Diffusing wave spectroscopy of dense colloids: Liquid,crystal and glassy states

Using intensity autocorrelation of multiply scattered light, we show that the increase in interparticle interaction in dense, binary colloidal fluid mixtures of particle diameters 0.115μm and 0.089μm results in freezing into a crystalline phase at volume fractionφ of 0.1 and into a glassy state atφ=0.2. The functional form of the field autocorrelation functiong ⁽¹⁾(t) for the binary fluid phase is fitted to exp[−γ(6k ₀ ² D _eff t)^1/2] wherek ₀ is the magnitude of the incident light wavevector andγ is a parameter inversely proportional to the photon transport mean free pathl*. TheD _eff is thel* weighted average of the individual diffusion coefficients of the pure species. Thel* used in calculatingD _eff was computed using the Mie theory. In the solid (crystal or glass) phase, theg ⁽¹⁾(t) is fitted (only with a moderate success) to exp[−γ(6k ₀ ² W(t))^1/2] where the mean-squared displacementW(t) is evaluated for a harmonically bound overdamped Brownian oscillator. It is found that the fitted parameterγ for both the binary and monodisperse suspensions decreases significantly with the increase of interparticle interactions. This has been justified by showing that the calculated values ofl* in a monodisperse suspension using Mie theory increase very significantly with the interactions incorporated inl* via the static structure factor.     

A rigorous theory of finite-size scaling at first-order phase transitions

A large class of classical lattice models describing the coexistence of a finite number of stable states at low temperatures is considered. The dependence of the finite-volume magnetizationM _per(h, L) in cubes of sizeL ^d under periodic boundary conditions on the external fieldh is analyzed. For the case where two phases coexist at the infinite-volume transition pointh _t , we prove that, independent of the details of the model, the finite-volume magnetization per lattice site behaves likeM _per(h _t )+M tanh[ML ^d (h–h_t)] withM _per(h) denoting the infinite-volume magnetization and M=1/2[M _per(h _t +0)–M _per(h _t –0)]. Introducing the finite-size transition pointh _m (L) as the point where the finite-volume susceptibility attains the maximum, we show that, in the case of asymmetric field-driven transitions, its shift ish _t –h _m (L)=O(L ^–2d ), in contrast to claims in the literature. Starting from the obvious observation that the number of stable phases has a local maximum at the transition point, we propose a new way of determining the pointh _t from finite-size data with a shift that is exponentially small inL. Finally, the finite-size effects are discussed also in the case where more than two phases coexist.On leave from: Institut für Theoretische Physik, FU-Berlin, D-1000 Berlin 33, Federal Republic of Germany.     

Feldgleichungen der TREDERschen Gravitationstheorie,die aus einem Variationsprinzip ableitbar sind. I

In the frame work of TREDER 's gravitational theory we consider two classes of field equations which are derivable from two classes of LAGRANGE ian densities Ω⁽¹⁾(ω₁, ω₂), Ω⁽²⁾(s?₁, s?₂). ω₁, ω₂; s?₁, s?₂ are parameters. Ω⁽²⁾(ω₁, ω₂) gives us field equations which are up to the post-NEWTON ian approximation in the sense of NORDTVEDT , THORNE and WILL equivalent to the field equations given by BRANS and DICKE . For ω₂ = ?1 ?2ω₁ field equations follow from Ω⁽¹⁾(ω₁, ?1 ?2ω₁) which are in the above mentioned sense of post-NEWTON ian approximation equivalent to EINSTEIN 's equations. The field equations following from Ω⁽¹⁾(ω₁, ω₂) have a cosmological model with the well known cosmological singularities for T → ± ∞ in case that ω₁/(1 +3ω₁ +ω₂) ? γ > 0. For ω₁/(1 +3ω₁ +ω₂) ≤ 0 cosmological models with no cosmological singularities exist. From Ω⁽²⁾(s?₁, s?₂) we obtain field equations which at the best give us perihelion rotation 7% above EINSTEIN 's value and light deflection 7% below the corresponding EINSTEIN 's value. But in that case we are able to show the existence of a cosmological model without any cosmological singularity.     

