The generalized second law of thermodynamics in generalized gravity theories

We investigate the generalized second law of thermodynamics (GSL) in generalized theories of gravity. We examine the total entropy evolution with time including the horizon entropy, the non-equilibrium entropy production, and the entropy of all matter, field and energy components. We derive a universal condition to protect the generalized second law and study its validity in different gravity theories. In Einstein gravity (even in the phantom-dominated universe with a Schwarzschild black hole), Lovelock gravity and braneworld gravity, we show that the condition to keep the GSL can always be satisfied. In f ( R) gravity and scalar-tensor gravity, the condition to protect the GSL can also hold because the temperature should be positive, gravity is always attractive and the effective Newton constant should be an approximate constant satisfying the experimental bounds.

Crossing the phantom divide in brane cosmology with curvature corrections and brane-bulk energy transfer

We consider the Randall-Sundrum brane-world model with bulk-brane energy transfer where the Einstein-Hilbert action is modified by curvature correction terms: a four-dimensional scalar curvature from induced gravity on the brane, and a five-dimensional Gauss-Bonnet curvature term. It is remarkable that these curvature terms will not change the dynamics of the brane universe at low energy. Parameterizing the energy transfer and taking the dark radiation term into account, we find that the phantom divide of the equation of state of effective dark energy could be crossed, without the need of any new dark energy components. Fitting the two most reliable and robust SNIa datasets, the 182 Gold dataset and the Supernova Legacy Survey (SNLS), our model indeed has a small tendency of phantom divide crossing for the Gold dataset, but not for the SNLS dataset. Furthermore, combining the recent detection of the SDSS baryon acoustic oscillations peak (BAO) with lower matter density parameter prior, we find that the SNLS dataset also mildly favors phantom divide crossing.

Dynamical horizon entropy and equilibrium thermodynamics of generalized gravity theories

We study the relation between the thermodynamics and field equations of generalized gravity theories on the dynamical trapping horizon with sphere symmetry. We assume the entropy of a dynamical horizon as the Noether charge associated with the Kodama vector and point out that it satisfies the second law when a Gibbs equation holds. We generalize two kinds of Gibbs equations to Gauss-Bonnet gravity on any trapping horizon. Based on the quasilocal gravitational energy found recently for f(R) gravity and scalar-tensor gravity in some special cases, we also build up the Gibbs equations, where the nonequilibrium entropy production, which is usually invoked to balance the energy conservation, is just absorbed into the modified Wald entropy in the Friedmann-Robertson-Walker spacetime with slowly varying horizon. Moreover, the equilibrium thermodynamic identity remains valid for f(R) gravity in a static spacetime. Our work provides an alternative treatment to reinterpret the nonequilibrium correction and supports the idea that the horizon thermodynamics is universal for generalized gravity theories.

Studies on coarsening of microdomains in binary polymer mixtures by Lattice Boltzmann methods

An improved free energy approach Lattice Boltzmann model(LBM) is proposed by introducing a forcing term instead of the pressure tensor. This model can reach the proper thermodynamic equilibrium after enough simulation time. On the basis of this model, the phase separation in binary polymer mixtures is studied by applying a Flory-Huggins-type free energy. The numerical results show good agreement with the analytic coexistence curve. This model can also be used to study the coarsening of microdomains in binary polymer mixtures at the early and intermediate stages.

Theoretical studies of nonlinear optical properties of compounds K(4)Ln(2)(CO3)(3)F-4 (Ln=Pr, Nd, Sm, Eu, Gd)

K(4)Ln(2)(CO3)(3)F-4 (Ln=Pr, Nd, Sm, Eu, Gd) is a special type of frequency doubling compound, whose crystal structure exhibits a scarcity of fluorine ions. This leads to two different coordination polyhedrons in the general position of K(2) atoms: [K(2)O6F(1)(2)F(2)] and [K(21)O6F(1)(2)] in a 2/1 ratio. The chemical bonding structures of all constituent atoms of the compound K4Gd2(CO3)(3)F-4 (KGCOF) are comprehensively studied; moreover, the relationship between the chemical bonding structure and the nonlinear optical (NLO) properties is investigated from the chemical bond viewpoint. The theoretical prediction of the NLO tensor coefficient d(11) of KGCOF is in agreement with experimental observation. Theoretical analyses show that the nonlinearity of this crystal type mainly originates from K-O bonds. In addition, the correlation between the NLO tensor d(11) and the refractive index n(0) of KGCOF is discussed. (C) 2000 American Institute of Physics. [S0021-8979(00)07506-X].

