Transport properties of the Lorentz gas: Fourier's law

We investigate the stationary nonequilibrium (heat transporting) states of the Lorentz gas. This is a gas of classical point particles moving in a region gL containing also fixed (hard sphere) scatterers of radiusR. The stationary state considered is obtained by imposing stochastic boundary conditions at the top and bottom of , i.e., a particle hitting one of these walls comes off with a velocity distribution corresponding to temperaturesT ₁ andT ₂ respectively,T ₁ <T ₂. Letting be the average density of the randomly distributed scatterers we show that in the Boltzmann-Grad limit,,R 0 with the mean free path fixed, the stationary distribution of the Lorentz gas converges in theL ¹-norm to the stationary distribution of the corresponding linear Boltzmann equation with the same boundary conditions. In particular, the steady state heat flow in the Lorentz gas converges to that of the linear Boltzmann equation, which is known to behave as (T ₂-T ₁)/L for largeL, whereL is the distance from the bottom to the top wall: i.e., Fourier's law of heat conduction is valid in the limit. The heat flow converges even in probability. Generalizations of our result for scatterers with a smooth potential as well as the related diffusion problem are discussed.Research supported in part by NSF Grant no. Phy 77-22302.On leave of absence from the Fachbereich Physik der Universität, München. Work supported by a DFG fellowship.     

Organomineral sorbents based on clinoptilolite-containing tuffs

The anion-exchange properties of a new organomineral sorbent obtained by modification of clinoptilolite-containing tuffs by polyhexamethyleneguanidine have been studied after different periods of storage (time after synthesis) and numbers of sorption-regeneration cycles. The sorbent can be used as a cation- and an anion-exchanger simultaneously. Selectivity coefficients (exchange constants) for F^–, SO₄ ^2–, and HPO₄ ^2– ionsvs. Cl^– ions on modified clinoptilolite-containing tuffs have been determined. The modification improves the mechanical properties of clinoptilolite tuffs.For part 1, see Ref. 1.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1554–1556, September, 1994.     

Improving the lower detection limit of potentiometric sensors by covalently binding the ionophore to a polymer backbone

The lower detection limit of polymeric membrane ion-selective electrodes (ISEs) is impaired by zero-current ion fluxes through the organic phase. This adverse effect is largely eliminated by covalently attaching the ionophore to a polymer backbone. To this purpose, the Pb²⁺-selective ligand, 4-tert-butylcalix[4] arene-tetrakis(N,N′-dimethylthioacetamide) is substituted on its upper rim by a diol derivative which is subsequently copolymerized with poly(tetrahydrofuran)diol and 2,2,4-trimethylhexamethylene diisocyanate to the corresponding polyurethane. By measurements on sandwich membranes, it is shown that through binding the ionophore to the polymer, the mobility of Pb²⁺ in the ISE membrane is strongly reduced. As a consequence, the response range of such an ISE is extended by several orders of magnitude. This is the case even when using an internal electrolyte that with an ISE based on a mobile ionophore leads to strong deviations from the linear response because of ion uptake from the sample into the membrane or ion release from the membrane into the sample. With a conventional inner filling solution of 10⁻¹ M Pb(NO₃)₂, a lower detection limit of 1.7×10⁻⁹ M Pb²⁺ has been achieved in the presence of 10⁻⁴ M Na⁺.     

Derivation of the transport equation for electrons moving through random impurities

A single (nonrelativistic, spinless) electron subject to a constant external electric field interacts with impurities located on an infinitely extended lattice by a potential of random strength. The random strength is given by a field of Gaussian random variables. We show the existence of the averaged dynamics and prove that in the weak coupling limit, 0, ₂ t= fixed, one obtains the usual transport equation for the velocity distribution.Work supported by a Max Kade Foundation fellowship.On leave of absence of the Fachbereich Physik der Universität München.     

A central limit theorem for age- and density-dependent population processes

Consider a population consisting of one type of individual living in a fixed region with area A. In [8], we constructed a stochastic population model in which the death rate is affected by the age of the individual and the birth rate is affected by the population density P_A(t), i.e., the population size divided by the area A of the given region. In [8], we proposed a continuous deterministic model which in general is a nonlinear Volterra type integral equation and proved that under appropriate conditions the sequence P_A(t) would converge to the solution P(t) of our integral equation in the sense that

$\text{lim}\text{→∞}\text{P}\text{sup}\text{0?s?t}\text{|P}{}_{\mathrm{A}}\text{(s) ? P(s)|>ε}\text{=0}\text{for every}\text{ε > 0}$

.In this paper, we obtain a “central limit theorem” for the random element √A(P_A(t)?P(t)). We prove that under appropriate conditions √A(P_A(t)?P(t)) will converge to a Gaussian process. (See Theorem 3.4 for the explicit formula of this Gaussian process.)     

The spherical limit forn-vector correlations

We investigate then limit of then-vector model single-spin and pairspin correlation functions. In this limit we show that the correlation functions become those of the corresponding spherical model.     

