Twenty Years of Magnon Bose Condensation and Spin Current Superfluidity in 3He-B

20 years ago a new quantum state of matter was discovered and identified (Borovik-Romanov et al. in JETP Lett. 40:1033, 1984; 45:124, 1987; 47:478, 1988; Fomin in JETP Lett. 40:1037, 1984; Borovik-Romanov et al. in Sov. Phys. JETP 61:1199, 1985; Fomin in Sov. Phys. JETP 61:1207, 1985; Bunkov et al. in JETP Lett. 43:168, 1986). The observed dynamic quantum state of spin precession in superfluid ³He-B bears the properties of spin current superfluidity, Bose condensation of spin waves—magnons, off-diagonal long-range order and related phenomena of quantum coherence.     

Minimum theorems in 3D incremental linear elastic fracture mechanics

The crack propagation problem for linear elastic fracture mechanics has been studied by several authors exploiting its analogy with standard dissipative systems theory (see e.g. Nguyen in Appl Mech Rev 47, 1994, Stability and nonlinear solid mechanics. Wiley, New York, 2000; Mielke in Handbook of differential equations, evolutionary equations. Elsevier, Amsterdam, 2005; Bourdin et al. in The variational approach to fracture. Springer, Berlin, 2008). In a recent publication (Salvadori and Carini in Int J Solids Struct 48:1362–1369, 2011) minimum theorems were derived in terms of crack tip “quasi static velocity” for two-dimensional fracture mechanics. They were reminiscent of Ceradini’s theorem (Ceradini in Rendiconti Istituto Lombardo di Scienze e Lettere A99, 1965, Meccanica 1:77–82, 1966) in plasticity. Following the cornerstone work of Rice (1989) on weight function theories, Leblond et al. (Leblond in Int J Solids Struct 36:79–103, 1999; Leblond et al. in Int J Solids Struct 36:105–142, 1999) proposed asymptotic expansions for stress intensity factors in three dimensions—see also Lazarus (J Mech Phys Solids 59:121–144, 2011). As formerly in 2D, expansions can be given a Colonnetti’s decomposition (Colonnetti in Rend Accad Lincei 5, 1918, Quart Appl Math 7:353–362, 1950) interpretation. In view of the expression of the expansions proposed in Leblond (Int J Solids Struct 36:79–103, 1999), Leblond et al. (Int J Solids Struct 36:105–142, 1999) however, symmetry of Ceradini’s theorem operators was not evident and the extension of outcomes proposed in Salvadori and Carini (Int J Solids Struct 48:1362–1369, 2011) not straightforward. Following a different path of reasoning, minimum theorems have been finally derived.     

Theoretical Analysis of Neutron and X-ray Scattering Data on 3He

X-ray scattering experiments on bulk liquid ³He (Albergamo et al. in Phys. Rev. Lett. 99:205301, 2007; Schmets and Montfrooij in Phys. Rev. Lett. 100:239601, 2008; Albergamo et?al. in Phys. Rev. Lett. 100:239602, 2008) have indicated the possibility of the existence of a sharp collective mode at large momentum transfers. We address this issue within a manifestly microscopic theory of excitations in a Fermi fluid that can be understood as proper generalization of the time-honored theory of Jackson, Feenberg, and Campbell (Jackson in Phys. Rev. A 8:1529, 1973; Feenberg in Theory of Quantum Fluids, 1969; Chang and Campbell in Phys. Rev. B 13:3779, 1976) of excitations in ⁴He. We show that both neutron and X-ray data can be well explained within a theory where the high momentum excitations lie in fact inside the particle-hole continuum. ??Pair fluctuations?? contribute a sharpening of the mode compared to the random phase approximation (RPA). When the theoretical results are convoluted with the experimental resolution, the agreement between theory and X-ray data is quite good.     

