Animal Guts as Nonideal Chemical Reactors: Partial Mixing and Axial Variation in Absorption Kinetics

Animal guts have been idealized as axially uniform plug-flow reactors (PFRs) without significant axial mixing or as combinations in series of such PFRs with other reactor types. To relax these often unrealistic assumptions and to provide a means for relaxing others, I approximated an animal gut as a series of n continuously stirred tank reactors (CSTRs) and examined its performance as a Function of n. For the digestion problem of hydrolysis and absorption in series, I suggest as a first approximation that a tubular gut of length L and diameter D comprises n=L/D tanks in series. For n greater than or equal to 10, there is little difference between performance of the nCSTR model and an ideal PFR in the coupled tasks of hydrolysis and absorption. Relatively thinner and longer guts, characteristic of animals feeding on poorer forage, prove more efficient in both conversion and absorption by restricting axial mixing, in the same total volume, they also give a higher rate of absorption. I then asked how a fixed number of absorptive sites should be distributed among the n compartments. Absorption rate generally is maximized when absorbers are concentrated in the hindmost few compartments, but high food quality or suboptimal ingestion rates decrease the advantage of highly concentrated absorbers. This modeling approach connects gut function and structure at multiple scales and can be extended to include other nonideal reactor behaviors observed in real animals.

Partial pressure of carbon dioxide along the Transatlantic section from 7 November till 19 December 2000

Along a transatlantic section from 57°N to 60°S that was carried out from November 7 till December 19, 2000 on board R/V Horizont II concentrations of CO2 were measured in the near-water layer of the air and differences between partial pressures in water and air in various climatic zones were calculated. It was shown that variations of CO2 concentrations in the near-water layer of air and those of values of water-air partial pressure difference were from 324x10**-6 to 426x10**-6 and from 150x10**-6 to 100x10**-6 atm, respectively. Maximum value of CO2 partial pressure in air in the near-water layer (426x10**-6 atm) was noted at 45°-47°N; minimum of 324x10**-6 atm was found in Antarctica at 59°S. During measurenents maximum value of CO2 partial pressure difference in water and air (150 x10**-6) was observed at 45°-48°N; maximum flux in this case was directed from the atmosphere to water. Maximum value of CO2 partial pressure difference in water and air for flux directed from the ocean to air (100 x10**-6) was observed at 59°-60°S. Comparison of calculated values of partial pressure difference in water and air with previous data points to more intense exchange of CO2 between the ocean and atmosphere during the survey period was considered. According to values of CO2 partial pressure difference in air and water as compared to 1975, exchange intensity in the Northern Hemisphere (absorption from the atmosphere) increased. A well-pronounced latitudinal effect of distribution of CO2 partial pressure in air was observed. Along the route variations in CO2 concentrations in zones of water divergence and convergence were registered.

Properties of seawater (partial pressure of carbon dioxide (pCO2)) from a ProOceanus CO2-Pro sensor mounted on the continuous surface water sampling system during the Tara Oceans expedition 2009-2013

The Tara Oceans Expedition (2009-2013) sampled the world oceans on board a 36 m long schooner, collecting environmental data and organisms from viruses to planktonic metazoans for later analyses using modern sequencing and state-of-the-art imaging technologies. Tara Oceans Data are particularly suited to study the genetic, morphological and functional diversity of plankton. The present data set provides continuous measurements of partial pressure of carbon dioxide (pCO2), using a ProOceanus CO2-Pro instrument mounted on the flowthrough system. This automatic sensor is fitted with an equilibrator made of gas permeable silicone membrane and an internal detection loop with a non-dispersive infrared detector of PPSystems SBA-4 CO2 analyzer. A zero-CO2 baseline is provided for the subsequent measurements circulating the internal gas through a CO2 absorption chamber containing soda lime or Ascarite. The frequency of this automatic zero point calibration was set to be 24 hours. All data recorded during zeroing processes were discarded with the 15-minute data after each calibration. The output of CO2-Pro is the mole fraction of CO2 in the measured water and the pCO2 is obtained using the measured total pressure of the internal wet gas. The fugacity of CO2 (fCO2) in the surface seawater, whose difference with the atmospheric CO2 fugacity is proportional to the air-sea CO2 fluxes, is obtained by correcting the pCO2 for non-ideal CO2 gas concentration according to Weiss (1974). The fCO2 computed using CO2-Pro measurements was corrected to the sea surface condition by considering the temperature effect on fCO2 (Takahashi et al., 1993). The surface seawater observations that were initially estimated with a 15 seconds frequency were averaged every 5-min cycle. The performance of CO2-Pro was adjusted by comparing the sensor outputs against the thermodynamic carbonate calculation of pCO2 using the carbonic system constants of Millero et al. (2006) from the determinations of total inorganic carbon (CT ) and total alkalinity (AT ) in discrete samples collected at sea surface. AT was determined using an automated open cell potentiometric titration (Haraldsson et al. 1997). CT was determined with an automated coulometric titration (Johnson et al. 1985; 1987), using the MIDSOMMA system (Mintrop, 2005). fCO2 data are flagged according to the WOCE guidelines following Pierrot et al. (2009) identifying recommended values and questionable measurements giving additional information about the reasons of the questionability.

