. Pseudopotentials Part IV. Determination of Electronic Structure, The Three Basic Methods: 12. Plane waves and grids: basics 13. Plane waves and grids: full calculations 14. Localized orbitals: tight binding 15. Localized orbitals: full calculations 16. Augmented functions: APW, KKR, MTO 17. Augmented functions: linear methods Part V. Predicting Properties of Matter from Electronic Structure - Recent Developments: 18. Quantum molecular dynamics (QMD) 19. Response functions: photons, magnons ... 20. Excitation spectra and optical properties 21. Wannier functions 22. Polarization, localization and Berry's phases 23. Locality and linear scaling O (N) methods 24. Where to find more Appendixes References Index.

Electronic Structure: Basic Theory and Practical Methods

A momentum-space formalism for calculating the total energy of solids is derived. This formalism is designed particularly for application with the self-consistent pseudo- potential method. In the present formalism, the total energy is obtained through band- structure calculations without involving additional integrations. The Hellman-Feynman theorem is derived, as is a modified virial relation for the pseiidopotential Hamiltonian which provides an alternative way of calculating forces and total energies. The calculation of the total energy of solids and related derivatives with respect to structural degrees of freedom has been an ongoing problem since the early days of solid state physics (Wigner and Seitz 1933, 1934, Fuchs 1935). Quantum-mechanical calcu- lations on molecules suggest that correlation effects might sometimes be responsible for most of their binding energy (Schaefer 1972). The solid state approaches have concentrated on efforts to include most of these effects through an effective potential I/corr(p(r, Y')) (Hohenberg and Kohn 1964, Kohn and Sham 1965), rather than by complicated wave- function-related configuration interactions or many-electron perturbation techniques. Besides the problem of considering correlation effects, the self-consistent solution of the Schrodinger equation within a desired accuracy is quite difficult ; typically, the experi- mental binding energy of elemental solids is 10-4-10-5 times the total energy. These difficulties have inspired a large set of total-energy calculations that circumvents the complete solution of the Schrodinger equation (Harrison 1966, Heine and Weaire 1970). It is based on various approximations to the nearly-free-electron representation and may include the effect of more localised electrons (e.g. d states in transition metals) through specific interaction models (Moriarty 1974, 1977). As the variational self-consistent charge density remains unspecified in this approach, various forms of linear dielectric screening of the basic Coulomb interactions are introduced (Harrison 1966, Heine and Weaire 1970). Another set oftotal-energy calculations is based on direct solutions ofthe Schrodinger equation within a given interaction model : for example, Hartree-Fock (Harris and Monkhorst 1971, Wepfer et al 1974), density-functional (Ching and Callaway 1974,

https://iopscience.iop.org/article/10.1088/0022-3719/12/21/009/pdf

Momentum-space formalism for the total energy of solids

The stress theorem presented previously by the present authors is derived in detail and is related to the virial and force theorems. Stress fields are considered in two alternative forms, both of which give the same macroscopic stress and forces on nuclei when integrated over appropriate surfaces. A crucial concept is interactions that ``cross'' surfaces. Explicit forms of the stress field within the local-density approximation are given, together with a generalization of the approximate Liberman form for pressure. Reciprocal-space expressions and ab initio calculations are considered in detail in an accompanying paper.

Quantum-mechanical theory of stress and force.

Charge Density and Structural Properties of Covalent Semiconductors

On the dynamic stability of fluid dielectric films

Linear hydrodynamics of viscous thin films: II. Application to lipid films

Linear hydrodynamics of viscous thin films: I. General theory

The reptation model is generalized on the basis of a theory which accounts for hindered defect diffusion along the chain. A basic ingredient of the theory is a waiting time distribution for the hops of elementary defects which store length. Important rheological quantities are found to generally depend on fractional powers of the molecular mass rather than on integer powers as in the conventional reptation picture.

Generalized reptation model

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