There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

CHARMM (Chemistry at HARvard Macromolecular Mechanics) is a highly flexible computer program which uses empirical energy functions to model macromolecular systems. The program can read or model build structures, energy minimize them by first- or second-derivative techniques, perform a normal mode or molecular dynamics simulation, and analyze the structural, equilibrium, and dynamic properties determined in these calculations. The operations that CHARMM can perform are described, and some implementation details are given. A set of parameters for the empirical energy function and a sample run are included.

CHARMM: A program for macromolecular energy, minimization, and dynamics calculations

This review summarizes recent developments in the theory of spin glasses, as well as pertinent experimental data. The most characteristic properties of spin glass systems are described, and related phenomena in other glassy systems (dielectric and orientational glasses) are mentioned. The Edwards-Anderson model of spin glasses and its treatment within the replica method and mean-field theory are outlined, and concepts such as "frustration," "broken replica symmetry," "broken ergodicity," etc., are discussed. The dynamic approach to describing the spin glass transition is emphasized. Monte Carlo simulations of spin glasses and the insight gained by them are described. Other topics discussed include site-disorder models, phenomenological theories for the frozen phase and its excitations, phase diagrams in which spin glass order and ferromagnetism or antiferromagnetism compete, the Ne\'el model of superparamagnetism and related approaches, and possible connections between spin glasses and other topics in the theory of disordered condensed-matter systems.

Spin glasses: Experimental facts, theoretical concepts, and open questions

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

https://www.cell.com/cell/pdf/0092-8674(84)90301-5.pdf

Separation of yeast chromosome-sized DNAs by pulsed field gradient gel electrophoresis

Role of chain entanglements on fiber formation during electrospinning of polymer solutions: Good solvent, non-specific polymer-polymer interaction limit

https://onlinelibrary.wiley.com/doi/pdf/10.1002/bip.360210511

Why does the electrophoretic mobility of DNA in gels vary with the length of the molecule

After defining Fickian diffusion in rubbery polymers an overview of transport behavior in polymers is presented. Diffusion and sorption below the glass transition are discussed, followed by a review and classification of the various theoretical models which have been proposed to account for these phenomena. A short list of recommendations for future work is included.

Sorption and transport in glassy polymers–a review

During development of the embryonic chick limb the skeletal pattern is laid out as cartilaginous primordia, which emerge in a proximodistal sequence over a period of 4 days. The differentiation of cartilage is preceded by changes in cellular contacts at specific locations in the precartilage mesenchyme. Under realistic assumptions, the biosynthesis and diffusion through the extracellular matrix of a cell surface protein, such as fibronectin, will lead to spatial patterns of this molecule that could be the basis of the emergent primordia. As cellular differentiation proceeds, the size of the mesenchymal diffusion chamber is reduced in descrete steps, leading to sequential reorganizations of the morphogen pattern. The successive patterns correspond to observed rows of skeletal elements, whose emergence, in theory and in practice, depends on the maintenance of a unique boundary condition at the limb bud apex.

https://science.sciencemag.org/content/sci/205/4407/662.full.pdf

Dynamics of skeletal pattern formation in developing chick limb

The purpose of this brief review is to describe some recent, preliminary attempts to prepare nanocomposites in which polymer chains thread through the cavities or channels of several types of inorganic materials, specifically zeolites, a mesoporous hexagonal form of silica, and silica nanotubes. One goal is to determine the effects of the constraining geometry on the properties of the chains, in particular, their glass transition temperatures. Another is the hope that this molecular threading will provide such intimate interactions between the polymer chains and their inorganic environment that novel reinforcement effects will be obtained.

Harry L. Frisch

Papers

Role of chain entanglements on fiber formation during electrospinning of polymer solutions: Good solvent, non-specific polymer-polymer interaction limit

Why does the electrophoretic mobility of DNA in gels vary with the length of the molecule

Sorption and transport in glassy polymers–a review

Dynamics of skeletal pattern formation in developing chick limb

Nanocomposites Prepared by Threading Polymer Chains through Zeolites, Mesoporous Silica, or Silica Nanotubes