Un método de diferencias finitas generalizadas para simular la actividad eléctrica de un tejido cardiaco

Una evolución del método de diferencias finitas ha sido el desarrollo del método de diferencias finitas generalizadas (MDFG) que se puede aplicar a mallas irregulares o nubes de puntos. En este método se emplea una expansión en serie de Taylor junto con una aproximación por mínimos cuadrados móviles (MCM). De ese modo, las fórmulas explícitas de diferencias para nubes irregulares de puntos se pueden obtener fácilmente usando el método de Cholesky. El MDFG-MCM es un método sin malla que emplea únicamente puntos. Una contribución de esta Tesis es la aplicación del MDFG-MCM al caso de la modelización de problemas anisótropos elípticos de conductividad eléctrica incluyendo el caso de tejidos reales cuando la dirección de las fibras no es fija, sino que varía a lo largo del tejido. En esta Tesis también se muestra la extensión del método de diferencias finitas generalizadas a la solución explícita de ecuaciones parabólicas anisótropas. El método explícito incluye la formulación de un límite de estabilidad para el caso de nubes irregulares de nodos que es fácilmente calculable. Además se presenta una nueva solución analítica para una ecuación parabólica anisótropa y el MDFG-MCM explícito se aplica al caso de problemas parabólicos anisótropos de conductividad eléctrica. La evidente dificultad de realizar mediciones directas en electrocardiología ha motivado un gran interés en la simulación numérica de modelos cardiacos. La contribución más importante de esta Tesis es la aplicación de un esquema explícito con el MDFG-MCM al caso de la modelización monodominio de problemas de conductividad eléctrica. En esta Tesis presentamos un algoritmo altamente eficiente, exacto y condicionalmente estable para resolver el modelo monodominio, que describe la actividad eléctrica del corazón. El modelo consiste en una ecuación en derivadas parciales parabólica anisótropa (EDP) que está acoplada con un sistema de ecuaciones diferenciales ordinarias (EDOs) que describen las reacciones electroquímicas en las células cardiacas. El sistema resultante es difícil de resolver numéricamente debido a su complejidad. Proponemos un método basado en una separación de operadores y un método sin malla para resolver la EDP junto a un método de Runge-Kutta para resolver el sistema de EDOs de la membrana y las corrientes iónicas. ABSTRACT An evolution of the method of finite differences has been the development of generalized finite difference (GFD) method that can be applied to irregular grids or clouds of points. In this method a Taylor series expansion is used together with a moving least squares (MLS) approximation. Then, the explicit difference formulae for irregular clouds of points can be easily obtained using a simple Cholesky method. The MLS-GFD is a mesh-free method using only points. A contribution of this Thesis is the application of the MLS-GFDM to the case of modelling elliptic anisotropic electrical conductivity problems including the case of real tissues when the fiber direction is not fixed, but varies throughout the tissue. In this Thesis the extension of the generalized finite difference method to the explicit solution of parabolic anisotropic equations is also given. The explicit method includes a stability limit formulated for the case of irregular clouds of nodes that can be easily calculated. Also a new analytical solution for homogeneous parabolic anisotropic equation has been presented and an explicit MLS- GFDM has been applied to the case of parabolic anisotropic electrical conductivity problems. The obvious difficulty of performing direct measurements in electrocardiology has motivated wide interest in the numerical simulation of cardiac models. The main contribution of this Thesis is the application of an explicit scheme based in the MLS-GFDM to the case of modelling monodomain electrical conductivity problems using operator splitting including the case of anisotropic real tissues. In this Thesis we present a highly efficient, accurate and conditionally stable algorithm to solve a monodomain model, which describes the electrical activity in the heart. The model consists of a parabolic anisotropic partial differential equation (PDE), which is coupled to systems of ordinary differential equations (ODEs) describing electrochemical reactions in the cardiac cells. The resulting system is challenging to solve numerically, because of its complexity. We propose a method based on operator splitting and a meshless method for solving the PDE together with a Runge-Kutta method for solving the system of ODE’s for the membrane and ionic currents.

