Analytic Properties of the Structure Function for the One-Dimensional One-Component Log–Gas

The structure function S(k; ) for the one-dimensional one-component log–gas is the Fourier transform of the charge–charge, or equivalently the density–density, correlation function. We show that for |k|j in the power series expansion of f(k; ) about k=0 is of the form of a polynomial in /2 of degree j divided by (/2)^j. The bulk of the paper is concerned with calculating these polynomials explicitly up to and including those of degree 9. It is remarked that the small k expansion of S(k; ) for the two-dimensional one-component plasma shares some properties in common with those of the one-dimensional one-component log–gas, but these break down at order k⁸.     

A spectral characterization of KMS states

Let be a state on aC*-dynamical system . For each of the following properties of : (1) is -K MS with respect to for some given , 0<+, (2) is either a KMS state or a ground state, necessary and sufficient conditions are given involving only the spectral subspaces of associated with . The results provide a new insight in the concept of passivity, introduced by W. Pusz and S. L. Woronowicz.Aangesteld navorser N.F.W.O., Belgium, on leave from Katholieke Universiteit Leuven. Research partially supported by N.A.T.O.     

Random surfaces with two-sided constraints: An application of the theory of dominant ground states

We consider some models of classical statistical mechanics which admit an investigation by means of the theory of dominant ground states. Our models are related to the Gibbs ensemble for the multidimensional SOS model with symmetric constraints _x m/2. The main result is that for ₀, where ₀ does not depend onm, the structure of thermodynamic phases in the model is determined by dominant ground states: for an evenm a Gibbs state is unique and for an oddm the number of space-periodic pure Gibbs states is two.     

Fluorescence Probes for Cyclodextrin Interiors

6-Propionyl-2-(dimethylamino)naphthalene (PRODAN) emits two fluorescence bands, at 510 and 435 run, when dissolved in -cyclodextrin (CD) aqueous solutions. The relative contributions of these two bands were found to depend on time and temperature. These emissions are attributed to the inclusion of PRODAN with the dimethylamino group toward the larger and smaller rims inside the -CD cavities, respectively. The first position corresponds to a slightly polar and slightly rigid environment, while the second corresponds to a hydrophobic and rigid environment relative to the aqueous polar bulk. In contrast, PRODAN in either -CD or -CD aqueous solutions emits a single fluorescence band at 525 and 510 nm, respectively. The emission of PRODAN in -CD is similar to that in water and indicates no inclusion at all. In -CD, only one kind of inclusion is possible with the dimethylamino group of PRODAN toward the larger rims of -cavities. These results are supported by fluorescence decay lifetime measurements and are consistent with our previous observations made for 4-dimethylaminobenzonitrile (DMABN) and 4-diethylaminobenzonitrile (DEABN) in - and -CD aqueous solutions [23,24]. Therefore the possibility of twisted intramolecular charge transfer (TICT) state formation in PRODAN in terms of environmental polarity and local free volume of CD cavities is discussed. These observations put PRODAN, DMABN, and other TICT compounds as fluorescence probes for CD interiors.     

К В. Ч. НАГРЕВУ РАЗРЕЖЕННОЙ ПЛАЗМЫ

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An upper bound on the critical temperature for a continuous system with short-range interaction

A classical gas with short-range interaction in the grand canonical ensemble is studied. Ifp(, z) denotes the thermodynamic pressure at inverse temperature and activityz, then it follows from the Mayer expansion thatp(, z) is infinitely differentiable provided andz are sufficiently small. Here it is shown that there exists ₀>0 such thatp(, z) is infinitely differentiable if< ₀ andz>0. One can interpret this result as saying that ( ₀)^–1 is an upper bound on the critical temperature for the system.     

Gentle perturbations

By introducing a specific type of perturbation,A, in the Hamiltonian, we define a class of gently perturbed states, ,A, of a canonical ensemble, . The perturbations are chosen so as to preserve a relationship of the form ,A constant ×. Applications in ergodic theory and phase transitions are described.     

Three-Mode Entangled State Representation of Continuum Variables and Optical Four-Wave Mixing

We establish a new three-mode entangled state representation , of continuum variables, which make up a complete set. Using optical four-wave mixing and a beam splitter transform we can prepare , . Based on , a new number-difference--operational-phase uncertainty relation is established and the corresponding squeezing dynamics is discussed.     

The low-temperature phase of Kac-Ising models

We analyze the low-temperature phase of ferromagnetic Kax-Ising models in dimensionsd2. We show that if the range of interactions is ^–1, then two disjoint translation-invariant Gibbs states exist if the inverse temperature satisfies –1^N, where =d(1–)/(2d+2)(d+1), for any >0. The proof involves the blocking procedure usual for Kac models and also a contour representation for the resulting long-range (almost) continuous-spin system which is suitable for the use of a variant of the Peierls argument.     

Strategies for the synthesis of novel indole alkaloid-based screening libraries for drug discovery

A series of diverse indole-based chemotypes were synthesized from -tetrahydrocarboline (-THC) scaffolds prepared from commercially and readily available tryptamines and -ketoesters. Diversity can be generated within these chemotypes through the following strategies: (a) appendage of substituents to the -THC scaffold, prepared in situ or as a template, through further elaboration and (b) skeletal modifications to the -THC scaffold via ring forming or ring breaking reactions. The strategies described here are amenable to high throughput solution-phase parallel synthesis, providing access to novel indole-based screening libraries for drug discovery.Dedicated to Professor Spyros P. Perlepes     

Exact determination of phase information in spin-polarized neutron specular reflectometry

A comparative study of the magnetic properties of shunted and unshunted two-dimensional Josephson junction arrays (2D-JJA) is presented. Using a single-plaquette approximation of the 2D-JJA model, we were able to successfully fit all our experimental data (for the temperature, AC and DC field dependencies of susceptibility) and demonstrate that the dynamic reentrance of AC susceptibility is directly linked to the value of the Stewart-McCumber parameter C. Based on extensive numerical simulations, a phase diagram C-L is plotted which demarcates the border between the reentrant and non-reentrant behavior in the arrays.     

