Tsallis statistics generalization of non-equilibrium work relations

We use third constraint formulation of Tsallis statistics and derive the $q$-statistics generalization of non-equilibrium work relations such as the Jarzynski equality and the Crooks fluctuation theorem which relate the free energy differences between two equilibrium states and the work distribution of the non-equilibrium processes.Comment: 5 page

Influence of surfactants on the structure of titanium oxide gels : experiments and simulations

We report here on experimental and numerical studies of the influence of surfactants on mineral gel synthesis. The modification of the gel structure when the ratios water-precursor and water-surfactant vary is brought to the fore by fractal dimension measures. A property of {\em polydispersity of the initial hydrolysis} is proposed to explain these results, and is successfuly tested through numerical experiments of three dimensional chemically limited aggregation.Comment: 12 pages, 4 Postscript figures, uses RevTe

Universal Static and Dynamic Properties of the Structural Transition in Pb(Zn1/3Nb2/3)O3

The relaxors Pb(Zn$_{1/3}$Nb$_{2/3}$)O$_{3}$ (PZN) and Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_{3}$ (PMN) have very similar properties based on the dielectric response around the critical temperature $T_{c}$ (defined by the structural transition under the application of an electric field). It has been widely believed that these materials are quite different below $T_{c}$ with the unit cell of PMN remaining cubic while in PZN the low temperature unit cell is rhombohedral in shape. However, this has been clarified by recent high-energy x-ray studies which have shown that PZN is rhombohedral only in the skin while the shape of the unit cell in the bulk is nearly cubic. In this study we have performed both neutron elastic and inelastic scattering to show that the temperature dependence of both the diffuse and phonon scattering in PZN and PMN is very similar. Both compounds show a nearly identical recovery of the soft optic mode and a broadening of the acoustic mode below $T_{c}$. The diffuse scattering in PZN is suggestive of an onset at the high temperature Burns temperature similar to that in PMN. In contrast to PMN, we observe a broadening of the Bragg peaks in both the longitudinal and transverse directions below $T_{c}$. We reconcile this additional broadening, not observed in PMN, in terms of structural inhomogeneity in PZN. Based on the strong similarities between PMN and PZN, we suggest that both materials belong to the same universality class and discuss the relaxor transition in terms of the three-dimensional Heisenberg model with cubic anisotropy in a random field.Comment: 11 pages, 10 figures. Updated version after helpful referee comment

A Universal Phase Diagram for PMN-xPT and PZN-xPT

The phase diagram of the Pb(Mg1/3Nb2/3)O3 and PbTiO3 solid solution (PMN-xPT) indicates a rhombohedral ground state for x < 0.32. X-ray powder measurements by Dkhil et al. show a rhombohedrally split (222) Bragg peak for PMN-10%PT at 80 K. Remarkably, neutron data taken on a single crystal of the same compound with comparable q-resolution reveal a single resolution-limited (111) peak down to 50 K, and thus no rhombohedral distortion. Our results suggest that the structure of the outer layer of these relaxors differs from that of the bulk, which is nearly cubic, as observed in PZN by Xu et al.Comment: Replaced Fig. 3 with better versio

Thermodynamic Field Theory with the Iso-Entropic Formalism

A new formulation of the thermodynamic field theory (TFT) is presented. In this new version, one of the basic restriction in the old theory, namely a closed-form solution for the thermodynamic field strength, has been removed. In addition, the general covariance principle is replaced by Prigogine's thermodynamic covariance principle (TCP). The introduction of TCP required the application of an appropriate mathematical formalism, which has been referred to as the iso-entropic formalism. The validity of the Glansdorff-Prigogine Universal Criterion of Evolution, via geometrical arguments, is proven. A new set of thermodynamic field equations, able to determine the nonlinear corrections to the linear ("Onsager") transport coefficients, is also derived. The geometry of the thermodynamic space is non-Riemannian tending to be Riemannian for hight values of the entropy production. In this limit, we obtain again the same thermodynamic field equations found by the old theory. Applications of the theory, such as transport in magnetically confined plasmas, materials submitted to temperature and electric potential gradients or to unimolecular triangular chemical reactions can be found at references cited herein.Comment: 35 page

The opposite of Dante's hell? The transfer of ideas for social housing at international congresses in the 1850s–1860s

