Group Symmetry in Interior-Point Methods for Semidefinite Program

A class of group symmetric Semi-Definite Program (SDP) is introduced by using the framework of group representation theory. It is proved that the central path and several search directions of primal-dual interior-point methods are group symmetric. Preservation of group symmetry along the search direction theoretically guarantees that the numerically obtained optimal solution is group symmetric. As an illustrative example, we show that the optimization problem of a symmetric truss under frequency constraints can be formulated as a group symmetric SDP. Numerical experiments using an interior-point algorithm demonstrate convergence to strictly group symmetric solutions.     

Stability analysis of undrained adiabatic shearing of a rock layer with Cosserat microstructure

Stability of undrained shearing in a classical Cauchy continuum has been first analyzed by Rice (J Geophys Res 80(11):1531–1536, 1975) who showed that instability occurs when the underlying drained deformation becomes unstable (i.e. in the softening regime of the corresponding drained stress-strain curve). However Vardoulakis (Int J Numer Anal Methods Geomech 9:339–414, 1985; Int J Numer Anal Methods Geomech 10:177–190, 1986) has shown that Rice’s linear stability analysis, if performed at the state of maximum deviator, leads to a sharp transition from infinitely stable to infinitely unstable behaviour, which indicates that the solution of the considered initial-value problem does not exist and consequently that the corresponding problem is mathematically ill-posed. Vardoulakis (Géotechnique 46(3):441–456, 1996; Géotechnique 46(3):457–472, 1996) proposed a regularization of the ill-posed problem in the softening regime by resorting to a second grade extension of plasticity theory. In this paper, the kinetics of a granular material is described by a Cosserat continuum as first suggested by Mühlhaus and Vardoulakis (Géotechnique 37:271–283, 1987) and we incorporate the effect of shear heating due to the dissipation of the frictional work. The undrained adiabatic limit is applicable as soon as the slip event is sufficiently rapid and the shear zone broad enough to effectively preclude heat or fluid transfer as it is the case during an earthquake or a landslide. It is shown that shear heating has a destabilizing effect and that instability can occur in the hardening regime if the amount of dilatant strengthening is not sufficient as compared to the effect of thermal pressurization of the pore fluid. It is shown that the linear stability analysis with macro and micro inertia terms leads to the selection of a preferred wave length of the instability mode corresponding to the instability mode with fastest (but finite) growth coefficient.     

Subsampling weakly dependent time series and application to extremes

This paper provides extensions of the work on subsampling by Bertail et al. in J. Econ. 120:295–326 (2004) for strongly mixing case to weakly dependent case by application of the results of Doukhan and Louhichi in Stoch. Proc. Appl. 84:313–342 (1999). We investigate properties of smooth and rough subsampling estimators for sampling distributions of converging and extreme statistics when the underlying time series is η- or λ-weakly dependent.     

Global optimization of robust truss topology via mixed integer semidefinite programming

This paper discusses a global optimization method of robust truss topology under the load uncertainties and slenderness constraints of the member cross-sectional areas. We consider a non-stochastic uncertainty of the external load, and attempt to minimize the maximum compliance corresponding to the most critical load. A design-dependent uncertainty model in the external load is proposed in order to consider the variation of truss topology rigorously. It is shown that this optimization problem can be formulated as a 0–1 mixed integer semidefinite programming (0–1MISDP) problem. We propose a branch-and-bound method for computing the global optimal solution of the 0–1MISDP. Numerical examples illustrate that the topology of robust optimal truss depends on the magnitude of uncertainty. The presented method can provide global optimal solutions for benchmark examples, which can be used for evaluating the performance of any other local optimization method for robust structural optimization.     

