Semi-Classical Mechanics in Phase Space: A Study of Wigner's Function

We explore the semi-classical structure of the Wigner functions ($\Psi $(q, p)) representing bound energy eigenstates $|\psi \rangle $ for systems with f degrees of freedom. If the classical motion is integrable, the classical limit of $\Psi $ is a delta function on the f-dimensional torus to which classical trajectories corresponding to ($|\psi \rangle $) are confined in the 2f-dimensional phase space. In the semi-classical limit of ($\Psi $ ($\hslash $) small but not zero) the delta function softens to a peak of order ($\hslash ^{-\frac{2}{3}f}$) and the torus develops fringes of a characteristic 'Airy' form. Away from the torus, $\Psi $ can have semi-classical singularities that are not delta functions; these are discussed (in full detail when f = 1) using Thom's theory of catastrophes. Brief consideration is given to problems raised when ($\Psi $) is calculated in a representation based on operators derived from angle coordinates and their conjugate momenta. When the classical motion is non-integrable, the phase space is not filled with tori and existing semi-classical methods fail. We conjecture that (a) For a given value of non-integrability parameter ($\epsilon $), the system passes through three semi-classical regimes as ($\hslash $) diminishes. (b) For states ($|\psi \rangle $) associated with regions in phase space filled with irregular trajectories, ($\Psi $) will be a random function confined near that region of the 'energy shell' explored by these trajectories (this region has more than f dimensions). (c) For ($\epsilon \neq $0, $\hslash $) blurs the infinitely fine classical path structure, in contrast to the integrable case ($\epsilon $ = 0, where $\hslash $ )imposes oscillatory quantum detail on a smooth classical path structure.

The virial expansion of a classical interacting system

We consider N particles interacting pairwise by an inverse square potential in one dimension (Calogero-Sutherland-Moser model). For a system placed in a harmonic trap, its classical partition function for the repulsive regime is recognised in the literature. We start by presenting a concise re-derivation of this result. The equation of state is then calculated both for the trapped and the homogeneous gas. Finally, the classical limit of Wu's distribution function for fractional exclusion statistics is obtained and we re-derive the classical virial expansion of the homogeneous gas using this distribution function.

Binding and regulatory properties of phosphofructokinase from swine kidney

The influence of fructose 2,6-bisphosphate on the activation of purified swine kidney phosphofructokinase as a function of the concentration of fructose 6P, ATP and citrate was investigated. The purified enzyme was nearly completely inhibited in the presence of 2 mM ATP. The addition of 20 nM fructose 2,6-P2 reversed the inhibition and restored more than 80% of the activity. In the absence of fructose 2,6-P2 the reaction showed a sigmoidal dependence on fructose-6-phosphate. The addition of 10 nM fructose 2,6-bisphosphate decreased the K0.5 for fructose 6-phosphate from 3 mM to 0.4 mM in the presence of 1.5 mM ATP. These results clearly show that fructose 2,6-bisphosphate increases the affinity of the enzyme for fructose 6-phosphate and decreases the inhibitory effect of ATP. The extent of inhibition by citrate was also significantly decreased in the presence of fructose 2,6-phosphate. The influence of various effectors of phosphofructokinase on the binding of ATP and fructose 6-P to the enzyme was examined in gel filtration studies. It was found that kidney phosphofructokinase binds 5.6 moles of fructose 6-P per mole of enzyme, which corresponds to about one site per subunit of tetrameric enzyme. The KD for fructose 6-P was 13 microM and in the presence of 0.5 mM ATP it increased to 27 microM. The addition of 0.3 mM citrate also increased the KD for fructose 6-P to about 40 microM. AMP, 10 microM, decreased the KD to 5 microM and the addition of fructose 2,6-phosphate decreased the KD for fructose 6-P to 0.9 microM. The addition of these compounds did not effect the maximal amount of fructose 6-P bound to the enzyme, which indicated that the binding site for these compounds might be near, but was not identical to the fructose 6-P binding site. The enzyme bound a maximum of about 12.5 moles of ATP per mole, which corresponds to 3 moles per subunit. The KD of the site with the highest affinity for ATP was 4 microM, and it increased to 15 microM in the presence of fructose 2,6-bisphosphate. The addition of 50 microM fructose 1,6-bisphosphate increased the KD for ATP to 5.9 microM. AMP increased the KD to 5.9 microM whereas 0.3 mM citrate decreased the KD for ATP to about 2 microM.(ABSTRACT TRUNCATED AT 400 WORDS).

Hay fever: An underappreciated and chronic disease

Allergic rhinitis continues to be a significant chronic disease that affects younger, usually healthier people, with considerable impacts on school performance and work productivity. Symptom-directed treatment is usually sufficient but specific immunotherapy should be considered in severely affected patients.