With the advent of industrialization, the question of developing adequate housing for the emergent working classes became more pressing than before. Moreover, the problem of unhygienic houses in industrial cities did not stop at the borders of a particular nation-state; sometimes literally as pandemic diseases spread out 'transnationally'. It is not a coincidence that in the nineteenth century the number of international congresses on hygiene and social topics expanded substantially. However, the historiography about social policy in general and social housing in particular, has often focused on individual cases because of the different pace of industrial and urban development and is thus dominated by national perspectives. In this paper, I elaborate on transnational exchange processes and local adaptations and transformations. I focus on the transfer of the housing model of SOMCO in Mulhouse, (a French house building association) during social international congresses. I examine whether cross-national networking enabled and facilitated the implementation of ideas on the local scale. I will elaborate on the transmission and the local adaptation of the Mulhouse-model in Belgium. Convergences, divergences, and different factors that influenced the local transformations (personal choice, political situation, socioeconomic circumstances) will be taken into accoun

General Non-equilibrium Theory of Colloid Dynamics

A non-equilibrium extension of Onsager's canonical theory of thermal fluctuations is employed to derive a self-consistent theory for the description of the statistical properties of the instantaneous local concentration profile n(r,t) of a colloidal liquid in terms of the coupled time evolution equations of its mean value n(r,t) and of the covariance {\sigma}(r,r';t) \equiv of its fluctuations {\delta}n(r, t) = n(r, t) - n(r, t). These two coarse-grained equations involve a local mobility function b(r, t) which, in its turn, is written in terms of the memory function of the two-time correlation function C(r, r' ; t, t') \equiv <{\delta}n(r, t){\delta}n(r',t')>. For given effective interactions between colloidal particles and applied external fields, the resulting self-consistent theory is aimed at describing the evolution of a strongly correlated colloidal liquid from an initial state with arbitrary mean and covariance n^0(r) and {\sigma}^0(r,r') towards its equilibrium state characterized by the equilibrium local concentration profile n^(eq)(r) and equilibrium covariance {\sigma}^(eq)(r,r'). This theory also provides a general theoretical framework to describe irreversible processes associated with dynamic arrest transitions, such as aging, and the effects of spatial heterogeneities

Ground State of Relaxor Ferroelectric Pb(Zn1/3Nb2/3)O3Pb(Zn_{1/3}Nb_{2/3})O_3

High energy x-ray diffraction measurements on Pb(Zn$_{1/3}$Nb$_{2/3}$)O$_3$ (PZN) single crystals show that the system does not have a rhombohedral symmetry at room temperature as previously believed. The new phase (X) in the bulk of the crystal gives Bragg peaks similar to that of a nearly cubic lattice with a slight tetragonal distortion. The Bragg profile remains sharp with no evidence of size broadening due to the polar micro crystals (MC). However, in our preliminary studies of the skin, we have found the expected rhombohedral (R) phase as a surface state. On the other hand, studies on an electric-field poled PZN single crystal clearly indicate a rhombohedral phase at room temperature.Comment: 11 pages with 3 figure

Dynamics of the rotational degrees of freedom in a supercooled liquid of diatomic molecules

Using molecular dynamics computer simulations, we investigate the dynamics of the rotational degrees of freedom in a supercooled system composed of rigid, diatomic molecules. The interaction between the molecules is given by the sum of interaction-site potentials of the Lennard-Jones type. In agreement with mode-coupling theory (MCT), we find that the relaxation times of the orientational time correlation functions C_1^(s), C_2^(s) and C_1 show at low temperatures a power-law with the same critical temperature T_c, and which is also identical to the critical temperature for the translational degrees of freedom. In contrast to MCT we find, however, that for these correlators the time-temperature superposition principle does not hold well and that also the critical exponent gamma depends on the correlator. We also study the temperature dependence of the rotational diffusion constant D_r and demonstrate that at high temperatures D_r is proportional to the translational diffusion constant D and that when the system starts to become supercooled the former shows an Arrhenius behavior whereas the latter exhibits a power-law dependence. We discuss the origin for the difference in the temperature dependence of D (or the relaxation times of C_l^(s) and D_r. Finally we present results which show that at low temperatures 180 degree flips of the molecule are an important component of the relaxation dynamics for the orientational degrees of freedom.Comment: 17 pages of RevTex, 12 figure

Double excitation transitions in Mn2+ -doped alkali halides

4 págs.; 4 figs.It is shown in this work that the room-temperature excitation spectra of as-grown crystals of LiF, NaF, NaCl, KCl, and KBr doped with Mn2+ reveal the existence of double excitation peaks. These peaks are related to the formation of precipitated phases containing Mn2+ in the alkali halide lattice. In the case of LiF:Mn2+ the position of the [A14(G), E4(G)] and T14(G) peaks suggests an anomalously small Mn2+- F- distance for the precipitated phase. © 1983 The American Physical Society.Financial support by the Comision Asesora para la Investigacion Cientifica y Tecnica, is gratefully acknowledged.Peer Reviewe