A time-discrete model for dynamic fracture based on crack regularization

We propose a discrete time model for dynamic fracture based on crack regularization. The advantages of our approach are threefold: first, our regularization of the crack set has been rigorously shown to converge to the correct sharp-interface energy Ambrosio and Tortorelli (Comm. Pure Appl. Math., 43(8): 999–1036 (1990); Boll. Un. Mat. Ital. B (7), 6(1):105–123, 1992); second, our condition for crack growth, based on Griffith’s criterion, matches that of quasi-static settings Bourdin (Interfaces Free Bound 9(3): 411–430, 2007) where Griffith originally stated his criterion; third, solutions to our model converge, as the time-step tends to zero, to solutions of the correct continuous time model Larsen (Math Models Methods Appl Sci 20:1021–1048, 2010). Furthermore, in implementing this model, we naturally recover several features, such as the elastic wave speed as an upper bound on crack speed, and crack branching for sufficiently rapid boundary displacements. We conclude by comparing our approach to so-called “phase-field” ones. In particular, we explain why phase-field approaches are good for approximating free boundaries, but not the free discontinuity sets that model fracture.     

Model checks for parametric regression models

In the paper we deal with the problem of model selection among fixed-design regression models. We establish a new test that indicates whether or not the model fits the data. The test statistic is based on the difference between a parametric estimator for the model variance and a nonparametric difference-based estimator, see Hall et al. (Biometrika 77:521–528, 1990). The weights in the nonparametric estimator depend on n, and they are chosen by solving an optimisation problem in order to obtain a test with high power.     

Case Studies in Optimization: Catenary Problem

This is the second paper in a series presenting case studies in modern large-scale constrained optimization 9 In this paper, we consider the shape of a hanging chain, which, in equilibrium, minimizes the potential energy of the chain. In addition to the tutorial aspects of this paper, we also emphasize the importance of certain modeling issues such as convex vs. nonconvex formulations of given problem. We will present several models of the problem and demonstrate differences in the number of iterations and solution time.     

Formation of new materials based on cast aluminum alloy

We show the dynamic formation of composite materials using the polycrystalline cast alloy Al + 12% Si as the example. The volume fraction of the synthesized framework (“influence zones”) of the composite material has been estimated to be at a level of 11%. Upon the introduction of lead a material practically insoluble under the experimental conditions was synthesized in the framework. Upon the introduction into the Al + 12% Si cast alloy of silicon carbide particles, we obtained a material with a specific corrosion exceeding by a factor of 5.6 the given index of the source matrix material.[1–7]     

Understanding the role of open peer review and dynamic academic articles

We welcome the commentary by L. Egghe (Scientometrics, this issue) stimulating discussion on our recent article “Natural selection of academic papers” (NSAP) (Scientometrics, 85(2):553–559, 2010) that focuses on an important modern issue at the heart of the scientific enterprise—the open and continuous evaluation and evolution of research. We are also grateful to the editor of Scientometrics for giving us the opportunity to respond to some of the arguments by L. Egghe that we believe are inaccurate or require further comment.     

Influence diagnostics in a general class of beta regression models

In this article, we consider the issue of assessing influence of observations in the general class of beta regression models introduced by Simas et al. (Comput. Stat. Data Anal. 54:348–366, 2010), which is very useful in situations in which the response is restricted to the standard unit interval (0,1). Our results generalize those in Espinheira et al. (Comput. Stat. Data Anal. 52:4417–4431, 2008a; J. Appl. Stat. 35:407–419, 2008b), which only apply to linear beta regression models. We define some residuals, and a Portmanteau test for serial correlation. Further, some influence methods, such as the global, local, and total local influence of an individual and generalized leverage, are discussed. Moreover, we also derive the normal curvatures of local influence under various perturbation schemes. Finally, simulation results and an application to real data show the usefulness of our results.     

Nonlinear forced vibration of damped plates coupling asymptotic numerical method and reduction models

This work concerns the computation of the nonlinear solutions of forced vibration of damped plates. In a recent work (Boumediene et al. in Comput Struct 87:1508–1515, 2009), a numerical method coupling an asymptotic numerical method (ANM), harmonic balance method and Finite Element method was proposed to resolve this type of problem. The harmonic balance method transforms the dynamic equations to equivalent static ones which are solved by using a perturbation method (ANM) and the finite element method. The numerical results presented in reference (Boumediene et al. in Comput Struct 87:1508–1515, 2009) show that the ANM is very efficient and permits one to obtain the nonlinear solutions with few matrix triangulation numbers compared to a classical incremental iterative method. However, putting a great number of harmonics (6 or greater) into the load vector leads to tangent matrices with a great size. The computational time necessary for the triangulation of such matrices can then be large. In this paper, reduced order models are proposed to decrease the size of these matrices and consequently the computational time. We consider two reduced bases. In the first one, the reduced basis is obtained by the resolution of a classical eigenvalue problem. The second one is obtained by using the nonlinear solutions computed during the first step of the calculus which is realized with the ANM. Several classical benchmarks of nonlinear damped plates are presented to show the efficiency of the proposed numerical methods.     

