Derivation of the nonlinear fluctuating hydrodynamic equation from underdamped Langevin equation

We derive the fluctuating hydrodynamic equation for the number and momentum densities exactly from the underdamped Langevin equation. This derivation is an extension of the Kawasaki-Dean formula in underdamped case. The steady state probability distribution of the number and momentum densities field can be expressed by the kinetic and potential energies. In the massless limit, the obtained fluctuating hydrodynamic equation reduces to the Kawasaki-Dean equation. Moreover, the derived equation corresponds to the field equation derived from the canonical equation when the friction coefficient is zero.Comment: 16 page

Universal and non-universal features of glassy relaxation in propylene carbonate

It is demonstrated that the susceptibility spectra of supercooled propylene carbonate as measured by depolarized-light-scattering, dielectric-loss, and incoherent quasi-elastic neutron-scattering spectroscopy within the GHz window are simultaneously described by the solutions of a two-component schematic model of the mode-coupling theory (MCT) for the evolution of glassy dynamics. It is shown that the universal beta-relaxation-scaling laws, dealing with the asymptotic behavior of the MCT solutions, describe the qualitative features of the calculated spectra. But the non-universal corrections to the scaling laws render it impossible to achieve a complete quantitative description using only the leading-order-asymptotic results.Comment: 37 pages, 16 figures, to be published in Phys. Rev.

Critical Decay at Higher-Order Glass-Transition Singularities

Within the mode-coupling theory for the evolution of structural relaxation in glass-forming systems, it is shown that the correlation functions for density fluctuations for states at A_3- and A_4-glass-transition singularities can be presented as an asymptotic series in increasing inverse powers of the logarithm of the time t: $\phi(t)-f\propto \sum_i g_i(x)$, where $g_n(x)=p_n(\ln x)/x^n$ with p_n denoting some polynomial and x=ln (t/t_0). The results are demonstrated for schematic models describing the system by solely one or two correlators and also for a colloid model with a square-well-interaction potential.Comment: 26 pages, 7 figures, Proceedings of "Structural Arrest Transitions in Colloidal Systems with Short-Range Attractions", Messina, Italy, December 2003 (submitted

The evolution of vibrational excitations in glassy systems

The equations of the mode-coupling theory (MCT) for ideal liquid-glass transitions are used for a discussion of the evolution of the density-fluctuation spectra of glass-forming systems for frequencies within the dynamical window between the band of high-frequency motion and the band of low-frequency-structural-relaxation processes. It is shown that the strong interaction between density fluctuations with microscopic wave length and the arrested glass structure causes an anomalous-oscillation peak, which exhibits the properties of the so-called boson peak. It produces an elastic modulus which governs the hybridization of density fluctuations of mesoscopic wave length with the boson-peak oscillations. This leads to the existence of high-frequency sound with properties as found by X-ray-scattering spectroscopy of glasses and glassy liquids. The results of the theory are demonstrated for a model of the hard-sphere system. It is also derived that certain schematic MCT models, whose spectra for the stiff-glass states can be expressed by elementary formulas, provide reasonable approximations for the solutions of the general MCT equations.Comment: 50 pages, 17 postscript files including 18 figures, to be published in Phys. Rev.

Multiple-scattering effects on incoherent neutron scattering in glasses and viscous liquids

Incoherent neutron scattering experiments are simulated for simple dynamic models: a glass (with a smooth distribution of harmonic vibrations) and a viscous liquid (described by schematic mode-coupling equations). In most situations multiple scattering has little influence upon spectral distributions, but it completely distorts the wavenumber-dependent amplitudes. This explains an anomaly observed in recent experiments

Dynamics in Colloidal Liquids near a Crossing of Glass- and Gel-Transition Lines

Within the mode-coupling theory for ideal glass-transitions, the mean-squared displacement and the correlation function for density fluctuations are evaluated for a colloidal liquid of particles interacting with a square-well potential for states near the crossing of the line for transitions to a gel with the line for transitions to a glass. It is demonstrated how the dynamics is ruled by the interplay of the mechanisms of arrest due to hard-core repulsion and due to attraction-induced bond formation as well as by a nearby higher-order glass-transition singularity. Application of the universal relaxation laws for the slow dynamics near glass-transition singularities explains the qualitative features of the calculated time dependence of the mean-squared displacement, which are in accord with the findings obtained in molecular-dynamics simulation studies by Zaccarelli et. al [Phys. Rev. E 66, 041402 (2002)]. Correlation functions found by photon-correlation spectroscopy in a micellar system by Mallamace et. al [Phys. Rev. Lett. 84, 5431 2000)] can be interpreted qualitatively as a crossover from gel to glass dynamics.Comment: 13 pages, 12 figure

Cross-sectional evaluation of the periapical status as related to quality of root canal fillings and coronal restorations in a rural adult male population of Turkey

<p>Abstract</p> <p>Background</p> <p>To determine the prevalence of periapical lesions in root canal-treated teeth in a rural, male adult, Turkish population and to investigate the influence of the quality of root canal fillings on prevalence of periapical lesions.</p> <p>Methods</p> <p>The sample for this cross-sectional study consisted of 552 adult male patients, 18-32 years of age, presenting consecutively as new patients seeking routine dental care at the Dental Sciences of Gulhane Military Medicine, Ankara. The radiographs of the 1014 root canal-treated teeth were evaluated. The teeth were grouped according to the radiographic quality of the root canal filling and the coronal restoration. The criteria used for the examination were slightly modified from those described by De Moor. Periapical status was assessed by the Periapical Index scores (PAI) proposed by Orstavik.</p> <p>Results</p> <p>The overall success rate of root canal treatment was 32.1%. The success rates of adequately root canal treatment were significantly higher than inadequately root canal treatment, regardless of the quality or presence of the coronal restoration (P < .001). In addition, the success rate of inadequate root canal treatment was also significantly affected by the quality of coronal restorations.</p> <p>Conclusions</p> <p>Our results revealed a high prevalence of periapical lesions in root canal treatment, which is comparable to that reported in other methodologically compatible studies from diverse geographical locations. In addition, the results from the present study confirm the findings of other studies that found the quality of the root canal treatment to be a key factor for prognosis with or without adequate coronal restoration.</p