Calculation of second-order nonlinear optical coefficients of KTiOPO4 and KTiOAsO4

The second-order nonlinear optical tensor coefficients of both KTiOPO4 (KTP) and KTiOAsO4 (KTA) are calculated from the chemical bond viewpoint. All constituent chemical bonds of both crystals are considered, and contributions of each type of bond to the total linearity and nonlinearity are determined. Calculated results agree satisfactorily with experimental data in both signs and numerical values. The calculation shows that though TiO6 groups and P(1)O-4 or As(1)O-4 groups have relatively larger linear contributions, they can only produce an advantageous environment for KOx (x = 8, 9) groups and P(2)O-4 or As(2)O-4 groups in nonlinear optical contributions. The origin of nonlinearity of KTP family crystals comes from the KOx (x = 8, 9) and P(2)O-4 groups in their crystal structures. Furthermore, the difference in optical nonlinearities of KTP type crystals is analyzed, based on the detailed calculation of nonlinearities of both KTP and KTA. (C) 1999 Academic Press.

Structural analysis of nonlinearities of Ca4ReO(BO3)(3) (Re = La, Nd, Sm, Gd, Er, Y)

From the chemical bond viewpoint, second-order nonlinear optical (NLO) tensor coefficients of the family of new oxoborates Ca4ReO(BO3)(3) (CReOB, Re = La, Nd, Sm, Gd, Er, and Y) have been theoretically predicted. The d(11) tensor coefficient of CReOB is predicted to be -11 d(36)(KDP), which is the largest d(ij) tensor that has been found in borate crystals. From the structural characteristic of CReOB, we find the isolated BO33- clusters play a dominant role in contributions to the total nonlinearity, and the largest d(11) tensor of CReOB-type crystals is also ascribed to these BO33- clusters. We also find the NLO property of this family does not change dramatically for different rare-earth elements. The details of the calculation of CGdOB only are presented.

Calculation of nonlinear optical coefficients of orthorhombic Re-2(MoO4)(3) crystals

From the chemical bond viewpoint, the second-order nonlinear optical (NLO) tensor coefficients of some Re-2(MoO4)(3) (ReMO)-type tare earth molybdates, with Re = Pr, Nd, Sm, Eu, Gd, Tb and Dy, have been calculated by using the chemical bond theory of complex crystals and the modified bond charge model. All kinds of constituent chemical bonds are considered in the calculation. The major part of the NLO properties of these ReMO crystals is found from the ReO7 groups. The NLO coefficients of these ReMO crystals decrease with Re from Pr to Dy. (C) 1998 Elsevier Science Ltd. All rights reserved.

Linear and nonlinear optical properties of KNbO3

Linear and nonlinear optical (NLO) properties of KNbO3 in various phases are calculated from their crystal structures. Nonlinear optical tensor coefficients are found to be very sensitive to the atomic geometry, changing as much as 85% between the ferroelectric tetragonal and rhombohedral phases. The predicted principal refractive indices are also found to be sensitive to their structural changes. In the tetragonal phase KNbO3 has the largest NLO responses, in the orthorhombic phase KNbO3 has the relative larger NLO coefficients, and in the rhombohedral structure KNbO3 has the large and homogeneous NLO properties. (C) 1998 Elsevier Science B.V. All rights reserved.