A comment to the paper by Waltman et al., Scientometrics, 87, 467–481, 2011

In reaction to a previous critique (Opthof and Leydesdorff, J Informetr 4(3):423–430, 2010), the Center for Science and Technology Studies (CWTS) in Leiden proposed to change their old “crown” indicator in citation analysis into a new one. Waltman (Scientometrics 87:467–481, 2011a) argue that this change does not affect rankings at various aggregated levels. However, CWTS data is not publicly available for testing and criticism. Therefore, we comment by using previously published data of Van Raan (Scientometrics 67(3):491–502, 2006) to address the pivotal issue of how the results of citation analysis correlate with the results of peer review. A quality parameter based on peer review was neither significantly correlated with the two parameters developed by the CWTS in the past citations per paper/mean journal citation score (CPP/JCSm) or CPP/FCSm (citations per paper/mean field citation score) nor with the more recently proposed h-index (Hirsch, Proc Natl Acad Sci USA 102(46):16569–16572, 2005). Given the high correlations between the old and new “crown” indicators, one can expect that the lack of correlation with the peer-review based quality indicator applies equally to the newly developed ones.     

On Comparison of Experiment and Theory for Ultrasonic Attenuation in Polycrystalline Niobium

In this communication comparison of experimental attenuation results in polycrystalline niobium (Zeng et al., J. Nondestruct. Eval. 29:93–103, 2010) with scattering-induced attenuation models is reexamined. Reasonable agreement is found between those results and the standard Stanke and Kino model (in J. Acoust. Soc. Am. 75:665–681, 1984) contradicting the conclusions of Zeng et al.     

Tabu search algorithm for flexible flow path design of unidirectional automated-guided vehicle systems

The unidirectional flow path design problem is one of the most important but difficult problems for the efficient design of automated-guided vehicle systems. As the problem was first formulated by Gaskins and Tanchoco, many researchers have studied the problem. However, the existing solution methods fail to provide an efficient solution approach. In this paper, a mathematical model for the unidirectional flow path design problem is developed. To obtain a near-to-optimal solution in reasonable computation time, a tabu search algorithm is presented. A fast construction algorithm first obtains a feasible initial solution, and a long-term memory structure and a neighbor solution generation approach are adapted to the problem characteristics and embedded in the proposed tabu search algorithm. Computational experiments show that the developed tabu search algorithm outperforms the Ko and Egbelu’s algorithm, Int J Prod Res, 41:2325–2343, (2003).     

The development of forced convection heat transfer near a forward stagnation point with Newtonian heating

A mathematical model for the unsteady forced convection boundary-layer flow near a forward stagnation point is considered when there is Newtonian heating on the surface whereby the heat transfer is proportional to the local surface temperature. In a previous paper (Salleh et al. J Eng Math 69:101–110, 2011), a critical value γ _c, dependent on the Prandtl number σ, of the heat transfer coefficient γ was identified, with solutions for the corresponding steady problem possible only for γ < γ _c. The unsteady problem considered here shows that these steady states are attained at large times when γ < γ _c. For γ > γ _c, the solution still continues to large time, now growing exponentially with time. This rate of growth is determined by an eigenvalue problem which we solve numerically for general values of γ and σ and asymptotically for large γ and both large and small σ.     

