On the Entire Radial Solutions of the Chern–Simons SU(3) System

In this paper, we study the entire radial solutions of the self-dual equations arising from the relativistic SU(3) Chern–Simons model proposed by Kao and Lee (Phys Rev D 50:6626–6632, 1994) and Dunne (Phys Lett B 345:452–457, 1995; Nuclear Phys B 433:333–348, 1995). Understanding the structure of entire radial solutions is one of the fundamental issues for the system of nonlinear equations. In this paper, we prove that any entire radial solutions must be one of topological, non-topological and mixed type solutions, and completely classify the asymptotic behaviors at infinity of these solutions. Even for radial solutions, this classification has remained an open problem for many years. As an application of this classification, we prove that the two components u and v have intersection at most finite times.     

Existence of the Harmonic Measure for Random Walks on Graphs and in Random Environments

We give a sufficient condition for the existence of the harmonic measure from infinity of transient random walks on weighted graphs. In particular, this condition is verified by the random conductance model on ? ^d , d≥3, when the conductances are i.i.d. and the bonds with positive conductance percolate. The harmonic measure from infinity also exists for random walks on supercritical clusters of ?². This is proved using results of Barlow (Ann. Probab. 32:3024–3084, 2004) and Barlow and Hambly (Electron. J. Probab. 14(1):1–27, 2009).     

A Very Smooth Ride in a Rough Sea

It has been known for some time that a 3D incompressible Euler flow that has initially a barely smooth velocity field nonetheless has Lagrangian fluid particle trajectories that are analytic in time for at least a finite time Serfati (C. R. Acad. Sci. Paris Série I 320:175–180, 1995), Shnirelman (Glob. Stoch. Anal., http://arxiv.org/abs/1205.5837v1, 2012). Here an elementary derivation is given, based on Cauchy’s form of the Euler equations in Lagrangian coordinates. This form implies simple recurrence relations among the time-Taylor coefficients of the Lagrangian map, used here to derive bounds for the C ^1,γ Hölder norms of the coefficients and infer temporal analyticity of Lagrangian trajectories when the initial velocity is C ^1,γ.     

The Z=Z(t/z)-Type Plane Wave Solutions of the Field Equations of General Relativity in a Plane Symmetric Space-Time

Taub (Ann. Math., 53:472?C490, 1951) has studied plane symmetry in Riemannian space-time by considering empty space-time admitting a three parameter group of motions. In this paper, we have deduced the line element of such a space-time for Z=Z(t/z)-type plane gravitational waves using suitable transformations following the concept of Takeno (Sci. Rep. Inst. Theor. Phys. Hiroshima Univ. 1, 1961), Lal and Ali (Tensor 20:281?C302, 1969). Furthermore it has been shown that the deduced space-time admit plane wave solutions of the field equations of general relativity containing electromagnetic terms. Also we have studied electromagnetic field except gauge transformation with particular cases with respect to ??.     

Bianchi Type-II String Cosmological Model with Magnetic Field in f (R,T) Gravity

The spatially homogeneous and totally anisotropic Bianchi type-II cosmological solutions of massive strings have been investigated in the presence of the magnetic field in the framework of f(R,T) gravity proposed by Harko et al. (Phys Rev D 84:024020, 2011). With the help of special law of variation for Hubble^’s parameter proposed by Berman (Nuovo Cimento B 74:182, 1983) cosmological model is obtained in this theory. We consider f(R,T) model and investigate the modification R+f(T) in Bianchi type-II cosmology with an appropriate choice of a function f(T)=μ T. We use the power law relation between average Hubble parameter H and average scale factor R to find the solution. The assumption of constant deceleration parameter leads to two models of universe, i.e. power law model and exponential model. Some physical and kinematical properties of the model are also discussed.     

Approximate Lifshitz Law for the Zero-Temperature Stochastic Ising Model in any Dimension

We study the Glauber dynamics for the zero-temperature stochastic Ising model in dimension d ≥ 4 with “plus” boundary condition. Let ${\mathcal{T}_+}$ be the time needed for an hypercube of size L entirely filled with “minus” spins to become entirely “plus”. We prove that ${\mathcal{T}_+}$ is O(L ²(log L) ^c ) for some constant c, not depending on the dimension. This brings further rigorous justification for the so-called “Lifshitz law” ${\mathcal{T}_{+} = O(L^{2})}$ (Fischer and Huse in Phys Rev B 35:6841–6848, 1987; Lifshitz in Sov Phys JETP 15:939–942, 1962) conjectured on heuristic grounds. The key point of our proof is to use the detailed knowledge that we have on the three-dimensional problem: results for fluctuation of monotone interfaces at equilibrium and mixing time for monotone interfaces dynamics extracted from Caputo et al. (Comm Pure Appl Math 64:778–831, 2011) to get the result in higher dimension.     

