A 2D numerical model for simulating the physics of fault systems

Simulations provide a powerful means to help gain the understanding of crustal fault system physics required to progress towards the goal of earthquake forecasting. Cellular Automata are efficient enough to probe system dynamics but their simplifications render interpretations questionable. In contrast, sophisticated elasto-dynamic models yield more convincing results but are too computationally demanding to explore phase space. To help bridge this gap, we develop a simple 2D elastodynamic model of parallel fault systems. The model is discretised onto a triangular lattice and faults are specified as split nodes along horizontal rows in the lattice. A simple numerical approach is presented for calculating the forces at medium and split nodes such that general nonlinear frictional constitutive relations can be modeled along faults. Single and multi-fault simulation examples are presented using a nonlinear frictional relation that is slip and slip-rate dependent in order to illustrate the model.

A model of seller holdout

We model a buyer who wishes to combine objects owned by two separate sellers in order to realize higher value. Sellers are able to avoid entering into negotiations with the buyer, so that the order in which they negotiate is endogenous. Holdout occurs if at least one of the sellers is not present in the first round of negotiations. We demonstrate that complementarity of the buyer's technology is a necessary condition for equilibrium holdout. Moreover, a rise in complementarity leads to an increased likelihood of holdout, and an increased efficiency loss. Applications include patents, the land assembly problem, and mergers.

Stabilization of native protein fold by intein-mediated covalent cyclization

A mutant version of the N-terminal domain of Escherichia coli DnaB helicase was used as a model system to assess the stabilization against unfolding gained by covalent cyclization. Cyclization was achieved in vivo by formation of an amide bond between the N and C termini with the help of a split mini-intein. Linear and circular proteins were constructed to be identical in amino acid sequence. Mutagenesis of Phe102 to Glu rendered the protein monomeric even at high concentration. A difference in free energy of unfolding, DeltaDeltaG, between circular and linear protein of 2.3(+/-0.5) kcal mol(-1) was measured at 10degreesC by circular dichroism. A theoretical estimate of the difference in conformational entropy of linear and circular random chains in a three-dimensional cubic lattice model predicted DeltaDeltaG = 2.3 kcal mol(-1), suggesting that stabilization by protein cyclization is driven by the reduced conformational entropy of the unfolded state. Amide-proton exchange rates measured by NMR spectroscopy and mass spectrometry showed a uniform, approximately tenfold decrease of the exchange rates of the most slowly exchanging amide protons, demonstrating that cyclization globally decreases the unfolding rate of the protein. The amide proton exchange was found to follow EX1 kinetics at near-neutral pH, in agreement with an unusually slow refolding I measured by stopped-flow circular dichroism. rate of less than 4 min(-1) The linear and circular proteins differed more in their unfolding than in their folding rates. Global unfolding of the N-terminal domain of E. coli DnaB is thus promoted strongly by spatial separation of the N and C termini, whereas their proximity is much less important for folding. (C) 2005 Elsevier Ltd. All rights reserved.

Ground-State Entanglement of the BCS Model

The concept of local concurrence is used to quantify the entanglement between a single qubit and the remainder of a multiqubit system. For the ground state of the BCS model in the thermodynamic limit the set of local concurrences completely describes the entanglement. As a measure for the entanglement of the full system we investigate the average local concurrence (ALC). We find that the ALC satisfies a simple relation with the order parameter. We then show that for finite systems with a fixed particle number, a relation between the ALC and the condensation energy exposes a threshold coupling. Below the threshold, entanglement measures besides the ALC are significant.