A comparative study between two smoothing strategies for the simulation of contact with large sliding

The numerical simulation of contact problems is still a delicate matter especially when large transformations are involved. In that case, relative large slidings can occur between contact surfaces and the discretization error induced by usual finite elements may not be satisfactory. In particular, usual elements lead to a facetization of the contact surface, meaning an unavoidable discontinuity of the normal vector to this surface. Uncertainty over the precision of the results, irregularity of the displacement of the contact nodes and even numerical oscillations of contact reaction force may result of such discontinuity. Among the existing methods for tackling such issue, one may consider mortar elements (Fischer and Wriggers, Comput Methods Appl Mech Eng 195:5020–5036, 2006; McDevitt and Laursen, Int J Numer Methods Eng 48:1525–1547, 2000; Puso and Laursen, Comput Methods Appl Mech Eng 93:601–629, 2004), smoothing of the contact surfaces with additional geometrical entity (B-splines or NURBS) (Belytschko et al., Int J Numer Methods Eng 55:101–125, 2002; Kikuchi, Penalty/finite element approximations of a class of unilateral contact problems. Penalty method and finite element method, ASME, New York, 1982; Legrand, Modèles de prediction de l’interaction rotor/stator dans un moteur d’avion Thèse de doctorat. PhD thesis, École Centrale de Nantes, Nantes, 2005; Muñoz, Comput Methods Appl Mech Eng 197:979–993, 2008; Wriggers and Krstulovic-Opara, J Appl Math Mech (ZAMM) 80:77–80, 2000) and, the use of isogeometric analysis (Temizer et al., Comput Methods Appl Mech Eng 200:1100–1112, 2011; Hughes et al., Comput Methods Appl Mech Eng 194:4135–4195, 2005; de Lorenzis et al., Int J Numer Meth Eng, in press, 2011). In the present paper, we focus on these last two methods which are combined with a finite element code using the bi-potential method for contact management (Feng et al., Comput Mech 36:375–383, 2005). A comparative study focusing on the pros and cons of each method regarding geometrical precision and numerical stability for contact solution is proposed. The scope of this study is limited to 2D contact problems for which we consider several types of finite elements. Test cases are given in order to illustrate this comparative study.     

Analysis of left-truncated right-censored or doubly censored data with linear transformation models

We analyze left-truncated right-censored (LTRC) data or doubly censored data using semiparametric transformation models. It is demonstrated that the extended estimating equations of both?Cheng et al. (Biometrika 82:835?C845,?1995) and?Chen et al. (Biometrika 89:659?C668,?2002) can be used to analyze LTRC data or doubly censored data when left-censored variables are always observed. The asymptotic properties of the proposed estimators are derived. A simulation study is conducted to investigate the performance of the proposed estimators.     

Research evaluation. Part II: gender effects of evaluation: are men more productive and more cited than women?

Productivity and citedness of the staff of a German medical research institution are analyzed. It was found in our previous study (Pudovkin et al.: Scientometrics, doi:10.1007/s11192-012-0659-z, 2012) that male scientists are more prolific and cited more often than female scientists. We explain in our present study one of the possible causes for obtaining this result with reference to Abramo et al. (Scientometrics 84(3): 821?C833, 2009), who found in the small subgroups of star scientists a higher performance of male star scientists with respect to female star scientists; but in the remaining complementary subpopulations the performance gap between the two sexes is marginal. In agreement with Abramo et al. (2009), in our small subgroup of star scientists a higher performance of male star scientists with respect to female star scientists could be found. Contrasting, in the large complementary subgroup even a slightly higher performance of female scientists with respect to male scientists was identified. The last is even stronger expressed in favor of women than Abramo??s result that the performance gap between the two sexes is truly marginal. In addition to Abramo et al. (2009), we already found in our previous study, special indexes characterizing the quality of papers (but not quantity) are not substantially different among sexes compared.     

Transverse deflection of a clamped mild-steel plate

The theory of plastic flow by extended slip (Acta Mech 223:655–668, 2012; Philos Mag A 91:3343–3357, 2011; Z Angew Math Mech 84:266–279, 2004; Q J Mech Appl Math 52:645–662, 1999) is applied to a problem of bi-axial strain: the transverse plastic deflection, by means of a flat-ended punch, of a clamped plate of mild-steel. Two new theorems concerned with the Mechanics of Plates are presented. It is shown that, if the static shear yield stress of the plate material remains independent of strain, then the load–deflection relation for the punch, in the case of quasi-static punching of a plate clamped along a closed arbitrary contour, obeys an exactly linear theoretical relation. This prediction is then confirmed by experiments carried out at quasi-static rates of loading with thin plates of hot-rolled mild-steel. It is demonstrated by experiment, in the case of concentric circular punch and clamp contours, that the load–deflection relation for the punch remains linear to within <1 % provided that the maximum principal strain within the free domain of the plate does not exceed the yield-point elongation strain of the mild-steel concerned.     

