A new analytic solution for the Zwanzig-Lauritzen model of polymer chain folding

A two-dimensional model of polymer chain folding invented by Zwanzig and Lauritzen is here studied using a grand ensemble and transfer matrix method. Due to the character of the model, there are no extensive parameters in the grand ensemble and the dispersion in system size is large, raising doubts about the validity and usefulness of the ensemble. We find it possible to define a thermodynamic limit such that it leads to near equivalence between the canonical and grand ensembles in the limit of large systems. The transfer matrix in this case is a nonlocal operator on a space of L₂ functions, and the eigenvalue equation is a homogeneous Fredholm integral equation of the second kind which can be completely solved in terms of Bessel functions. The grand partition function can then be expressed as a sum of powers of the known eigenvalues. It is an easy matter to reproduce the second-order phase transition in the canonical ensemble found in the original work on the model. The investigation is extended to yield the probability densities describing the length of a segment and the correlations among segments. The concept of a local width of the folded chain is found to break down at higher temperatures, while critical correlations are characterized by infinite range, as expected. Apart from physical and methodological implications, the new solution provides striking illustrations of some basic ideas concerning phase transitions.     

Analysis and calibration of a three-invariant plasticity model for granular materials

Summary In this paper we briefly review issues related to the characterization of properties of granular materials subjected to micro-gravity and one-gravity conditions at very low effective stress levels. We describe the development of a three-invariant plasticity model that resembles the model devised by Lade. An inverseidentification scheme where the analysis tools are used to extract constitutive model parameters from experiments is also discussed.

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Untersuchung und Kalibrierung eines mit drei Spannungsinvarianten formulierten Plastizitätsmodells für granulare Stoffe

Zusammenfassung Übersicht: Über Resultate, die mit der Charakterisierung der Eigenschaften von granularen Stoffen in schwachen Schwerefeldern bzw. dem der Erde bei sehr kleinen Spannungen zusammenhängen, wird ein kurzer Überblick gegeben. Beschrieben wird ein mit drei Spannungsinvarianten formuliertes plastisches Stoffgesetz, welches dem von Lade entwickelten Modell ähnlich ist. Weiterhin wird ein inverses Identifikationsschema diskutiert, bei dem mit analytische Methoden benutzt werden, um die Parameter des Stoffmodells zu gewinnen.

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Presented at the workshop on Limit Analysis and Bifurcation Theory, held at the University of Karlsruhe (FRG), February 22–25, 1988     

In silico prediction of drug solubility: 4. Will simple potentials suffice?

In view of the extreme importance of reliable computational prediction of aqueous drug solubility, we have established a Monte Carlo simulation procedure which appears, in principle, to yield reliable solubilities even for complex drug molecules. A theory based on judicious application of linear response and mean field approximations has been found to reproduce the computationally demanding free energy determinations by simulation while at the same time offering mechanistic insight. The focus here is on the suitability of the model of both drug and solvent, i.e., the force fields. The optimized potentials for liquid simulations all atom (OPLS‐AA) force field, either intact or combined with partial charges determined either by semiempirical AM1/CM1A calculations or taken from the condensed‐phase optimized molecular potentials for atomistic simulation studies (COMPASS) force field has been used. The results illustrate the crucial role of the force field in determining drug solubilities. The errors in interaction energies obtained by the simple force fields tested here are still found to be too large for our purpose but if a component of this error is systematic and readily removed by empirical adjustment the results are significantly improved. In fact, consistent use of the OPLS‐AA Lennard‐Jones force field parameters with partial charges from the COMPASS force field will in this way produce good predictions of amorphous drug solubility within 1 day on a standard desktop PC. This is shown here by the results of extensive new simulations for a total of 47 drug molecules which were also improved by increasing the water box in the hydration simulations from 500 to 2000 water molecules. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2009     

Effect of a portable ultra-clean exponential airflow unit on the particle distribution in an operating room

The effects of a mobile laminar airflow unit on the concentration,deposition and distribution of bacteriacarrying particles in an operating room are investigated.The exploration is carried out using numerical calculation schemes(computational fluid dynamics approach).The model validation was performed through result comparisons with published measurement data from literature.Two types of mobile screen units were evaluated as an extension of turbulent-mixing operating-room ventilation.Airborne particle concentration/sedimentation was recorded with and without a screen unit on the operating table and two instrument tables.Both active and passive air sampling were examined and the results are compared.It was found that the additional mobile ultra-clean laminar airflow unit reduces the counts of airborne bacteria and surface contamination to a level acceptable for infection-prone surgeries.     

Quantized RRK theory of unimolecular reaction rates

The main difference between the simple RRK theory and the better based but more complex RRKM theory is explained. Starting from the premise that the classical versus quantum mechanical estimation of the density of states is the major source of the difference, earlier attempts to incorporate the quantum effects in an effective value for the number of oscillators s are noted. By examining the expression for the RRKM rate coefficient it is found that a single effective s value will generally not suffice, but a much better representation of the quantum effects can be obtained if it is recognized that the problem inherently contains two different effective s values. A theory based on this analysis is constructed. It reproduces RRKM results to much improved accuracy, removing difficulties found earlier with single-s-value theories.     

The use of computed tomography in non-destructive testing of polymeric materials, aluminium and concrete: Part 2—applications

Computed tomography has been used to detect imperfections in polymeric products such as aeroplane tyres, rubber shock absorbers and fibre-reinforced materials of various types and shapes. It has also been shown that computed tomography can be used to investigate aluminium and concrete.

There is some evidence which indicates that computed tomography can be used to measure cross-link density gradients in polymeric products, e.g. thick-walled rubber products such as dynamic springs and dampers.     

On statistical mechanical equations of state for simple fluids : Effective hard spheres and quantum corrections

Nordholm, S., Greberg, H. and Penfold, R., 1991. On statistical mechanical equations of state for simple fluids. Effective hard spheres and quantum corrections. Fluid Phase Equilibria, 90: 307-332.

A comparison is made of the mean field generalised van der Waals theory, based on a variationally determined hard sphere diameter, with the recent equation of state proposed by Song and Mason incorporating a temperature-dependent hard sphere diameter and correlation effects through the second virial coefficient. The simple cell theory ansatz of the former is less accurate but permits a wide range of applications including the estimation of quantum effects on the bulk properties of light fluids at low temperatures. Results for the critical parameters of ³He, ⁴He, H₂, Ne, CH₄ and Ar are examined. The relevance to the corresponding theory of non-uniform fluids is noted.     

Generalized finite element method applied to the calculation of continuum states

A new method for the calculation of continuum energy eigenfunctions in one dimension is presented. It is based on a numerical coupling method first exploited in the so-called finite element method which does not require explicit fitting of boundary conditions. Results from simple test calculations for square well and Morse potentials show the method to be highly accurate and efficient.