Rate processes with dynamical disorder: a direct variational approach

Using path integral approach, we develop variational approximations to the calculation of survival probability for rate processes with dynamical disorder. We derive both upper and lower bounds to the survival probability using Jensen's inequality. The inequalities involve the use of a trial action for which the path integrals can be evaluated exactly. Any parameter in the trial action can be varied to optimize the bounds. We have also derived a lower bound to the rate of the process. As a simple illustration, we apply the method to the problem of a particle undergoing Brownian motion in a harmonic potential well, in the presence of a delta function sink, for which one can calculate the exact survival probability numerically. The calculation confirms the two inequalities. The method should be very useful in similar but more complex problems where even numerical solution is not possible.     

Acidity of a Cu-bound histidine in the binuclear center of cytochrome C oxidase

Cytochrome c oxidase (CcO) is a crucial enzyme in the respiratory chain. Its function is to couple the reduction of molecular oxygen, which takes place in the Fea3-CuB binuclear center, to proton translocation across the mitochondrial membrane. Although several high-resolution structures of the enzyme are known, the molecular basis of proton pumping activation and its mechanism remain to be elucidated. We examine a recently proposed scheme (J. Am. Chem. Soc. 2004, 126, 1858; FEBS Lett. 2004, 566, 126) that involves the deprotonation of the CuB-bound imidazole ring of a histidine (H291 in mammalian CcO) as a key element in the proton pumping mechanism. The central feature of that proposed mechanism is that the pKa values of the imidazole vary significantly depending on the redox state of the metals in the binuclear center. We use density functional theory in combination with continuum electrostatics to calculate the pKa values, successively in bulk water and within the protein, of the Cu-bound imidazole in various Cu- and Cu-Fe complexes. From pKas in bulk water, we derived a value of -266.34 kcal.mol(-1) for the proton solvation free energy (Delta). This estimate is in close agreement with the experimental value of -264.61 kcal.mol(-1) (J. Am. Chem. Soc. 2001, 123, 7314), which reinforces the conclusion that Delta is more negative than previous values used for pKa calculations. Our approach, on the basis of the study of increasingly more detailed models of the CcO binuclear center at different stages of the catalysis, allows us to examine successively the effect of each of the two metals' redox states and of solvation on the acidity of imidazole, whose pKa is approximately 14 in bulk water. This analysis leads to the following conclusions: first, the effect of Cu ligation on the imidazole acidity is negligible regardless of the redox state of the metal. Second, results obtained for Cu-Fe complexes in bulk water indicate that Cu-bound imidazole pKa values lie within the range of 14.8-16.6 throughout binuclear redox states corresponding to the catalytic cycle, demonstrating that the effect of the Fe oxidation states is also negligible. Finally, the low-dielectric CcO proteic environment shifts the acid-base equilibrium toward a neutral imidazole, further increasing the corresponding pKa values. These results are inconsistent with the proposed role of the Cu-bound histidine as a key element in the pumping mechanism. Limitations of continuum solvation models in pKa calculations are discussed.     

The Kolkata Paise Restaurant problem and resource utilization

We study the dynamics of the “Kolkata Paise Restaurant problem”. The problem is the following: In each period, N agents have to choose between N restaurants. Agents have a common ranking of the restaurants. Restaurants can only serve one customer. When more than one customer arrives at the same restaurant, one customer is chosen at random and is served; the others do not get the service. We first introduce the one-shot versions of the Kolkata Paise Restaurant problem which we call one-shot KPR games. We then study the dynamics of the Kolkata Paise Restaurant problem (which is a repeated game version of any given one shot KPR game) for large N. For statistical analysis, we explore the long time steady state behavior. In many such models with myopic agents we get under-utilization of resources, that is, we get a lower aggregate payoff compared to the social optimum. We study a number of myopic strategies, focusing on the average occupation fraction of restaurants.     

General derivation of the total electromagnetic cross sections for an arbitrary particle

This work concerns a common problem in electromagnetic scattering; calculation of the total scattering, extinction, and absorption cross sections for an arbitrary particle. Typical expressions for the cross sections are obtained in terms of the vector spherical wave function expansions for the incident and scattered waves. The unique aspect of this work is that the derivation is carried out specifically without use of the far-field zone approximation. The resulting expressions, valid at any distance, exactly match those obtained from the far-field approximation. This demonstrates that the cross sections are independent of the distance from the particle at which they are calculated as one would expect from energy conservation. Numerical simulations of the near and far-field zone energy flows due to a spherical particle are presented to illustrate several implications of this result.     

Computer modeling of MWIR single heterojunction photodetector based on mercury cadmium telluride

In the present paper, an abrupt heterojunction photodetector based on Hg_1 − xCd_xTe (MCT) has been simulated theoretically for mid-infrared applications. A semi-analytical simulation of the device has been carried out in order to study the performance ratings of the photodetector for operation at room temperature. The energy band diagram, carrier concentration, electric field profile, dark current, resistance–area product, quantum efficiency and detectivity have been calculated and optimized as a function of different parameters such as device thickness, applied reverse voltage and operating wavelength. The effect of energy band offsets in conduction and valance band on the transportation of minority carriers has been studied. The influences of doping concentration, electron affinity gradient and the p–n junction position within heterostructure on potential barrier have been analyzed. The optical characterization has been carried out in respect of quantum efficiency, and detectivity of the heterojunction photodetector. In present model the Johnson–Nyquist and shot noise has been considered in calculation of detectivity. The simulated results has been compared and contrasted with the available experimental results. Results of our analytical-cum-simulation study reveal that under suitable biasing condition, the photodetector offers a dark current, I_D ≈ 6.5 × 10⁻¹² A, a zero-bias resistance–area product, R₀A ≈ 11.3 Ω m², quantum efficiency, η ≈ 78%, NEP = 2 × 10⁻¹² W Hz^1/2 and detectivity D^* ≈ 4.7 × 10¹⁰ mHz^1/2/W.     

Electrical characterisation of phosphorus-doped ZnO thin films grown by pulsed laser deposition

Phosphorus-doped ZnO films were grown by pulsed laser deposition using a ZnO:P₂O₅-doped target as the phosphorus source with the aim of producing p-type ZnO material. ZnO:P layers (with phosphorus concentrations of between 0.01 to 1 wt%) were grown on a pure ZnO buffer layer. The electrical properties of the films were characterised from temperature dependent Hall-effect measurements. The samples typically showed weak n-type conduction in the dark, with a resistivity of 70 Ω cm, a Hall mobility of μ_n0.5 cm² V ⁻¹ s⁻¹ and a carrier concentration of n3×10¹⁷ cm⁻³ at room temperature. After exposure to an incandescent light source, the samples underwent a change in conduction from n- to p-type, with an increase in mobility and decrease in concentration for temperatures below 300 K.     

Singlet-Higgs-Boson signals at hadron colliders

Many extensions of the Standard Model includeSU(2) _L ×U(1) _Y singlet higgs bosons,h ⁰, and also vector-like fermions which couple to it. The production and detection possibilities of such singlet neutral scalars at hadron colliders are considered for different scenarios of vectorlike fermions. We find that for some values of masses and couplings, detection at the CERN large hadron collider (LHC) appears to be a distinct possibility, while at the Fermilab Tevatron upgrade theh ⁰ might be observed only in very favourable circumstances.