An Integrated Procedure for the Structural Design of a Composite Rotor-Hydrofoil of a Water Current Turbine (WCT)

This paper shows an integrated structural design optimization of a composite rotor-hydrofoil of a water current turbine by means the finite elements method (FEM), using a Serial/Parallel mixing theory (Rastellini et al. Comput. Struct. 86:879–896, 2008, Martinez et al., 2007, Martinez and Oller Arch. Comput. Methods. 16(4):357–397, 2009, Martinez et al. Compos. Part B Eng. 42(2011):134–144, 2010) coupled with a fluid-dynamic formulation and multi-objective optimization algorithm (Gen and Cheng 1997, Lee et al. Compos. Struct. 99:181–192, 2013, Lee et al. Compos. Struct. 94(3):1087–1096, 2012). The composite hydrofoil of the turbine rotor has been design using a reinforced laminate composites, taking into account the optimization of the carbon fiber orientation to obtain the maximum strength and lower rotational-inertia. Also, these results have been compared with a steel hydrofoil remarking the different performance on both structures. The mechanical and geometrical parameters involved in the design of this fiber-reinforced composite material are the fiber orientation, number of layers, stacking sequence and laminate thickness. Water pressure in the rotor of the turbine is obtained from a coupled fluid-dynamic simulation (CFD), whose detail can be found in the reference Oller et al. (2012). The main purpose of this paper is to achieve a very low inertia rotor minimizing the start-stop effect, because it is applied in axial water flow turbine currently in design by the authors, in which is important to take the maximum advantage of the kinetic energy. The FEM simulation codes are engineered by CIMNE (International Center for Numerical Method in Engineering, Barcelona, Spain), COMPack for the solids problem application, KRATOS for fluid dynamic application and RMOP for the structural optimization. To validate the procedure here presented, many turbine rotors made of composite materials are analyzed and three of them are compared with the steel one.     

An extension of the noncommutative Bergman’s ring with a large number of noninvertible elements

For a prime number \(p\) , Bergman (Israel J Math 18:257–277, 1974) established that \(\mathrm {End}(\mathbb {Z}_{p} \times \mathbb {Z}_{p^{2}})\) is a semilocal ring with \(p^{5}\) elements that cannot be embedded in matrices over any commutative ring. In an earlier paper Climent et al. (Appl Algebra Eng Commun Comput 22(2):91–108, 2011), the authors presented an efficient implementation of this ring, and introduced a key exchange protocol based on it. This protocol was cryptanalyzed by Kamal and Youssef (Appl Algebra Eng Commun Comput 23(3–4):143–149, 2012) using the invertibility of most elements in this ring. In this paper we introduce an extension of Bergman’s ring, in which only a negligible fraction of elements are invertible, and propose to consider a key exchange protocol over this ring.     

Toward free-surface modeling of planing vessels: simulation of the Fridsma hull using ALE-VMS

In this paper we focus on a class of applications involving surface vessels moving at high speeds, or ??planing??. We introduce a Fridsma planing hull benchmark problem, and simulate it using the finite-element-based ALE-VMS (Bazilevs et?al. in Math Models Methods Appl Sci 2012; Takizawa et?al. in Arch Comput Methods Eng 19: 171?C225, 2012) approach. The major reasons for selecting this problem is the relative simplicity of the hull geometry and the existence of high-quality experimental data used for the purposes of validation. The ALE-VMS approach is formulated in the context of the Mixed Interface-Tracking/Interface-Capturing Technique (MITICT) (Tezduyar in Arch Comput Methods Eng 8:83?C130, 2001; Akin et?al. in Comput Fluids 36:2?C11, 2007; Cruchaga et?al. in Int J Numer Methods Fluids 54:1021?C1031, 2007), where the level set technique is used for capturing the air?Cwater interface, and the Arbitrary Lagrangian Eulerian (ALE) method is employed to track the interface between the fluid and structure. In this work, the planing hull structure is treated as a six-degree-of-freedom rigid object. The computational results obtained for the Fridsma hull, which include convergence of the trim angle and drag under mesh refinement, match well with the experimental data.     