An optimized model for rat liver perfusion studies

Conditions which influence the viability, integrity, and extraction efficiency of the isolated perfused rat liver were examined to establish optimal conditions for subsequent work in reperfusion injury studies including the choice of buffer, use of oncotic agents, hematocrit, perfusion flow rate, and pressure. Rat livers were perfused with MOPS-buffered Ringer solution with or without erythrocytes. Perfusates were collected and analyzed for blood gases, electrolytes, enzymes, radioactivity in MID studies, and lignocaine in extraction studies. Liver tissue was sampled for histological examinations, and wet:dry weight of the liver was also determined. MOPS-buffered Ringer solution was found to be superior to Krebs bicarbonate buffer, in terms of pH control and buffering capacity, especially during any prolonged period of liver perfusion. A pH of 7.2 is chosen for perfusion since this is the physiological pH of the portal blood. The presence of albumin was important as an oncotic agent, particularly when erythrocytes were used in the perfusate. Perfusion pressure, resistance, and vascular volume are how-dependent and the inclusion of erythrocytes in the perfusate substantially altered the flow characteristics for perfusion pressure and resistance but not vascular volume. Lignocaine extraction was relatively flow-independent. Perfusion injury as defined by enzyme release and tissue fine structure was closely related to the supply of O-2. The optimal conditions for liver perfusion depend upon an adequate supply of oxygen. This can be achieved by using either erythrocyte-free perfusate at a how rate greater than 6 ml/min/g liver or a 20% erythrocyte-containing perfusate at 2 ml/min/g. (C) 1996 Academic Press, Inc.

Analysis of dynamic process models for structural insight and model reduction .1. Structural identification measures

An important consideration in the development of mathematical models for dynamic simulation, is the identification of the appropriate mathematical structure. By building models with an efficient structure which is devoid of redundancy, it is possible to create simple, accurate and functional models. This leads not only to efficient simulation, but to a deeper understanding of the important dynamic relationships within the process. In this paper, a method is proposed for systematic model development for startup and shutdown simulation which is based on the identification of the essential process structure. The key tool in this analysis is the method of nonlinear perturbations for structural identification and model reduction. Starting from a detailed mathematical process description both singular and regular structural perturbations are detected. These techniques are then used to give insight into the system structure and where appropriate to eliminate superfluous model equations or reduce them to other forms. This process retains the ability to interpret the reduced order model in terms of the physico-chemical phenomena. Using this model reduction technique it is possible to attribute observable dynamics to particular unit operations within the process. This relationship then highlights the unit operations which must be accurately modelled in order to develop a robust plant model. The technique generates detailed insight into the dynamic structure of the models providing a basis for system re-design and dynamic analysis. The technique is illustrated on the modelling for an evaporator startup. Copyright (C) 1996 Elsevier Science Ltd

Analysis of dynamic models for structural insight and model reduction .2. A multi-stage compressor shutdown case-study

In this second paper, the three structural measures which have been developed are used in the modelling of a three stage centrifugal synthesis gas compressor. The goal of this case study is to determine the essential mathematical structure which must be incorporated into the compressor model to accurately model the shutdown of this system. A simple, accurate and functional model of the system is created via three structural measures. It was found that the model can be correctly reduced into its basic modes and that the order of the differential system can be reduced from 51(st) to 20(th). Of the 31 differential equational 21 reduce to algebraic relations, 8 become constants and 2 can be deleted thereby increasing the algebraic set from 70 to 91 equations. An interpretation is also obtained as to which physical phenomena are dominating the dynamics of the compressor add whether the compressor will enter surge during the shutdown. Comparisons of the reduced model performance against the full model are given, showing the accuracy and applicability of the approach. Copyright (C) 1996 Elsevier Science Ltd

Satellite observation and climate system model simulation of the St. Lawrence Island polynya