Lack of agreement between tonometric and gastric juice partial carbon dioxide tension

Our goal was to compare measurement of tonometered saline and gastric juice partial carbon dioxide tension (PCO2). In this prospective observational study, 112 pairs of measurements were simultaneously obtained under various hemodynamic conditions, in 15 critical care patients. Linear regression analysis showed a significant correlation between the two methods of measuring PCO2 (r 2 = 0.43; P < 0.0001). However, gastric juice PCO2 was systematically higher (mean difference 51 mmHg). The 95% limits of agreement were 315 mmHg and the dispersion increased as the values of PCO2 increased. Tonometric and gastric juice PCO2 cannot be used interchangeably. Gastric juice PCO2 measurement should be interpreted with caution.

Partial molar volume, surface area, and hydration changes for equilibrium unfolding and formation of aggregation transition state: High-pressure and cosolute studies on recombinant human IFN-γ

The equilibrium dissociation of recombinant human IFN-γ was monitored as a function of pressure and sucrose concentration. The partial molar volume change for dissociation was −209 ± 13 ml/mol of dimer. The specific molar surface area change for dissociation was 12.7 ± 1.6 nm2/molecule of dimer. The first-order aggregation rate of recombinant human IFN-γ in 0.45 M guanidine hydrochloride was studied as a function of sucrose concentration and pressure. Aggregation proceeded through a transition-state species, N*. Sucrose reduced aggregation rate by shifting the equilibrium between native state (N) and N* toward the more compact N. Pressure increased aggregation rate through increased solvation of the protein, which exposes more surface area, thus shifting the equilibrium away from N toward N*. The changes in partial molar volume and specific molar surface area between the N* and N were −41 ± 9 ml/mol of dimer and 3.5 ± 0.2 nm2/molecule, respectively. Thus, the structural change required for the formation of the transition state for aggregation is small relative to the difference between N and the dissociated state. Changes in waters of hydration were estimated from both specific molar surface area and partial molar volume data. From partial molar volume data, estimates were 25 and 128 mol H2O/mol dimer for formation of the aggregation transition state and for dissociation, respectively. From surface area data, estimates were 27 and 98 mol H2O/mol dimer. Osmotic stress theory yielded values ≈4-fold larger for both transitions.

On some solutions of a functional equation related to the partial sums of the Riemann zeta function

In this paper, we prove that infinite-dimensional vector spaces of α-dense curves are generated by means of the functional equations f(x)+f(2x)+⋯+f(nx)=0, with n≥2, which are related to the partial sums of the Riemann zeta function. These curves α-densify a large class of compact sets of the plane for arbitrary small α, extending the known result that this holds for the cases n=2,3. Finally, we prove the existence of a family of solutions of such functional equation which has the property of quadrature in the compact that densifies, that is, the product of the length of the curve by the nth power of the density approaches the Jordan content of the compact set which the curve densifies.

Mathematical programming model for heat exchanger design through optimization of partial objectives

Mathematical programming can be used for the optimal design of shell-and-tube heat exchangers (STHEs). This paper proposes a mixed integer non-linear programming (MINLP) model for the design of STHEs, following rigorously the standards of the Tubular Exchanger Manufacturers Association (TEMA). Bell–Delaware Method is used for the shell-side calculations. This approach produces a large and non-convex model that cannot be solved to global optimality with the current state of the art solvers. Notwithstanding, it is proposed to perform a sequential optimization approach of partial objective targets through the division of the problem into sets of related equations that are easier to solve. For each one of these problems a heuristic objective function is selected based on the physical behavior of the problem. The global optimal solution of the original problem cannot be ensured even in the case in which each of the sub-problems is solved to global optimality, but at least a very good solution is always guaranteed. Three cases extracted from the literature were studied. The results showed that in all cases the values obtained using the proposed MINLP model containing multiple objective functions improved the values presented in the literature.

The Zeros of Riemann Zeta Partial Sums Yield Solutions to f(x) + f(2x) + · · · + f(nx) = 0

This paper proves that every zero of any n th , n ≥ 2, partial sum of the Riemann zeta function provides a vector space of basic solutions of the functional equation f(x)+f(2x)+⋯+f(nx)=0,x∈R . The continuity of the solutions depends on the sign of the real part of each zero.

An efficient numerical method for highly oscillatory ordinary differential equations /

"Supported in part by the Department of Energy under contract ENERGY/EY-76-S-02-2383, and submitted in partial fulfillment of the requirements of the Graduate College for the degree of doctor of philosophy."

On Newton-iterative methods for the solution of systems of nonlinear equations /

Based on the author's thesis, Yale.

Unified modified divided difference implementation of Adams and BDF formulas /

"March 1980."

Block envelope solution of finite difference systems /

"November, 1975."--T.p.

The use of Chebyshev matrix polynomials in the iterative solution of linear equations compared to the method of successive overrelaxtion /

"(This is being submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics, June 1959.)"