Suhl Instability as a Mechanism of the Catastrophic Relaxation in the Superfluid 3He–B

In order to explain catastrophic relaxation, bulk mechanism based on Suhl instability (J. Phys. Chem. Solids 1, 209, 1957) is studied. It is shown, that at sufficiently low temperatures homogeneous precession of spin becomes unstable in the whole region of tipping angles of spin 0≤β≤π. In comparison with the previous publication of Surovtsev and Fomin (J. Exp. Theor. Phys. Lett. 83, 410, 2006) the leading zero temperature increments for the angles θ ₀≃104°≤β≤π are found. Estimation of the temperature of transition to the unstable state for the angle of 105°, that corresponds to the region of tipping angles in homogeneously precessing domain (HPD), is made.     

Sustainability metrics for eco-technologies assessment, part I: preliminary screening

This work presents a preliminary screening of eco-technologies for dimethyl carbonate (DMC) production. Through sustainability metrics, the assessment of six different chemical routes allows comparisons according to economical and environmental criteria, to determine the most sustainable route. CO₂ sequestration potential is also considered. The alternatives are scored according to the adopted metrics, leading to the decision of a suitable route based on economic and environmental grounds, prioritizing pollution-preventing technologies herein referred to as eco-technologies. Casting of technologies was based on alternatives available in the literature: Route 1 production of DMC from methanol and phosgene [Ono in Pure Appl Chem 68(2):367–375, 1996]; Route 2 production of DMC from methyl nitrite and CO [Ono in Pure Appl Chem 68(2):367–375, 1996]; Route 3 production of DMC from CO and methanol [Ono in Pure Appl Chem 68(2):367–375, 1996]; Route 4 production of DMC from urea and methanol (Wang et al. in Ind Eng Chem Res 46:8972–8979, 2007); Route 5 production of DMC from ethylene oxide and CO₂ [Ono in Pure Appl Chem 68(2):367–375, 1996]; Route 6 production of DMC from CO₂ and methanol (Choi et al. in Green Chem 4:230–234, 2002). The analysis shows that Routes 4 and 5 combine intermediate values of the total (sustainability) score, CO₂ sequestration potential and industrial feasibility, therefore entitled as eco-technologies, based on the adopted metrics. Although the two technologies are potentially ecological, they are recommended for a more rigorous analysis on the grounds of process simulation and life cycle analysis.     

Optimal pairing computation over families of pairing-friendly elliptic curves

Vercauteren introduced the concept of optimal pairing, which by definition can be computed by using at most (log₂ r)/φ(k) + log₂ k basic Miller iterations, where r is the order of the groups involved and k is the embedding degree Vercauteren (IEEE Trans Inf Theory 56(1):455–461, 2010). Freeman et al. summarized and proposed all of the new constructions of pairing-friendly elliptic curves that currently exist Freeman et al. (J Cryptol 23(2):224–280, 2010). In this paper, we give an optimal pairing for each family of pairing-friendly curves in Freeman et al. (J Cryptol 23(2):224–280, 2010) by taking the Ate or R-ate pairing approach.     

Another generalization of the geometric distribution

A new generalization of the geometric distribution with parameters α>0 and 0<θ<1 is obtained in this paper. This can be done either by using the Marshall and Olkin (Biometrika 84(3), 641–652, 1997) scheme and adding a parameter to the geometric distribution or by starting with the generalized exponential distribution in Marshall and Olkin (Biometrika 84(3), 641–652, 1997) and discretizing this continuous distribution. The particular case α=1 led us to the geometric distribution. After reviewing some of its properties, we investigated the question of parameter estimation. The new distribution is unimodal with a failure rate that is monotonically increasing or decreasing, depending on the value of the parameter α. Expected frequencies were calculated for two overdispersed and infradispersed examples, and the distribution was found to provide a very satisfactory fit.     

A cellular automaton for segregation during granular avalanches

Segregation is a complex and poorly understood phenomenon that is prevalent in many industrial and natural granular flows. When grains flow down a slope [1–5], are spun in a rotating drum [6–8] or shaken in a box [9], we observe those grains organising into intriguing patterns. Kinetic sieving is the dominant mode of segregation in granular avalanches, where separation of particles occurs according to size. Using a cellular automaton we have modelled kinetic sieving as the swapping of particles in a one-dimensional system. From the cellular automaton we have deduced a continuum model to describe the segregation.