Hanle-Zeeman redistribution matrix. I. Classical theory expressions in the laboratory frame

Polarized scattering in spectral lines is governed by a 4; 4 matrix that describes how the Stokes vector is scattered and redistributed in frequency and direction. Here we develop the theory for this redistribution matrix in the presence of magnetic fields of arbitrary strength and direction. This general magnetic field case is called the Hanle- Zeeman regime, since it covers both of the partially overlapping weak- and strong- field regimes in which the Hanle and Zeeman effects dominate the scattering polarization. In this general regime, the angle-frequency correlations that describe the so-called partial frequency redistribution (PRD) are intimately coupled to the polarization properties. We develop the theory for the PRD redistribution matrix in this general case and explore its detailed mathematical properties and symmetries for the case of a J = 0 -> 1 -> 0 scattering transition, which can be treated in terms of time-dependent classical oscillator theory. It is shown how the redistribution matrix can be expressed as a linear superposition of coherent and noncoherent parts, each of which contain the magnetic redistribution functions that resemble the well- known Hummer- type functions. We also show how the classical theory can be extended to treat atomic and molecular scattering transitions for any combinations of quantum numbers.

A semi-classical model of the electron containing tachyonic matter

It is shown that the mass of the electron could be conceived as the energy associated with its spinning motion and the angular velocity is such that the linear velocities at the surface exceed the velocity of light; this in fact accounts for its stability against the centrifugal forces in the core region.

Molecular theory of solvation and solvation dynamics of a classical ion in a dipolar liquid

A microscopic theory of equilibrium solvation and solvation dynamics of a classical, polar, solute molecule in dipolar solvent is presented. Density functional theory is used to explicitly calculate the polarization structure around a solvated ion. The calculated solvent polarization structure is different from the continuum model prediction in several respects. The value of the polarization at the surface of the ion is less than the continuum value. The solvent polarization also exhibits small oscillations in space near the ion. We show that, under certain approximations, our linear equilibrium theory reduces to the nonlocal electrostatic theory, with the dielectric function (c(k)) of the liquid now wave vector (k) dependent. It is further shown that the nonlocal electrostatic estimate of solvation energy, with a microscopic c(k), is close to the estimate of linearized equilibrium theories of polar liquids. The study of solvation dynamics is based on a generalized Smoluchowski equation with a mean-field force term to take into account the effects of intermolecular interactions. This study incorporates the local distortion of the solvent structure near the ion and also the effects of the translational modes of the solvent molecules.The latter contribution, if significant, can considerably accelerate the relaxation of solvent polarization and can even give rise to a long time decay that agrees with the continuum model prediction. The significance of these results is discussed.

A simple classical approach for the melting temperature of inert-gas nanoparticles

Like the metal and semiconductor nanoparticles, the melting temperature of free inert-gas nanoparticles decreases with decreasing size. The variation is linear with the inverse of the particle size for large nanoparticles and deviates from the linearity for small nanoparticles. The decrease in the melting temperature is slower for free nanoparticles with non-wetting surfaces, while the decrease is faster for nanoparticles with wetting surfaces. Though the depression of the melting temperature has been reported for inert-gas nanoparticles in porous glasses, superheating has also been observed when the nanoparticles are embedded in some matrices. By using a simple classical approach, the influence of size, geometry and the matrix on the melting temperature of nanoparticles is understood quantitatively and shown to be applicable for other materials. It is also shown that the classical approach can be applied to understand the size-dependent freezing temperature of nanoparticles.

Hantavirus glycoprotein GN in virion assembly and regulation of interferon response