The role of Li-O bonds in calculations of nonlinear optical coefficients of LiXO3-type complex crystals

The second-order nonlinear optical (NLO) tenser coefficients of LiXO3 (X = I; Nb or Ta) type complex crystals have been calculated using the chemical bond theory of complex crystals. Contributions of each type of bond to the total second-order NLO coefficient d(ij) and the linear susceptibility X are quantitatively determined. All tensor values thus calculated are in good agreement with experimental data. The Li-O bonds are found to be an important group in the contributions to the total NLO tenser coefficient, especially for those in LiNbO3 and LiTaO3. The importance of Li-O bonds depends on the environment of Li atom in these crystals.

Calculation of nonlinear optical properties of KNdP4O12

The second-order nonlinear optical (NLO) tensor coefficients of KNdP4O12 (KNP) are theoretically predicted from its crystal structural data, by using the chemical bond theory of complex crystals and the modified bond charge model. Linear and nonlinear optical contributions of each type of bond to the total linearity (chi) and nonlinearity (d(ij)) of KNP are quantitatively determined. The structure-property relationship of KNP is systematically investigated, from the chemical bond viewpoint. Based on the discussion of its structural modifications, we point out that NLO properties of I(NP can be improved effectively using the doping method. Theoretical predictions show KNP to be a promising: self-frequency-doubling laser material.

Bond-charge calculation of nonlinear optical susceptibilities of LiXO3 type complex crystals

Second order nonlinear optical (NLO) tensor coefficients of LiXO3 (X = I, Nb, Ta) type crystals have been evaluated on the basis of the dielectric theory of complex crystals and the modified bond charge model. The current method is capable of calculating single bond contributions to the total second order NLO susceptibility. The tenser values thus calculated agree well with experimental data. By introducing the subformula equation and the concept of the effective charge of one valence electron, we are able to successfully treat such complex crystals as LiXO3 type compounds. In addition, the bond charge expression is modified to a more reasonable form for complex crystals. (C) 1998 Elsevier Science B.V.

Nonlinear optical properties of (B3O7)(5-) and (B3O6)(3-) groups

From the chemical bond viewpoint, LiB3O5 (LBO) crystal has been studied by using the bond valence theory of complex crystals. Chemical bond parameters and linear and nonlinear optical (NLO) properties of each type of constituent chemical bonds are quantitatively determined. Because of the different crystal structure characteristics of LBO from those of beta-BaB2O4 (BBO), the two anionic groups, (B3O7)(5-) in LBO and (B3O6)(3-) in BBO, play different roles in contributions to their own total NLO tensor coefficients of LBO and BBO, respectively. By comparison, we find that planar (B3O6)(3-) groups are the ideal structure model, leading to little cancellation of contributions of each kind of bond in these groups, and this gives us a useful guide to design new NLO materials in the future.

The effect of stoichiometry on nonlinear optical properties of LiNbO3

From the chemical bond viewpoint, second-order nonlinear optical (NLO) tensor coefficients of LiNbO3 have been investigated. The single-bond contributions to the second-order NLO susceptibility and the linear susceptibility were determined. The tensor values thus calculated are in good agreement with experimental data. Based on theoretical results of LiNbO3 with Li/Nb = 1, we also have calculated linear and nonlinear optical properties of nonstoichiometric samples with Li/Nb < 1. In the calculation, we find that the Li-O bond is an important type of chemical bond in these LiNbO3 samples, which have large NLO contributions to the total nonlinearities. The refractive indices and second-order NLO tensor coefficients have been determined as a function of the stoichiometry.

Dependence of linear electro-optic coefficient on difference in the atomic sizes in zinc blende crystals

Covalent radii of the bonding elements have strong effects on the linear electro-optic coefficients of zinc blende crystals; these effects can be quantitatively determined by investigating the relation between the difference in the atomic sizes rho and the magnitude of the linear electro-optic tensor coefficient r(41). It is interesting to note that for the same cation Zn2+, Ga3+, or In3+ the magnitude of r(41) increases with increased covalent radius of the bonded anion r(beta). Especially with the increasing tendency of the parameter rho, the magnitude of r(41) of crystals that have a same cation will increase suddenly when the value of r(beta) becomes larger. (C) 1997 Academic Press.