Electrogravitational induction and rotation

The Faradayan hypothesis of inductive coupling of the electromagnetic and gravitational fields is briefly discussed. An experiment designed to test the hypothesis wherein samples are spun to see if any electrogravitational charge is induced is described. Results of the experiment are reported. They imply the induction of a charge density * for spinning samples that behaves as *=_ma, where _m is the mass density of an element of matter experiencing an acceleration a, and is the coupling coefficient for the hypothetical electrogravitational induction effect. In this experiment, is found to have the value(9.6±3.3)×10 ^–13 statcoulombs/dyne. Tests that seem to rule out explanations of the observed charges in terms of conventional charging mechanisms are considered.     

Новый тип рентгеновс кого спектрографа

. 1', . . .     

Surface Tension of an Ideal Dielectric-Electrolyte Boundary: Exactly Solvable Model

The model under consideration is a semi-infinite two-dimensional two-component plasma (Coulomb gas), stable against bulk collapse for the dimensionless coupling constant <2, in contact with a dielectric wall of dielectric constant =0. The model is mapped onto an integrable sine-Gordon theory with a free Neumann boundary condition. Using recent results on a reflection relationship between the boundary Liouville and sine-Gordon theories, an explicit expression is derived for the surface tension at a rectilinear dielectric – Coulomb gas interface. This expression reproduces the Debye-Hückel 0 limit and the exact result at the bulk collapse border, the free-fermion point =2, where the surface tension keeps a finite value. The surface collapse, identified with the divergence of the surface tension, occurs at =3.     

Allowed β-γ angular correlations induced by magnetic interactions

Allowed - angular correlations from nuclei of paramagnetic ions is considered. It is shown that a magnetic hyperfine interaction creates an anisotropy of the -ray if a static magnetic field is simultaneously present.     

Analysis of steady states for different media in optically pumped sub-millimeter laser

The paper analyses steady states of optically pumped sub-millimeter laser on resonance. The steady state of (=0, ) gives three unstable regions. The steady state curve of ( 0,) varies much by choosing media with different damping rates of the corresponding variables, G_p/K_p and G_a/K_a.     

Betatron-synchrotron resonance in free electron laser

In terms of Bogoliubov's nonlinear theory, the first five betatron-synchrotron resonances of _s=(p q)2K, p/q=1/2, 1, 3/2, 1/3, 2/3 which may occur during laser satulation establishing process have been generally examined. Contrast to previous studies we found that the most dangerous resonance does not take place in the vicinity of _s=2k, but in that of _s=k. The width of region of _s=k is proportional to with (k _w ² /k) remittance, the passing time over the region due to the laser field being amplified is only one pass over the undulator at most and depends on the gain, and the increment of synchrotron amplitude in passing time is proportional to .In summary we conclude that the betatron-synchrotron resonances do not have any significant effect for detrapping off-axis electrons in a practical case.     

Thermodynamic formalism and localization in Lorentz gases and hopping models

The thermodynamic formalism expresses chaotic properties of dynamical systems in terms of the Ruelle pressure (). The inverse-temperature-like variable allows one to scan the structure of the probability distributin in the dynamic phase space. This formalism is applied here to a lorentz lattice gas. where a particle moving on a lattice of sizeL ^d collides with fixed scatterers placed at random locations. Here we give rigorous arguments that the Ruelle pressure in the limit of infinite systems has two branches joining with a slope discontinuity at =1. The low- and high- branches correspond to localization of trajectories on respectively the most chaotic (highest density) region and the most deterministic (lowest density) region, i.e. () is completely controlled by rare fluctuations in the distribution of scatterers on the lattice. and it dose not carry and information on the global structure of the static disorder. As approaches unity from either side, a localization-delocalization transition leads to a state where trajectories are extended and carry information on transprot properties. At finiteL the narrow region around =1 where the trajectories are extended scales as (InL)^–2. where depends on the sign of 1–, ifd>1, and as (L InL)^–1 ifd=1. This result appears to be general for diffusive systems with static disorder, such as random walks in random environments or for the continuous Lorentz gas. Other models of random walks on disordered lattices, showing the same phenomenon, are discussed.     

The phase transition in a general class of Ising-type models is sharp

For a family of translation-invariant, ferromagnetic, one-component spin systems—which includes Ising and ⁴ models—we prove that (i) the phase transition is sharp in the sense that at zero magnetic field the high- and low-temperature phases extend up to a common critical point, and (ii) the critical exponent obeys the mean field bound 1/2. The present derivation of these nonperturbative statements is not restricted to regular systems, and is based on a new differential inequality whose Ising model version isMh+M ³+ M ²M/. The significance of the inequality was recognized in a recent work on related problems for percolation models, while the inequality itself is related to previous results, by a number of authors, on ferromagnetic and percolation models.     

The critical point indices of ferroelectric and ferromagnetic phase transitions

Magnetic transitions are described by the critical indices0,1/3,4/3 while some ferroelectric transitions appear to give0,R~1/2,1. It is pointed out that these two sets of values for the critical indices are allowed by the scaling laws and stability conditions near the phase transitions.The authors thank Prof. R. S. Krishnan for his encouragement and Mr. B. Viswanathan for some discussions. The financial assistance from DAE and CSIR is also acknowledged.