Hantaviruses have a tri-segmented negative-stranded RNA genome. The S segment encodes the nucleocapsid protein (N), M segment two glycoproteins, Gn and Gc, and the L segment the RNA polymerase. Gn and Gc are co-translationally cleaved from a precursor and targeted to the cis-Golgi compartment. The Gn glycoprotein consists of an external domain, a transmembrane domain and a C-terminal cytoplasmic domain. In addition, the S segment of some hantaviruses, including Tula and Puumala virus, have an open reading frame (ORF) encoding a nonstructural potein NSs that can function as a weak interferon antagonist. The mechanisms of hantavirus-induced pathogenesis are not fully understood but it is known that both hemorrhagic fever with renal syndrome (HFRS) and hantavirus (cardio) pulmonary syndrome (HCPS) share various features such as increased capillary permeability, thrombocytopenia and upregulation of TNF-. Several hantaviruses have been reported to induce programmed cell death (apoptosis), such as TULV-infected Vero E6 cells which is known to be defective in interferon signaling. Recently reports describing properties of the hantavirus Gn cytoplasmic tail (Gn-CT) have appeared. The Gn-CT of hantaviruses contains animmunoreceptor tyrosine-based activation motif (ITAM) which directs receptor signaling in immune and endothelial cells; and contain highly conserved classical zinc finger domains which may have a role in the interaction with N protein. More functions of Gn protein have been discovered, but much still remains unknown. Our aim was to study the functions of Gn protein from several aspects: synthesis, degradation and interaction with N protein. Gn protein was reported to inhibit interferon induction and amplication. For this reason, we also carried out projects studying the mechanisms of IFN induction and evasion by hantavirus. We first showed degradation and aggresome formation of the Gn-CT of the apathogenic TULV. It was reported earlier that the degradation of Gn-CT is related to the pathogenicity of hantavirus. We found that the Gn-CT of the apathogenic hantaviruses (TULV, Prospect Hill virus) was degraded through the ubiquitin-proteasome pathway, and TULV Gn-CT formed aggresomes upon treatment with proteasomal inhibitor. Thus the results suggest that degradation and aggregation of the Gn-CT may be a general property of most hantaviruses, unrelated to pathogenicity. Second, we investigated the interaction of TULV N protein and the TULV Gn-CT. The Gn protein is located on the Golgi membrane and its interaction with N protein has been thought to determine the cargo of the hantaviral ribonucleoprotein which is an important step in virus assembly, but direct evidence has not been reported. We found that TULV Gn-CT fused with GST tag expressed in bacteria can pull-down the N protein expressed in mammalian cells; a mutagenesis assay was carried out, in which we found that the zinc finger motif in Gn-CT and RNA-binding motif in N protein are indispensable for the interaction. For the study of mechanisms of IFN induction and evasion by Old World hantavirus, we found that Old World hantaviruses do not produce detectable amounts of dsRNA in infected cells and the 5 -termini of their genomic RNAs are monophosphorylated. DsRNA and tri-phosphorylated RNA are considered to be critical activators of innate immnity response by interacting with PRRs (pattern recognition receptors). We examined systematically the 5´-termini of hantavirus genomic RNAs and the dsRNA production by different species of hantaviruses. We found that no detectable dsRNA was produced in cells infected by the two groups of the old world hantaviruses: Seoul, Dobrava, Saaremaa, Puumala and Tula. We also found that the genomic RNAs of these Old World hantaviruses carry 5´-monophosphate and are unable to trigger interferon induction. The antiviral response is mainly mediated by alpha/beta interferon. Recently the glycoproteins of the pathogenic hantaviruses Sin Nombre and New York-1 viruses were reported to regulate cellular interferon. We found that Gn-CT can inhibit the induction of IFN activation through Toll-like receptor (TLR) and retinoic acid-inducible gene I-like RNA helicases (RLH) pathway and that the inhibition target lies at the level of TANK-binding kinase 1 (TBK-1)/ IKK epislon complex and myeloid differentiation primary response gene (88) (MyD88) / interferon regulatory factor 7 (IRF-7) complex.

Learning Challenges in Biogas Production for Sustainability : An activity theoretical study of a network from a swine industry chain