The St. Lawrence Island polynya (SLIP) is a commonly occurring winter phenomenon in the Bering Sea, in which dense saline water produced during new ice formation is thought to flow northward through the Bering Strait to help maintain the Arctic Ocean halocline. Winter darkness and inclement weather conditions have made continuous in situ and remote observation of this polynya difficult. However, imagery acquired from the European Space Agency ERS-1 Synthetic Aperture Radar (SAR) has allowed observation of the St. Lawrence Island polynya using both the imagery and derived ice displacement products. With the development of ARCSyM, a high resolution regional model of the Arctic atmosphere/sea ice system, simulation of the SLIP in a climate model is now possible. Intercomparisons between remotely sensed products and simulations can lead to additional insight into the SLIP formation process. Low resolution SAR, SSM/I and AVHRR infrared imagery for the St. Lawrence Island region are compared with the results of a model simulation for the period of 24-27 February 1992. The imagery illustrates a polynya event (polynya opening). With the northerly winds strong and consistent over several days, the coupled model captures the SLIP event with moderate accuracy. However, the introduction of a stability dependent atmosphere-ice drag coefficient, which allows feedbacks between atmospheric stability, open water, and air-ice drag, produces a more accurate simulation of the SLIP in comparison to satellite imagery. Model experiments show that the polynya event is forced primarily by changes in atmospheric circulation followed by persistent favorable conditions: ocean surface currents are found to have a small but positive impact on the simulation which is enhanced when wind forcing is weak or variable.

Isolated limb perfusion with melphalan for human melanoma xenografts in the hindlimb of nude rats: A surviving animal model

We have established a surviving model of isolated limb perfusion using xenografts of the human melanoma cell line MM 96L injected subcutaneously into the hindlimb of a nude rat, The femoral artery and vein were cannulated via the left renal artery and vein and the hind limb was isolated using tourniquets. The limb was perfused with Krebs Heinseleit buffer at 37 degrees C containing 4.7% bovine serum albumin at a constant flow rate of 4 mi per min for 30-60 min with 100% survival of the animals, Tumour vascularization and blood flow were demonstrated using vascular casts and [Cr-51]-microspheres. Following the addition of melphalan (15 or 100 mu g/ml), drug concentrations in the perfusate, tissues and systemic circulation were determined using high pressure liquid chromatography (HPLC), Systemic leakage, assessed using [I-125]albumin and melphalan and detected by a gamma-counter and HPLC respectively, was <0.5%. The melphalan concentration and tissue flow rate in the tumour deposits were 40 and 30% respectively, when compared with the surrounding subcutaneous tissue, At a dose of 15 mu g/ml, melphalan caused a reduction in tumour growth after 60 min perfusion, and a significant reduction in tumour size was seen when the melphalan dose was 100 mu g/ml. The surviving nude rat model of isolated limb perfusion for recurrent melanoma will allow examination of optimal perfusion conditions, along with the pharmacokinetics, pharmacodynamics and efficacy of melphalan and other drugs.

A mathematical model for Escherichia coli debris size reduction during high pressure homogenisation based on grinding theory

Experimental data for E. coli debris size reduction during high-pressure homogenisation at 55 MPa are presented. A mathematical model based on grinding theory is developed to describe the data. The model is based on first-order breakage and compensation conditions. It does not require any assumption of a specified distribution for debris size and can be used given information on the initial size distribution of whole cells and the disruption efficiency during homogenisation. The number of homogeniser passes is incorporated into the model and used to describe the size reduction of non-induced stationary and induced E. coil cells during homogenisation. Regressing the results to the model equations gave an excellent fit to experimental data ( > 98.7% of variance explained for both fermentations), confirming the model's potential for predicting size reduction during high-pressure homogenisation. This study provides a means to optimise both homogenisation and disc-stack centrifugation conditions for recombinant product recovery. (C) 1997 Elsevier Science Ltd.