Finite and spectral cell method for wave propagation in heterogeneous materials

In the current paper we present a fast, reliable technique for simulating wave propagation in complex structures made of heterogeneous materials. The proposed approach, the spectral cell method, is a combination of the finite cell method and the spectral element method that significantly lowers preprocessing and computational expenditure. The spectral cell method takes advantage of explicit time-integration schemes coupled with a diagonal mass matrix to reduce the time spent on solving the equation system. By employing a fictitious domain approach, this method also helps to eliminate some of the difficulties associated with mesh generation. Besides introducing a proper, specific mass lumping technique, we also study the performance of the low-order and high-order versions of this approach based on several numerical examples. Our results show that the high-order version of the spectral cell method together requires less memory storage and less CPU time than other possible versions, when combined simultaneously with explicit time-integration algorithms. Moreover, as the implementation of the proposed method in available finite element programs is straightforward, these properties turn the method into a viable tool for practical applications such as structural health monitoring [1–3], quantitative ultrasound applications [4], or the active control of vibrations and noise [5, 6].     

Analogies between Kirchhoff plates and Saint-Venant beams under flexure

New exact solutions for isotropic Kirchhoff plates, with no kinematic boundary constraints, are inferred by an analogy with the cross-section warping of orthotropic, homogeneous Saint-Venant beams bent and twisted by a shear force. The procedure is based on a formal equivalence between the elastic equilibrium conditions, respectively, for the tangential stresses in terms of a warping function in a Saint-Venant beam and for the bending–twisting moment in a Kirchhoff plate. The analysis refers to simply or multiply connected plates with an isotropic elastic stiffness proportional to the beams warping function. The result extends the one provided by the author for the special case of simple torsion (Barretta, Acta Mech 224(12):2955–2964, 2013). An example for a circular plate is developed, thus providing a new benchmark for computational mechanics.     

Instability of a Crystal 4He Facet in the Field of Gravity

We analyze here the analog of the Rayleigh instability in the field of gravity for the superfluid?Ccrystal ⁴He interface provided that the heavier ⁴He crystal phase occupies the space over the lighter superfluid phase. We find that the conditions and onset of the gravitational instability are different in kind above and below the roughening transition temperature when the crystal ⁴He surface is in the rough or in the smooth faceted state, respectively. In the rough state of the surface the gravitational instability is fully analogous to the classical case of the fluid?Cfluid interface. In contrast, in the case of the crystal faceted surface the onset of the gravitational instability is associated with surmounting some potential barrier. The potential barrier results from nonzero magnitude of the facet step energy. The size and the tilting angle of the crystal facet are also important parameters for developing the instability. The initial stage of the instability can be described as a generation of crystallization waves at the superfluid?Ccrystal interface. In particular, we discuss the experiments (Demaria et al. in J. Low Temp. Phys. 89:385, 1992; Tsymbalenko in Fiz. Nizk. Temp. 21:162, 1995; Tsymbalenko in Low Temp. Phys. 21:120, 1995) which may concern the gravitational instability of the superfluid-crystal ⁴He interface.     

A general framework for describing diversity within systems and similarity between systems with applications in informetrics

Building on the ideas of Stirling (J R Soc Interface, 4(15), 707?C719, 2007) and Rafols and Meyer (Scientometrics, 82(2), 263?C287, 2010), we borrow models of genetic distance based on gene diversity and propose a general conceptual framework to investigate the diversity within and among systems and the similarity between systems. This framework can be used to reveal the relationship of systems weighted by the similarity of the corresponding categories. Application of the framework to scientometrics is explored to evaluate the balance of national disciplinary structures, and the homogeneity of disciplinary structures between countries.     

Mechanically Versus Thermally Generated Quantum Turbulence of 4He Superflow

An experiment on thermally driven ⁴He superflow (Chagovets and Skrbek in Phys. Rev. Lett. 100:215302, 2008; J. Low Temp. Phys. 153:162, 2008) yielded very different steady state turbulence properties from a nominally identical recent realisation where the helium fountain drive was replaced by bellows. Here we argue that differences are most likely not due to fundamental reasons, but to incorrect velocity calculation in the fountain drive version. We show by a combination of direct velocity measurements and indirect analysis that the real velocity is significantly lower than predicted, and one main reason for this is unaccounted heat spent to enhance helium evaporation. The velocity correction brings the two experiments in reasonable agreement. We also suggest that the transition to a new state of superfluid turbulence claimed in Refs. (Chagovets and Skrbek in Phys. Rev. Lett. 100:215302, 2008; J. Low Temp. Phys. 153:162, 2008) may be a spurious effect of an observed nonlinearity occurring between fountain heat current and superflow velocity.     

