Maximum Simplification Research Articles

Economical Technology of Creation of Cell-Free Matrix of Animal and Human Arterial Vessels

We present a technology of creation of blood vessel connective tissue framework by 2-3-h vessel perfusion with detergents. The technology ensures effective removal of vascular cells without damaging collagen and elastic fibers. The connective tissue frameworks prepared by this method can the used for restoring blood flow in various vascular pathologies. The presented approach attenuates the damaging effect of treatment on the vascular framework due to maximum simplification and shortening of the duration of treatment and is universal for human and animal vessels.

Minimal atmospheric finite-mode models preserving symmetry and generalized Hamiltonian structures

A typical problem with the conventional Galerkin approach for the construction of finite-mode models is to keep structural properties unaffected in the process of discretization. We present two examples of finite-mode approximations that in some respect preserve the geometric attributes inherited from their continuous models: a three-component model of the barotropic vorticity equation known as Lorenz’ maximum simplification equations [E.N. Lorenz, Maximum simplification of the dynamic equations, Tellus 12 (3) (1960) 243–254] and a six-component model of the two-dimensional Rayleigh–Bénard convection problem. It is reviewed that the Lorenz-1960 model respects both the maximal set of admitted point symmetries and an extension of the noncanonical Hamiltonian form (Nambu form). In a similar fashion, it is proved that the famous Lorenz-1963 model violates the structural properties of the Saltzman equations and hence cannot be considered as the maximum simplification of the Rayleigh–Bénard convection problem. Using a six-component truncation, we show that it is again possible to retain both symmetries and the Nambu representation in the course of discretization. The conservative part of this six-component reduction is related to the Lagrange top equations. Dissipation is incorporated using a metric tensor.

Electrochromatography in cyclic olefin copolymer microchips: A step towards field portable analysis

In order to develop a portable and disposable instrument for on-site analysis of neutral compounds, a lauryl methacrylate monolith has been synthesized into a cyclic olefin copolymer microdevice for reversed-phase electrochromatography purposes. This monolith was tested in capillary to evaluate electrochromatographic performances in terms of electroosmotic flow (EOF) mobility, retention and efficiency prior to its transfer into the microfluidic device. The produced monolithic bed exhibited a good run-to-run repeatability, column-to-column reproducibility and batch-to-batch reproducibility, with relative standard deviation (RSD) values below 9% for EOF mobility, retention factors and heights of theoretical plate. The electrochromatographic performances of the monolith were optimized by reducing irradiation time. Photopolymerization time of 10 min was found to be the best process in order to obtain a robust, retentive and efficient system. The on-chip performances of this monolith were evaluated in detail for the reversed-phase electrochromatographic separation of polycyclic aromatic hydrocarbons, with plate heights reaching down to 15 μm when working at optimal velocity. Aiming at the maximum simplification of instrumental fabrication and operation, a direct injection from a 2 μL droplet was compared with more conventional dynamic injection process.

Symmetry justification of Lorenz’ maximum simplification

In 1960 Edward Lorenz (1917-2008) published a pioneering work on the `maximum simplification' of the barotropic vorticity equation. He derived a coupled three-mode system and interpreted it as the minimum core of large-scale fluid mechanics on a `finite but unbounded' domain. The model was obtained in a heuristic way, without giving a rigorous justification for the chosen selection of modes. In this paper, it is shown that one can legitimate Lorenz' choice by using symmetry transformations of the spectral form of the vorticity equation. The Lorenz three-mode model arises as the final step in a hierarchy of models constructed via the component reduction by means of symmetries. In this sense, the Lorenz model is indeed the `maximum simplification' of the vorticity equation.

Diffraction of flexural waves by finite straight cracks in an elastic sheet over water

The diffraction of long-crested incident waves propagating within a thin flexible elastic sheet floating on water by narrow cracks is considered. The cracks are straight and each of finite length and must be parallel to one another. This arrangement lends itself to the use of Fourier transform methods, which allows the solution to a simpler problem to be used. For N cracks, 2N coupled integral equations results for 2N unknown functions related to the jump in displacement and slope across each crack as a function of distance along the cracks. These integral equations are hypersingular but, in approximating their solution using Galerkin's method, a judicious choice of trial function provides maximum simplification in the algebraic equations which result. Numerical results focus on the diffracted wave amplitudes, the maximum displacement of the elastic sheet and the stress intensity factor at the ends of the cracks. For two side-by-side cracks, large resonant motion can occur in the strip between the cracks.

Further Analysis of Lorenz’s Maximum Simplification Equations

AbstractThe goal of this paper is to provide a complete picture of the long-term behavior of Lorenz’s maximum simplification equations along with the corresponding meteorological interpretation for all initial conditions and all values of the parameter.

Tetrads in geometrodynamics

A new tetrad is introduced within the framework of geometrodynamics for non-null electromagnetic fields. This tetrad diagonalizes the electromagnetic stress-energy tensor and allows for maximum simplification of the expression of the electromagnetic field. The Einstein-Maxwell equations will also be simplified.