Asymptotic Expansion of β Matrix Models in the One-cut Regime

We prove the existence of a 1/N expansion to all orders in β matrix models with a confining, offcritical potential corresponding to an equilibrium measure with a connected support. Thus, the coefficients of the expansion can be obtained recursively by the “topological recursion” derived in Chekhov and Eynard (JHEP 0612:026, 2006). Our method relies on the combination of a priori bounds on the correlators and the study of Schwinger-Dyson equations, thanks to the uses of classical complex analysis techniques. These a priori bounds can be derived following (Boutet de Monvel et al. in J Stat Phys 79(3–4):585–611, 1995; Johansson in Duke Math J 91(1):151–204, 1998; Kriecherbauer and Shcherbina in Fluctuations of eigenvalues of matrix models and their applications, 2010) or for strictly convex potentials by using concentration of measure (Anderson et al. in An introduction to random matrices, Sect. 2.3, Cambridge University Press, Cambridge, 2010). Doing so, we extend the strategy of Guionnet and Maurel-Segala (Ann Probab 35:2160–2212, 2007), from the hermitian models (β = 2) and perturbative potentials, to general β models. The existence of the first correction in 1/N was considered in Johansson (1998) and more recently in Kriecherbauer and Shcherbina (2010). Here, by taking similar hypotheses, we extend the result to all orders in 1/N.     

Composite and Elementary Components in Hadron Resonances

In hadron resonances different structures of hadronic composite (molecule) and elementary (quark-intrinsic) natures may coexist. We sketch discussions based on our previous publications on the origin of hadron resonances (Hyodo et al. Phys. Rev. C 78:025203, 2008) on exotic ${\bar D (B)}$ meson–nucleons as candidates of hadronic composites (Yamaguchi et al. Phys. Rev. D 84:014032, 2011) and on a ₁ for the coexistence/mixing of the two different natures (Nagahiro et al. Phys. Rev. D 83:111504, 2011).     

A Few Endpoint Geodesic Restriction Estimates for Eigenfunctions

We prove a couple of new endpoint geodesic restriction estimates for eigenfunctions. In the case of general 3-dimensional compact manifolds, after a TT* argument, simply by using the L ²-boundedness of the Hilbert transform on ${\mathbb{R}}$ , we are able to improve the corresponding L ²-restriction bounds of Burq, Gérard and Tzvetkov (Duke Math J 138:445–486, 2007) and Hu (Forum Math 6:1021–1052, 2009). Also, in the case of 2-dimensional compact manifolds with nonpositive curvature, we obtain improved L ⁴-estimates for restrictions to geodesics, which, by Hölder’s inequality and interpolation, implies improved L ^p -bounds for all exponents p ≥ 2. We do this by using oscillatory integral theorems of Hörmander (Ark Mat 11:1–11, 1973), Greenleaf and Seeger (J Reine Angew Math 455:35–56, 1994) and Phong and Stein (Int Math Res Notices 4:49–60, 1991), along with a simple geometric lemma (Lemma 3.2) about properties of the mixed-Hessian of the Riemannian distance function restricted to pairs of geodesics in Riemannian surfaces. We are also able to get further improvements beyond our new results in three dimensions under the assumption of constant nonpositive curvature by exploiting the fact that, in this case, there are many totally geodesic submanifolds.     

Decoherent Histories of Spin Networks

The decoherent histories formalism, developed by Griffiths, Gell-Mann, and Hartle (in Phys. Rev. A 76:022104, 2007; arXiv:1106.0767v3 [quant-ph], 2011; Consistent Quantum Theory, Cambridge University Press, 2003; arXiv:gr-qc/9304006v2, 1992) is a general framework in which to formulate a timeless, ‘generalised’ quantum theory and extract predictions from it. Recent advances in spin foam models allow for loop gravity to be cast in this framework. In this paper, I propose a decoherence functional for loop gravity and interpret existing results (Bianchi et al. in Phys. Rev. D 83:104015, 2011; Phys. Rev. D 82:084035, 2010) as showing that coarse grained histories follow quasiclassical trajectories in the appropriate limit.     