Thermodynamics and thermal decomposition for shape memory effects with crystallization based on dissipation and logarithmic strain

The present effort provides a 3-D thermodynamic framework generalizing the 1-D modeling of 2-way shape memory materials described by Westbrook et al. (J. Eng. Mater. Technol. 312:041010, 2010) and Chung et al. (Macromolecules 41:184–192, 2008), while extending the strain-induced crystallization and shape memory approaches of Rao and Rajagopal (Interfaces Free Bound. 2:73–94, 2000; Int. J. Solids Struct. 38:1149–1167, 2001), Barot and Rao (Z. Angew. Math. Phys. 57:652–681, 2006), and Barot et al. (Int. J. Eng. Sci. 46:325–351, 2008) to include finite thermal expansion within a logarithmic strain basis. The free energy of newly-formed orthotropic crystallites is assumed additive, with no strains in their respective configurations of formation. A multiplicative decomposition is assumed for the assumed thermoelastic orthotropic expansional strains of the respective crystallites. The properties of the crystallites are allowed to depend both on current temperature and their respective temperatures of formation. The entropy production rate relation is written in the frame rotating with the logarithmic spin and produces stress and entropy relations incorporating the integrated configurational free energies, and a driving term for the crystallization analogous to that obtained by the previous studies of Rao et al. The salient attributes of the 1-D modeling of Westbrook et al. are recovered, and applications are discussed.     

Quantized Vortex State in hcp Solid 4He

The quantized vortex state appearing in the recently discovered new states in hcp ⁴He since their discovery (Kim and Chan, Nature, 427:225–227, 2004; Science, 305:1941, 2004) is discussed. Special attention is given to evidence for the vortex state as the vortex fluid (VF) state (Anderson, Nat. Phys., 3:160–162, 2007; Phys. Rev. Lett., 100:215301, 2008; Penzev et al., Phys. Rev. Lett., 101:065301, 2008; Nemirovskii et al., arXiv:0907.0330, 2009) and its transition into the supersolid (SS) state (Shimizu et al., arXiv:0903.1326, 2009; Kubota et al., J. Low Temp. Phys., 158:572–577, 2010; J. Low Temp. Phys., 162:483–491, 2011). Its features are described. The historical explanations (Reatto and Chester, Phys. Rev., 155(1):88–100, 1967; Chester, Phys. Rev. A, 2(1):256–258, 1970; Andreev and Lifshitz, JETP Lett., 29:1107–1113, 1969; Leggett, Phys. Rev. Lett., 25(22), 1543–1546, 1970; Matsuda and Tsuneto, Prog. Theor. Phys., 46:411–436, 1970) for the SS state in quantum solids such as solid ⁴He were based on the idea of Bose Einstein Condensation (BEC) of the imperfections such as vacancies, interstitials and other possible excitations in the quantum solids which are expected because of the large zero-point motions. The SS state was proposed as a new state of matter in which real space ordering of the lattice structure of the solid coexists with the momentum space ordering of superfluidity. A new type of superconductors, since the discovery of the cuprate high T _c superconductors, HTSCs (Bednorz and Mueller, Z. Phys., 64:189, 1986), has been shown to share a feature with the vortex state, involving the VF and vortex solid states. The high T _c s of these materials are being discussed in connection to the large fluctuations associated with some other phase transitions like the antiferromagnetic transition in addition to that of the low dimensionality. The supersolidity in the hcp solid ⁴He, in contrast to the new superconductors which have multiple degrees of freedom of the Cooper pairs with spin as well as angular momentum freedom, has a unique feature of possessing possibly only the momentum fluctuations and vortex ring excitations associated with the possible low dimensional fluctuations of the subsystem(s). The high onset temperature of the VF state can be understood by considering thermally excited low D quantized vortices and it may be necessary to seek low dimensional sub-systems in hcp He which are hosts for vortices.     

Permutation decoding of codes from generalized Paley graphs

The generalized Paley graphs $\text{ GP }(q,k)$ GP ( q , k ) are a generalization of the well-known Paley graphs. Codes derived from the row span of adjacency and incidence matrices from Paley graphs have been studied in Ghinellie and Key (Adv Math Commun 5(1):93–108, 2011) and Key and Limbupasiriporn (Congr Numer 170:143–155, 2004). We examine the binary codes associated with the incidence designs of the generalized Paley graphs obtaining the code parameters $[\frac{qs}{2}, q-1, s]$ [ q s 2 , q - 1 , s ] or $[qs, q-1,2s]$ [ q s , q - 1 , 2 s ] where $s=\frac{q-1}{k}$ s = q - 1 k . By finding explicit PD-sets we show that these codes can be used for permutation decoding.