Second-order approximation to the 3DVAR cost function: application to analysis/forecast

The analysis/forecast cycling scheme used in operational weather prediction centers involves repeated application of a 3DVAR assimilation phase followed by a forecast phase. In this paper we first derive a closed-form expression for the complete Hessian of the 3DVAR objective function. This facilitates the use of Newton-like algorithms in the 3DVAR assimilation phase. It is also shown that this algorithm includes the standard first-order method as a special case. Notwithstanding the method used in this optimization phase, if the iterative optimization is terminated prematurely before convergence (generally for the sake of economy), the resulting analysis incurs an error that will corrupt the initial condition of the model and thereby affect the forecast. Using Lorenz’s maximum simplification form of the barotropic vorticity equation, we examine the assimilation error and its dependency on the following factors: observational and background error covariances and the optimization strategy.

History and Epistemology of Models: Meteorology (1946-1963) as a Case Study

This paper focuses on scientific practices and problems of modeling in the case of meteorology. This domain is especially interesting because of its crucial influence on the conception of mathematical models and its links with numerical instability, computers, and the science of chaos and dynamic systems. All of these questions involve for their solution a considerable mathematical apparatus which was developed by several mathematicians. An early example is von Neumann’s and Charney’s Princeton Meteorological Project in the period 1946–53 which ended with daily numerical prediction in less than 2 hours. After this stage, the questions of long-range forecasting and general circulation of the atmosphere became of greater importance. The late 1950s saw the emergence of an alternative: were atmospheric models used mainly for prediction or understanding? This controversial debate in particular occurred during an important colloquium in Tokyo in 1960 which gathered together J. Charney, E. Lorenz, A. Eliassen, and B. Saltzman, among others, and witnessed discussions on statistical methods for predictions and/or maximum simplification of dynamic equations. This phase ended in 1963 with Lorenz’s seminal paper on “Deterministic non periodic flows.”

A novel, general method of analyzing magnetic circular dichroism spectra and magnetization curves of high-spin metal ions: Application to the protein oxidized rubredoxin, Desulfovibrio gigas

We have developed a general theoretical approach for analyzing the intensities of magnetic circular dichroism (MCD) spectra of paramagnetic species with S>1/2 in the nonlinear regions of temperature and magnetic field. The method takes full advantage of the irreducible tensor method in order to obtain maximum simplification from symmetry. The approach, which is based on a detailed treatment of spin-orbit coupling and Zeeman interaction in terms of the symmetry properties of basis sets of wave functions, factorizes contributions into bands with Gaussian and derivative shapes in order to extend earlier treatments based on the so-called linear field limit. The method is applied to analyze and fit the form of the MCD spectra and the MCD magnetization curves of pseudo-tetrahedral high-spin Fe(III), S=5/2, in the protein rubredoxin from Desulfovibrio gigas, a representative of a family of iron–sulphur proteins. This treatment provides for the first time a satisfactory fit of these curves over a temperature range between 1.6 and 10 K and up to magnetic fields of 5 T. We show that the forms of the magnetization curves are strongly dependent on the polarizations of the optical transitions and on both the sign and magnitude of D, the ground state axial zero-field parameter. The sign and magnitude of D is determined to be −0.6 cm−1 with a fixed value of E/D=0.25 obtained from an analysis of electron paramagnetic resonance data. This shows that earlier, simpler fitting procedures were inadequate.

System Considerations Favoring Rotary Artificial Hearts with Blood‐Immersed Bearings

Hydrodynamic blood pumps provide such advantages as not requiring an air vent or compliance chamber as well as a great reduction in mechanical complexity with the potential for very long durability. The detailed design of their bearings is emerging as the single most important determinant of long-term success. Three categories of bearings include remote force, such as magnetic suspension; blood-isolated, which require a shaft seal; and blood-immersed using either mechanical or hydrodynamic support. Blood-immersed bearings permit maximum simplification and miniaturization of the entire system, require no flush fluid, and require no electronics as with magnetic suspension. The Jarvik 2000 heart represents an example of their potential. The intraventricular titanium pump (25 mm diameter, 25 cc, 85 g), uses blood flow through the motor air gap with blood-immersed bearings. The longest in vitro bearing durability test is ongoing at 20,000,000,000 revolutions with minimal wear (3 years at 15,000 rpm). In vivo results include 5-month calf survival, no thromboembolism, plasma Hb 2-5 mg%, and power under 10 W.