This study is about the challenges of learning in the creation and implementation of new sustainable technologies. The system of biogas production in the Programme of Sustainable Swine Production (3S Programme) conducted by the Sadia food processing company in Santa Catarina State, Brazil, is used as a case example for exploring the challenges, possibilities and obstacles of learning in the use of biogas production as a way to increase the environmental sustainability of swine production. The aim is to contribute to the discussion about the possibilities of developing systems of biogas production for sustainability (BPfS). In the study I develop hypotheses concerning the central challenges and possibilities for developing systems of BPfS in three phases. First, I construct a model of the network of activities involved in the BP for sustainability in the case study. Next, I construct a) an idealised model of the historically evolved concepts of BPfS through an analysis of the development of forms of BP and b) a hypothesis of the current central contradictions within and between the activity systems involved in BP for sustainability in the case study. This hypothesis is further developed through two actual empirical analyses: an analysis of the actors senses in taking part in the system, and an analysis of the disturbance processes in the implementation and operation of the BP system in the 3S Programme. The historical analysis shows that BP for sustainability in the 3S Programme emerged as a feasible solution for the contradiction between environmental protection and concentration, intensification and specialisation in swine production. This contradiction created a threat to the supply of swine to the food processing company. In the food production activity, the contradiction was expressed as a contradiction between the desire of the company to become a sustainable company and the situation in the outsourced farms. For the swine producers the contradiction was expressed between the contradictory rules in which the market exerted pressure which pushed for continual increases in scale, specialisation and concentration to keep the production economically viable, while the environmental rules imposed a limit to this expansion. Although the observed disturbances in the biogas system seemed to be merely technical and localised within the farms, the analysis proposed that these disturbances were formed in and between the activity systems involved in the network of BPfS during the implementation. The disturbances observed could be explained by four contradictions: a) contradictions between the new, more expanded activity of sustainable swine production and the old activity, b) a contradiction between the concept of BP for carbon credits and BP for local use in the BPfS that was implemented, c) contradictions between the new UNFCCC1 methodology for applying for carbon credits and the small size of the farms, and d) between the technologies of biogas use and burning available in the market and the small size of the farms. The main finding of this study relates to the zone of proximal development (ZPD) of the BPfS in Sadia food production chain. The model is first developed as a general model of concepts of BPfS and further developed here to the specific case of the BPfS in the 3S Programme. The model is composed of two developmental dimensions: societal and functional integration. The dimension of societal integration refers to the level of integration with other activities outside the farm. At one extreme, biogas production is self-sufficient and highly independent and the products of BP are consumed within the farm, while at the other extreme BP is highly integrated in markets and networks of collaboration, and BP products are exchanged within the markets. The dimension of functional integration refers to the level of integration between products and production processes so that economies of scope can be achieved by combining several functions using the same utility. At one extreme, BP is specialised in only one product, which allows achieving economies of scale, while at the other extreme there is an integrated production in which several biogas products are produced in order to maximise the outcomes from the BP system. The analysis suggests that BP is moving towards a societal integration, towards the market and towards a functional integration in which several biogas products are combined. The model is a hypothesis to be further tested through interventions by collectively constructing the new proposed concept of BPfS. Another important contribution of this study refers to the concept of the learning challenge. Three central learning challenges for developing a sustainable system of BP in the 3S Programme were identified: 1) the development of cheaper and more practical technologies of burning and measuring the gas, as well as the reduction of costs of the process of certification, 2) the development of new ways of using biogas within farms, and 3) the creation of new local markets and networks for selling BP products. One general learning challenge is to find more varied and synergic ways of using BP products than solely for the production of carbon credits. Both the model of the ZPD of BPfS and the identified learning challenges could be used as learning tools to facilitate the development of biogas production systems. The proposed model of the ZPD could be used to analyse different types of agricultural activities that face a similar contradiction. The findings could be used in interventions to help actors to find their own expansive actions and developmental projects for change. Rather than proposing a standardised best concept of BPfS, the idea of these learning tools is to facilitate the analysis of local situations and to help actors to make their activities more sustainable.

Activation barriers for d.c. conductivity in ionic glasses: Classical calculations using the small-cluster approximation

A small-cluster approximation has been used to calculate the activation barriers for the d.c. conductivity in ionic glasses. The main emphasis of this approach is on the importance of the hitherto ignored polarization energy contribution to the total activation energy. For the first time it has been demonstrated that the d.c. conductivity activation energy can be calculated by considering ionic migration to a neighbouring vacancy in a smali cluster of ions consisting of face-sharing anion polyhedra. The activation energies from the model calculations have been compared with the experimental values in the case of highly modified lithium thioborate glasses.

E. C. G. Sudarshan and Symmetry in Classical Dynamics, Optics and Quantum Mechanics

We review work initiated and inspired by Sudarshan in relativistic dynamics, beam optics, partial coherence theory, Wigner distribution methods, multimode quantum optical squeezing, and geometric phases. The 1963 No Interaction Theorem using Dirac's instant form and particle World Line Conditions is recalled. Later attempts to overcome this result exploiting constrained Hamiltonian theory, reformulation of the World Line Conditions and extending Dirac's formalism, are reviewed. Dirac's front form leads to a formulation of Fourier Optics for the Maxwell field, determining the actions of First Order Systems (corresponding to matrices of Sp(2,R) and Sp(4,R)) on polarization in a consistent manner. These groups also help characterize properties and propagation of partially coherent Gaussian Schell Model beams, leading to invariant quality parameters and the new Twist phase. The higher dimensional groups Sp(2n,R) appear in the theory of Wigner distributions and in quantum optics. Elegant criteria for a Gaussian phase space function to be a Wigner distribution, expressions for multimode uncertainty principles and squeezing are described. In geometric phase theory we highlight the use of invariance properties that lead to a kinematical formulation and the important role of Bargmann invariants. Special features of these phases arising from unitary Lie group representations, and a new formulation based on the idea of Null Phase Curves, are presented.

Freezing of classical fluids in a quenched random potential

The phase diagram of a hard-sphere fluid in the presence of a random pinning potential is studied analytically and numerically. In the analytic work, replicas are introduced for averaging over the quenched disorder, and the hypernetted chain approximation is used to calculate density correlations in the replicated liquid. The freezing transition of the liquid into a nearly crystalline state is studied using a density-functional approach, and the liquid to glass transition is studied using a phenomenological replica symmetry breaking approach. In the numerical work, local minima of a discretized version of the Ramakrishnan-Yussouff free-energy functional are located and the phase diagram in the density-disorder plane is obtained from an analysis of the relative stability of these minima. Both approaches lead to similar results for the phase diagram. The first-order liquid to crystalline solid transition is found to change to a continuous liquid to glass transition as the strength of the disorder is increased above a threshold value.