On the validity of the dispersion model of hepatic drug elimination when intravascular transit time densities are long-tailed

The dispersion model with mixed boundary conditions uses a single parameter, the dispersion number, to describe the hepatic elimination of xenobiotics and endogenous substances. An implicit a priori assumption of the model is that the transit time density of intravascular indicators is approximated by an inverse Gaussian distribution. This approximation is limited in that the model poorly describes the tail part of the hepatic outflow curves of vascular indicators. A sum of two inverse Gaussian functions is proposed as ail alternative, more flexible empirical model for transit time densities of vascular references. This model suggests that a more accurate description of the tail portion of vascular reference curves yields an elimination rate constant (or intrinsic clearance) which is 40% less than predicted by the dispersion model with mixed boundary conditions. The results emphasize the need to accurately describe outflow curves in using them as a basis for determining pharmacokinetic parameters using hepatic elimination models. (C) 1997 Society for Mathematical Biology.

Proton transport model in the ionosphere .1. Multistream approach of the transport equations

The suprathermal particles, electrons and protons, coming from the magnetosphere and precipitating into the high-latitude atmosphere are an energy source of the Earth's ionosphere. They interact with ambient thermal gas through inelastic and elastic collisions. The physical quantities perturbed by these precipitations, such as the heating rate, the electron production rate, or the emission intensities, can be provided in solving the kinetic stationary Boltzmann equation. This equation yields particle fluxes as a function of altitude, energy, and pitch angle. While this equation has been solved through different ways for the electron transport and fully tested, the proton transport is more complicated. Because of charge-changing reactions, the latter is a set of two-coupled transport equations that must be solved: one for protons and the other for H atoms. We present here a new approach that solves the multistream proton/hydrogen transport equations encompassing the collision angular redistributions and the magnetic mirroring effect. In order to validate our model we discuss the energy conservation and we compare with another model under the same inputs and with rocket observations. The influence of the angular redistributions is discussed in a forthcoming paper.

An isolated perfused human placental lobule model for multiple indicator dilution studies

We describe a method for multiple indicator dilution studies in the isolated perfused human placental lobule developed to investigate the relationships between changes in pressure and flow and solute clearance. A peripheral lobule of a human placenta is perfused with a tissue culture-based medium and the perfusate oxygen tension, arterial and venous pressures, pH and perfusion temperature continuously monitored by a computerized system. Flow rates are readily changed. Bolus injections of vascular, extracellular and water space markers, and study compounds can be made into either maternal or fetal circulations, and precisely timed outflow fractions can be collected with computer-controlled fraction collectors, allowing simultaneous determination of concentration-time profiles of each marker. (C) 1997 Elsevier Science Inc.

Structural effects of lipophilic methotrexate conjugates on model phospholipid biomembranes

Lipophilic conjugates of the antitumor drug methotrexate (MTX) with lipoamino acids (LAAs) have been previously described as a tool to enhance MTX passive entrance into cells, overcoming a form of transport resistance which makes tumour cells insensitive to the antimetabolite. A knowledge of the mechanisms of interaction of such lipophilic derivatives with cell membranes could be useful for planning further lipophilic MTX derivatives with an optimal antitumour activity. To this aim, a calorimetric study was undertaken using a biomembrane model made from synthetic 1,2-dipalmitoyl-glycero-3-phosphocholine (DPPC) multilamellar liposomes. The effects of MTX and conjugates on the phase transition of liposomes were investigated using differential scanning calorimetry. The interaction of pure MTX with the liposomes was limited to the outer part of the phospholipid bilayers, due to the polar nature of the drug. Conversely, its lipophilic conjugates showed a hydrophobic kind of interaction, perturbing the packing order of DPPC bilayers. In particular, a reduction of the enthalpy of transition from the gel to the liquid crystal phase of DPPC membranes was observed. Such an effect was related to the structure and mole fraction of the conjugates in the liposomes. The antitumour activity of MTX conjugates was evaluated against cultures of a CCRF-CEM human leukemic T-cell line and a related MTX resistant sub-line. The in vitro cell growth inhibitory activity was higher for bis(tetradecyl) conjugates than for both the other shorter- and longer-chain derivatives. The biological effectiveness of the various MTX derivatives correlated very well with the thermotropic effects observed on the phase transition of DPPC biomembranes. (C), 2001 Elsevier Science B.V All rights reserved.