n-Orthodistributivity in Orthomodular Lattices

A useful generalization of distributivity in lattices n-distributivity, \(n \in \mathbb{N}\) , was introduced in Huhn (Acta Sci. Math. 33:297–305, 1972). In Mayet and Roddy (Contrib. Gen. Algebra 5:285–294, 1987), ‘orthogonalized’ versions, n-orthodistributivity, \(n \in \mathbb{N}\) , of these equations were introduced and discussed. The discussion and results of Mayet and Roddy (Contrib. Gen. Algebra 5:285–294, 1987) centered on the class of modular ortholattices. In this paper we discuss and present some preliminary results for these conditions in orthomodular lattices. In particular, we completely classify the n-(ortho)distributive orthomodular lattices arising from Greechie’s classical 1971 construction, and we prove that a certain simple atomless orthomodular lattice, presented in Roddy (Algebra Univers. 29:564–597, 1992), is 4-orthodistributive. It is not 3-orthodistributive.     

LRS Bianchi Type II Massive String Cosmological Model for Stiff Fluid Distribution with Decaying Vacuum Energy (Λ)

An LRS Bianchi Type II model formed by massive strings with decaying vacuum energy (Λ) for stiff fluid distribution is studied in the context of general relativity. To get the deterministic model, we have assumed that $\frac{\sigma}{\theta} =\mathrm{constant}$ where σ is shear and θ the expansion in the model and decaying vacuum energy (Λ) is proportional to H ² (H is Hubble parameter) as used in Arbab (Gen. Relativ. Gravit. 29:51, 1997). We find that the model represents decelerating and accelerating phases of universe. The decaying vacuum energy (Λ) is proportional to $\frac{1}{\tau^{2}}$ as obtained by Bertolami (Nuovo Cimento B 93:36, 1986) and Hubble parameter is proportional to $\frac{1}{\tau}$ which matches with the observation. The model in general represents anisotropic space-time. However, in special case, it isotropizes. The particle density (ρ _p ) and string tenson (λ) are initially large but decrease due to lapse of time. The model also admits particle horizon and entropy is inversely proportional absolute temperature. Thus the model is in good agreement with present age of universe.     

Thermodynamics and holography of tachyon cosmology

Recently, we have investigated the dynamics of the universe in tachyon cosmology with non-minimal coupling to matter (Farajollahi et al. in Mod Phys Lett A 26(15):1125–1135, 2011; Phys Lett B 711(3–4)15:225–231,2012; Phys Rev D 83:124042, 2011; JCAP 10:014, 20112011; JCAP 05:017, 2011). In particular, for the interacting holographic dark energy (IHDE), the model is studied in Farajollahi et al. (Astrophys Space Sci 336(2):461–467, 2011). In the current work, a significant observational program has been conducted to unveil the model’s thermodynamic properties. Our result shows that the IHDE version of our model better fits the observational data than $\Lambda $ CDM model. The first and generalized second thermodynamics laws for the universe enveloped by cosmological apparent and event horizon are revisited. From the results, both first and generalized second laws, constrained by the observational data, are satisfied on cosmological apparent horizon.In addition, the total entropy is verified with the observation only if the horizon of the universe is taken as apparent horizon. Then, due to validity of generalized second law, the current cosmic acceleration is also predicted.     

Nonsymmetrized Hyperspherical Harmonics with Realistic Potentials

The Schrödinger equation is solved for an A-nucleon system using an expansion of the wave function in nonsymmetrized hyperspherical harmonics. The present approach is based on a formalism developed by Gattobigio et al. (Phys. Rev. A 79:032513, 2009; Few-Body Syst. 45:127–131, 2009; Phys. Rev. C 83:024001, 2011). Spin and isospin degrees of freedom are included; this makes possible calculations with realistic NN potential models. The fermionic ground state is determined by introducing an additional potential term involving the Casimir operator such that the antisymmetric ground state becomes the lowest eigenstate of the A-body system. Results are discussed for ⁴He with the realistic AV18 NN potential and for ⁶Li with the semirealistic MTI/III NN potential.     