Rapid purification yielding highly active 17β-hydroxysteroid dehydrogenase: application of hydrophobic interaction and affinity fast protein liquid chromatography

Homogeneous human placental 17β-hydroxysteroid dehydrogenase was obtained by a procedure consisting of two fast protein liquid chromatographic (FPLC) steps using Phenyl-Sepharose hydrophobic interaction and Blue-Sepharose affinity columns. In the first chromatography, the enzyme eluted only when an additional decrease in ionic strength was inserted after the ammonium sulphate concentration had reached zero, thus enhancing the separation. In the affinity chromatography, separation of contaminating proteins occurred at different stages of loading and washing. The specific elution of the enzyme by the co-factor NADP + is very efficient in obtaining a homogeneous preparation in high yield. The rapidity of FPLC was further increased by a maximum simplification of the intermediate steps, and the whole procedure lasted only two days. This preparation has a yield of more than 50% and a high specific activity, catalysing the formation of 7.9 μmol of estrone from estradiol per minute at pH 9.2 and 23°C. It has an apparent molecular mass of 35 000. This provides an efficient candidate for the purification of other membrane-associated proteins.

Wavenumber transition and wavenumber vacillation in Eady‐type baroclinic flows

AbstractWavenumber transition and wavenumber vacillation are studied numerically in a ‘maximum simplification’ model of the Eady type with uneven Ekman dissipation. The spectral wave solution contains three waves having adjacent zonal wavenumbers and the gravest meridional mode. The model only allows for wave‐mean‐flow interaction.As the stratification parameter decreases away from the upper symmetric flow, we observe that baroclinic forcing increases faster than dissipation, implying the prevalence of a higher wave energy state. This state is realized by an increase in wave amplitude, number of temporal and/or spatial degrees of freedom, or dominant wavenumber. The first two occur first, but for small enough stratification, the flow transits to a higher wavenumber in order to realize the increased energy.Wavenumber vacillation is a flow regime observed at some parameter settings when the flow has at least two spatial and three temporal degrees of freedom. This regime is usually found in the region of parameter space where wavenumber transitions occur as parameters change.The balance between baroclinic forcing and damping adjusted by wave‐mean‐flow interaction seems to be a basic mechanism for wavenumber transition and wavenumber vacillation. Wave‐wave interaction is not necessary for such phenomena to exist.

Consequences of nonuniqueness in spin-relaxation theory

Various aspects of a general theorem, which asserts the lack of uniqueness of the density operator ρA for a composite system having subsystems B and C, are exploited in a systematic manner to obtain the maximum simplification in the equation of motion for the density operator ρB describing the subsystem. In particular, these ideas are applied to relaxation in spin systems in which only the second order terms in the interaction between subsystems B and C are retained in the master equation.

Maximum Simplification of the Dynamic Equations

When the dynamic equations are to be used to further our understanding of atmospheric phenomena, it is permissible to simplify them beyond the point where they can yield acceptable weather predictions. Through the use of double Fourier series, and with the omission of all but the largest scales of motion, the barotropic vorticity equation may be reduced to a system of three ordinary nonlinear differential equations. The analytic solutions of these equations are elliptic functions of time. The equations may also be solved rapidly by numerical integration. Particular solutions of the equations picture the motion of finite disturbances on a zonal flow, with exchanges of kinetic energy between the zonal flow and the disturbances accompanying the meridional transport of zonal momentum by the disturbances. Other solutions picture the initial growth and eventual cessation of growth of small disturbances on an unstable zonal current. Still further solutions picture the destruction of a stable zonal flow by large disturbances, and lead to a plausible hypothesis concerning index cycles in the atmosphere. Less extreme simplifications of the dynamic equations may be used when more complicated atmospheric phenomena are to be studied. DOI: 10.1111/j.2153-3490.1960.tb01307.x

Maximum Simplification of the Dynamic Equations

When the dynamic equations are to be used to further our understanding of atmospheric phenomena, it is permissible to simplify them beyond the point where they can yield acceptable weather predictions. Through the use of double Fourier series, and with the omission of all but the largest scales of motion, the barotropic vortidty equation may be reduced to a system of three ordinary nonlinear differential equations. The analytic solutions of these equations are elliptic functions of time. The equations may also be solved rapidly by numerical integration. Particular solutions of the equations picture the motion of finite disturbances on a zonal flow, with exchanges of kinetic energy between the zonal flow and the disturbances accompanying the meridional transport of zonal momentum by the disturbances. Other solutions picture the initial growth and eventual cessation of growth of small disturbances on an unstable zonal current. Still further solutions picture the destruction of a stable zonal flow by large disturbances, and lead to a plausible hypothesis concerning index cycles in the atmosphere. Less extreme simplifications of the dynamic equations may be used when more complicated atmospheric phenomena are to be studied.

MODULAR SIZE OF CLAY‐PRODUCTS UNITS*

AbstractIn cooperation with the Modular Service Association, studies have been made during the past two years on present unit masonry sizes as used in conventional building construction and their adaptability to a coordinated system. It was found that a significant relationship exists between present unit sizes in height, thickness, and length and a 4‐in. modular dimension. There is little consistency, however, in the assembly of these units in similar or composite walls and far less in the coordination with component building materials and equipment.Recommendations are made for single masonry units based on whole multiples of four inches with consideration given to the various joint thicknesses. Methods are shown for relating unit sizes in fractional multiples of four inches plus mortar joints to the grid pattern. Suggestions for standardization of unit sizes are proposed to obtain maximum simplification and corresponding economy to meet postwar construction requirements.