Indirect Analytic Representation of Foucault's Pendulum

A complex representation of the equations of motion of the Foucault's pendulum is considered and the inverse problem is solved to derive an indirect analytic representation. Both real L _R ⁽ⁱ⁾ and imaginary L _I ⁽ⁱ⁾ parts of the derived complex valued Lagrangian are found to reproduce the equations of motion via the Euler-Lagrange equations. The expressions for L _R ⁽ⁱ⁾ and L _I ⁽ⁱ⁾ are not connected by a gauge term thereby forming a set of inequivalent Lagrangians. In an appropriate limit L _I ⁽ⁱ⁾ is found to reproduce the Lagrangian obtained by implementing the usual Coriolis theorem while in some other limit L _R ⁽ⁱ⁾ and L _I ⁽ⁱ⁾ give the indirect and the direct analytic representations for a set of two uncoupled harmonic oscillators.     

T-band phenomena in 183Re

Abstact: High-spin states in ¹⁸³Re have been studied using the ¹⁷⁶Yb(¹¹B,4n) reaction at 52 and 57 MeV. Two high-K bands have been observed directly by a time-correlated γ-γ coincidence measurement. One of the bands is built on an isomeric K ^π=(25/2)⁺ state at E _x= 1908 keV with a half-life of 0.82(2) ms. The other band, assigned as K ^π=(29/2)⁻ at E _x= 2739 keV, decays to the (25/2)⁺ band. These bands are interpreted as three-quasiparticle structures, π(5/2)⁺[402] &⊗ν(9/2)⁺[624] ⊗ν(11/2)⁺[615] for the (25/2)⁺ band and π(9/2)⁻[514] ⊗ν(9/2)⁺[624] ⊗ν(11/2)⁺[615] for the (29/2)⁻ band. The K ^π= (29/2)⁻ band becomes strongly Coriolis mixed with increasing spin and is gradually changing into a low-K s-band structure. Received: 20 April 1998     

β-Relaxation in polymethylacrylate studied by light scattering

Summary The relaxation processes of glass-forming polymethylacrylate have been studied in a wide temperature range above the glass transition temperatureT _g by means of light scattering measurements. Experimental spectra give evidence of a self-similar behaviourI(ω) ∝ ω^−(1−a) over a spectral range of 2–3 decades, consistent with the predictions of the mode-coupling theory. Different from the prediction of the theory, the value ofa is strongly temperature dependent. This behaviour has been attributed to the presence of a slow secondary relaxation located in the GHz frequency region, whose strength progressively increases with temperature. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Solution of functional equations of restricted An−1(1) fused lattice models

Functional equations, in the form of fusion hierarchies, are studied for the transfer matrices of the fused restricted A_n−1⁽¹⁾ lattice models of Jimbo, Miwa and Okado. Specifically, these equations are solved analytically for the finite-size scaling spectra, central charges and some conformal weights. The results are obtained in terms of Rogers dilogarithm and correspond to coset conformal field theories based on the affine Lie algebra A_n−1⁽¹⁾ with GKO pair A_n−1⁽¹⁾ ⊕ A_n−1⁽¹⁾ ⊃ A_n−1⁽¹⁾.     

Observation of transitions involving core-excited states in Ar III and Ar IV and high-lying singly excited states in Ar I–Ar IV

In this paper we present a comprehensive analysis of beam-foil and beam-gas excited spectrum of argon observed in small wavelength region, 2965–3090 Å, using Ar^+/2+ ions in the energy range 200–650 keV. The comparison of beam-foil spectrum (BFS) at different incident beam energy and with that of beam-gas spectrum (BGS), one can find solution for blending problem in beam-foil spectroscopy. Many new transitions were identified on the basis of calculated wavelength from the accurately known energy levels of Ar I, Ar II, Ar III and Ar V. The transitions of Ar I originate from highly excited states (10p to 17p and 10f to 17f). Based on TOPbase estimates using close-coupling approximation five transitions involving core-excited states and nine transitions originating from highly excited states in the spectrum of Ar III and Ar IV were also identified. Radiative life time of two core excited quintet states (3s3p⁴(⁴P)6d ⁵D and 3s3p⁴(⁴P)8f⁵F^o) of Ar III were measured and found to be in ‘good’ agreement with that of the calculated value using close-coupling approximation.     