Translationally Invariant Calculations of Form Factors,Densities and Momentum Distributions for Finite Nuclei with Short–Range Correlations Included: A Fresh Look

The approach proposed in the 70s (Dementiji et al. in Sov J Nucl Phys 22:6–9, 1976), when describing the elastic and inelastic electron scattering off ⁴ He, and elaborated in (Shebeko et al.in Eur Phys J A27:143–155, 2006) for calculations of the one-body, two-body and more complex density matrices of finite bound systems has been applied (Shebeko and Grigorov in Ukr J Phys 52:830–842, 2007; Shebeko et al. in Eur. Phys. J. A48:153–172, 2012) in studying a combined effect of the center-of-mass motion and nucleon–nucleon short-range correlations on the nucleon density and momentum distributions in light nuclei beyond the independent particle model. Unlike a common practice, suitable for infinite bound systems, these distributions are determined as expectation values of appropriate intrinsic operators that depend upon the relative coordinates and momenta (Jacobi variables) and act on the intrinsic ground–state wave functions (WFs). The latter are constructed in the so-called fixed center-of-mass approximation, starting with a mean–field Slater determinant modified by some correlator (e.g., after Jastrow or Villars). Our numerical calculations of the charge form factors (F _CH (q)), densities and momentum distributions have been carried out for nuclei ⁴ He and ¹⁶ O choosing, respectively, the 1s and 1s?1p Slater determinants of the harmonic oscillator model as trial, nontranslationally invariant WFs.     

No-Core Shell Model for Nuclear Systems with Strangeness

We report on a novel ab initio approach for nuclear few- and many-body systems with strangeness. Recently, we developed a relevant no-core shell model technique (Navrátil et al. in J Phys G 36:083101, 2009) which we successfully applied in first calculations of the lightest Λ hypernuclei. The use of a translationally invariant finite harmonic oscillator basis allows us to employ large model spaces, compared to traditional shell model calculations, and use realistic nucleon–nucleon and nucleon–hyperon interactions [such as those derived from EFT (Polinder et al. in Nucl Phys A 779:244, 2006)]. We discuss formal aspects of the methodology, show first demonstrative results for _Λ ³ H, _Λ ⁴ H and ⁴ _Λ He, and give outlook.     

The Parafermionic Observable in SLE

The parafermionic observable has recently been used by number of authors to study discrete models, believed to be conformally invariant and to prove convergence results for these processes to SLE (Beffara and Duminil-Copin in arXiv:1010.0526v2, 2011; Duminil-Copin and Smirnov in arXiv:1007.0575v2, 2011; Hongler and Smirnov in arXiv:1008.2645v3, 2011; Ikhlef and Cardy in J. Phys. A 42:102001, 2009; Lawler in preprint, 2011; Rajabpour and Cardy in J. Phys. A 40:14703, 2007; Riva and Cardy in J. Stat. Mech. Theory Exp., 2006; Smirnov in International Congress of Mathematicians, vol. II, pp. 1421?C1451, 2006; Smirnov in Ann. Math. 172(2):1435?C1467, 2010; Smirnov in Proceedings of the International Congress of Mathematicians, Hyderabad 2010, vol.?I, pp. 595?C621, 2010). We provide a definition for a one parameter family of continuum versions of the parafermionic observable for SLE, which takes the form of a normalized limit of expressions identical to the discrete definition. We then show the limit defining the observable exists, compute the value of the observable up to a finite multiplicative constant, and prove this constant is non-zero for a wide range of ??. Finally, we show our observable for SLE becomes a holomorphic function for a particular choice of the parameter, which provides a new point of view on a fundamental property of the discrete observable.     

A response to ‘Comments on the effect of liquid layering on the thermal conductivity of nanofluids’, E. Doroodchi, T. M. Evans & B. Moghtaderi, 2009. J Nanopart Res 11(6):1501–1507

This article provides a response to a recent brief communication ‘Comments on the effect of liquid layering on the thermal conductivity of nanofluids’ by Doroodchi et al. in J Nanopart Res 11(6):1501–1507, 2009. It provides an opportunity for us to clarify the fundamental differences between the models of Yu and Choi (2003) and Leong et al. (2006) mentioned in the communication, followed by an explanation of the development of Leong et al.’s model. While we re-affirm that the model of Leong et al. (2006) was developed based on the right methodology, appropriate boundary conditions and mathematical basis and is therefore valid, there are at least three incorrect equations in Doroodchi et al.’s communication which raise serious doubts on their results calculated from the above models. Hence, the comments by Doroodchi et al. (2009) about the model of Leong et al. (2006) are not well-justified.