Conducting polymer membranes for low activity potentiometric ion sensing

Conducting polymer (CP) films, used as ion-sensing membranes under open circuit potentiometric conditions, are usually characterised with rather high detection limit, in the range of 10⁻⁴-10⁻⁵ mol dm⁻³. This effect is unfavourable, not only from the point of view of CP applications in potentiometry as ion sensitive membranes, but also when these materials are used as ion-to-electron transducers (solid contacts) for ion-selective electrodes. The theoretical considerations presented underline the crucial role of spontaneous processes of polymer charging/discharging—the source of observed high detection limit of sensors comprising CP layer under zero current conditions. Although the mechanism of occurring process is different from that observed for plastic, solvent polymeric based ion-selective electrodes, the ultimate result—alteration of activity of electrolyte at the membrane/solution interface leading to elevation of the detection limit—is the same.The method of estimation of parameters characterising spontaneous charge transfer processes is presented. The values obtained can be used to calculate the resulting polymer/solution interface activity of electrolyte ions, thus the detection limit of CP membrane can be theoretically predicted.A method of lowering of the detection limit of conducting polymer membranes, applying galvanostatic polarisation to compensate the spontaneous process of polymer charging/discharging, is presented.The experimental results obtained for poly(pyrrole), poly(N-methylpyrrole) and poly(3,4-ethylenedioxythiophene) are in good accordance with predictions of the presented model.     

Enhanced visible light photocatalytic activity of CeO2@Zn0.5Cd0.5S by facile Ce(IV)/Ce(III) cycle

In this study, CeO₂@Zn_0.5Cd_0.5S heterostructure (Ce@ZCS) is synthesized via a simple two-step hydrothermal method. The effect of CeO₂ loading on the visible-light photoactivity of Zn_0.5Cd_0.5S is mainly investigated. It is found that Ce@ZCS shows a 1.9 times activity as high as ZCS for the MB degradation. The improved activity mainly results from the significant enhanced charge separation by CeO₂, in which the electron transfer is obviously promoted by the facile Ce(IV)/Ce(III) cycle. The excited electrons of ZCS is easy to transfer to CeO₂, thus obviously increasing the charge separation of ZCS. The accepted electrons by CeO₂ may easily be captured by the adsorbed O₂ to form O₂⁻, and then O₂⁻ could combine with H⁺/H₂O to form HO₂, and OH. Finally, O₂⁻, h⁺ and OH are confirmed as the major oxidative species in photocatalytic reaction for Ce@ZCS, and a possible photocatalytic mechanism is proposed. The cheap, efficient Ce@ZCS photocatalyst could be applied for practical waste water treatment.     

Static electric properties of LiH: explicitly correlated coupled cluster calculations

Explicitly correlated MBPT-R12 and coupled cluster [up to CCSD(T)-R12] methods have been used in calculations of various (vibrationless) electrical properties for the LiH molecule, including the dipole and quadrupole moments, dipole and quadrupole polarizability tensors, dipole hyperpolarizability tensors, and the second dipole hyperpolarizability tensors. Generally, with extension of the basis set the R12 method did not lead to faster convergence for the calculated properties towards the basis limit. Nevertheless, R12 calculations serve as useful indicators to judge the reliability of the results, and substantially help in determining the accuracy. Results obtained with the 11s8p6d5f/9s8p6d5f basis and CCSD(T)-R12 calculated within this work should be close to the basis set limit. Received: 8 June 1998 / Accepted: 23 July 1998 / Published online: 7 October 1998     

Effects of glucose,glutamine, and malate on the metabolism of spodoptera frugiperda clone 9 (sf9) cells

Optimal design and operation of bioreactors for insect cell culture is facilitated by functional relations providing quantitative information on cellular metabolite consumption kinetics, as well as on the specific cell growth rates (μ_G). Initial specific consumption rates of glucose, malate, and oxygen, and associated changes in μ_G, were measured forSpodoptera frugiperda clone 9 (Sf9) cells grown in batch suspension culture in medium containing 7–35 mM glucose, 0–16 mM malate, and 4–16 mM glutamine. The initial specific glucose consumption rate (q _G ) could be described by a modified Michaelis-Menten equation treating malate as a “competitive” inhibitorK ₁ = 6.5 mM) and glutamine as a “noncompetitive” inhibitorK _I = 14 mM) ofq _G , with aK _m of 7.1 mM for glucose. All three carbon sources were found to increase μ_G in a saturable manner, and a modified Monod equation was employed to describe this relationship (μ_Gmax = 0.047 h^-1). The initial specific oxygen consumption rate (q_O2) in Sf9 cells could be related to μ_G by the maintenance energy model, and it was calculated that, under typical culture conditions, about 15–20% of the cellular energy demand comes from functions not related to growth. Fitted parameters in mathematical expression for μg: K₄, Monod constant for glucose (mM); K₅, modified Monod constant for malate (mM); K₆, Monod constant for glutamine (mM); m_o2, specific consumption rate of oxygen by the cells under zero-growth conditions (nmol/cell/h); q_F, initial specific fumarate production rate (nmol/cell/ h);q _G , initial specific glucose consumption rate (nmol/cell/h); q_Gmax, maximum initial specific glucose consumption rate (nmol/cell/h);q _M , initial specific malate consumption rate (nmol/cell/h); q_o2, initial specific oxygen consumption rate (nmol/cell/h); Y_o2, cell yield on oxygen (cells/nmol); μ, initial specific cell growth rate (h^-1); μ_g, initial specific cell growth rate (h^-1); μG_max, maximum initial specific cell growth rate (h^-1).