Explicit mathematical construction of relativistic nonlinear de Broglie waves described by three-dimensional (wave and electromagnetic) solitons “piloted” (controlled) by corresponding solutions of associated linear Klein-Gordon and Schrödinger equations

Starting from a nonlinear relativistic Klein-Gordon equation derived from the stochastic interpretation of quantum mechanics (proposed by Bohm-Vigier, ⁽¹⁾ Nelson, ⁽²⁾ de Broglie, ⁽³⁾ Guerra et al. ⁽⁴⁾ ), one can construct joint wave and particle, soliton-like solutions, which follow the average de Broglie-Bohm ⁽⁵⁾ real trajectories associated with linear solutions of the usual Schrödinger and Klein-Gordon equations.     

An O(N logN) alternating-direction finite difference method for two-dimensional fractional diffusion equations

Fractional diffusion equations model phenomena exhibiting anomalous diffusion that cannot be modeled accurately by the second-order diffusion equations. Because of the nonlocal property of fractional differential operators, the numerical methods for fractional diffusion equations often generate dense or even full coefficient matrices. Consequently, the numerical solution of these methods often require computational work of O(N³) per time step and memory of O(N²) for where N is the number of grid points.     

Perturbation allowed transitions in the infrared spectrum of 14ND3: determination of the K-dependent parameters in the ground state

ABSTRACT

Accurate values of the K-dependent constants ^{( i )} C, ^{( i )} D_K and ^{( i )} H_K in the ground state of ¹⁴ND₃, with i = s, a, have been determined for the first time thanks to the detections of ‘perturbation allowed’ transitions in the ν₁, ν₂, ν₃, ν₄ and 2ν₄ infrared bands. The rotation–inversion and inversion transitions from the literature, together with 7289 ground state combination differences from the infrared vibration–rotation–inversion transitions have been simultaneously analysed. The adopted rotation–inversion Hamiltonian includes distortion constants up to the eighth power and the Δk = ±3 and Δk = ±6 interaction terms. Precise values of the diagonal constants and of the Δk = ±3 interaction coefficients have been obtained. Accurate values of the ground state term values have been calculated for both s and a levels up to J = 21.     

Classical electrodynamics with nonlocal constitutive equations

It is assumed that the coupling of the field quantities D^μv (x) and F _αβ (x) is nonlocal. This hypothesis leads to a theory of an electromagnetic field that has the following properties.(1) The source of the field F _αβ (x) exhibits a center of charge and a center of mass that do not coincide, in general.(2) The field componentF _0i=?c²E_i is regular at the origin.(3) In the first-order approximation the new field equations are equivalent to the conventional Maxwell field equations.(4) The conventional cutoff procedure in momentum space as practiced in the Maxwell-Lorentz theory is equivalent to the first-order approximation in terms of an invariant length ξ².(5) The gyromagnetic ratio of the source of F _αβ (x) is equal toc/mc for a quantum of chargee and massm.     

On Quantum Phase Transition. I. Spinless Electrons Strongly Correlated with Ions

We study a large class F of models of the quantum statistical mechanics dealing with two types of particles. First the spinless electrons are quantum particles obeying to the Fermi statistics, they can hop. Secondly the ions which cannot move, are classical particles. The Falicov–Kimball (FK) model⁽¹⁾ is a well known model belonging to F, for which the existence of an antiferomagnetic phase transition was proven in the seminal paper of Kennedy and Lieb.⁽²⁾ This result was extended by Lebowitz and Macris.⁽³⁾ A new approach to this problem based on quantum selection of the ground states was proposed in ref. 4. In this paper we extend this approach to show that, under the strong insulating condition, any hamiltonian of the class F admits, at every temperature, an effective hamiltonian, which governs the behaviour of the ions interacting through forces mediated by the electrons. The effective hamiltonians are long range many body Ising hamiltonians, which can be computed by a cluster expansion expressed in term of the quantum fluctuations. Our main result is that we can apply the powerfull results of the classical statistical mechanics to our quantum models. In particular we can use the classical Pirogov–Sinai theory to establish a hierarchy of phase diagrams, we can also study of the behaviour of the quantum inter- faces,⁽²⁹⁾ and so on...     

Pressure evolution of two polymorphs of Tb 2(MoO 4)3

We have studied the high pressure behavior of the α and β^′-phases of Tb ₂(MoO ₄)₃ using a combination of powder X-ray diffraction and ab initio calculations. The α-Tb ₂(MoO ₄)₃ phase did not undergo any structural phase transition in the pressure range from 0 up to the maximum experimental pressure of 21 GPa. We observed line broadening of the diffraction patterns at pressures above 7 GPa, which may be due to non-hydrostatic conditions. The complete amorphization of the sample was not reached in the pressure range studied, as expected from previous Raman studies. The behavior under pressure of the β^′-Tb ₂(MoO ₄)₃ phase is similar to that of other rare-earths trimolybdates with the same structure at room temperature. A phase transition was observed at 2 GPa. The new phase, which can be identified as the δ-phase, has never been completely characterized by diffraction studies. A tentative indexation has been performed and good refined cell parameters were obtained. We detect indications of amorphization of the δ-Tb ₂(MoO ₄)₃ phase at 5 GPa.     

Solutions of Doubly and Higher Order Iterated Equations

Michael Fisher once studied the solution of the equation f(f(x))=x ²–2. We offer solutions to the general equation f(f(x))=h(x) in the form f(x)=g(ag ^–1(x)) where a is in general a complex number. This leads to solving duplication formulas for g(x). For the case h(x)=x ²–2, the solution is readily found, while the h(x)=x ²+2 case is challenging. The solution to these types of equations can be related to differential equations.     

Li and Nb codoping in dielectric properties and phase transitions of KTaO3: Reentrant dipolar glass and long-range dipole ordering

Abstract

The highly polarizable perovskite-type oxide, KTaO₃ doped simultaneously with Li⁺ and Nb⁵⁺ (K_1?xLi_xTa_1?yNb_yO₃, KLTN), reveals unexpected properties and ordering effects. Studies of the dielectric permittivity ?'(T, f) (10—300K, 100Hz-1 MHz) for x = 0.0014 and y = 0.024 show collective dipolar ordering effects with a transition from paraelectric into a mixed phase (coexisting dipole-glass-like and long-range ordered ferroelectric phases) taking place near 39 K. At 15 K another phase transition into a reentrant dipolar glass-like state is observed. Such a sequence of transitions and the existence of a reentrant glass state are unknown for electrical dipolar systems.     

A direct O(N log N) finite difference method for fractional diffusion equations

Fractional diffusion equations model phenomena exhibiting anomalous diffusion that can not be modeled accurately by the second-order diffusion equations. Because of the nonlocal property of fractional differential operators, the numerical methods have full coefficient matrices which require storage of O(N²) and computational cost of O(N³) where N is the number of grid points.     

Confinement of tensor gluons — a classical approach

We look at the confinement of tensor gluons (f _μν ^(c) field) in a strong gravity background and find that the strong gravity provides a trap for the confinement of colour waves of selected frequencies. We assume that the tensorf _μν ^(c) field (mediating quanta: tensor 2⁺ f-meson) satisfies Einstein-like equations with a cosmological constant. The colour field satisfy equations resembling Maxwell form of the linear theory of gravitation and see the effect off _μν ^(c) field as playing the role of a medium having space dependent dielectric permeabilities. The solution of colour field equations resemble harmonic oscillator type wave functions with equispaced energy levels (no continuum) leading to confinement.     

First order phase transition of Li3 ThF7 at 281 K: A comparative study between EPR and Raman scattering

Abstract

Electron Paramagnetic Resonance (EPR) and Raman Spectroscopy were used to study the low temperature phase transition of pulled Li₃ThF₇ single crystals, occurring at 281 K. In both cases, the room temperature spectra were very broad, owing to the statistical disorder and high ionic mobility of the lithium ions, which occupy only 3/4 of their structural sites. The results are compatible with a first order ferroelastic transition from the room temperature orthorhombic D_2h ²² phase to a monoclinic C_2h ^(x) one. The symmetry rules are well respected assuming a model with four lithium ions in average per chemical formula. The EPR spectra show also the appearing of additional ferroelastic domains.     

Miura maps and reductions

It is shown that the specialized forms of the generalized modified Korteweg-de Vries equations for the loop algebra A⁽¹⁾_n?1 reduce to the corresponding Korteweg-de Vries equations under certain Miura-type transformations.