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The He2 and Be2 ground state potential curves have been calculated by extrapolating to an infinite basis BSSE corrected MRCI total energies obtained with large Gaussian basis sets, large reference configuration spaces, and pseudo-natural molecular orbitals. The calculated D e = 11.0031 K and R e = 5.607 a.u. of He2 are in an excellent agreement with D e = 11.006 ± 0.004 K and R e = 5.608 ± 0.012 a.u. obtained recently by SAPT with SM energy correction. The obtained Be2 non-relativistic D e = 822 cm−1 and relativistically corrected D e = 818 cm−1 are in a good agreement with experimental D e = 790 ± 30 cm−1 and the value of 829 ± 64 cm−1 obtained recently by a quantum Monte Carlo method.

Extended Reissner/Mindlin shell kinematics are used to develop an exact shell that makes no further approximations on the deformation or strain. The formulation is fully tensorial. A three-dimensional isoparametric element is used as the reference configuration. The FE approximation introduces nodes on the mid-surface of the isoparametric element, with the thickness having a separately defined interpolation. The variational formulation is based on the nominal stress tensor. Isotropic linear and nonlinear elastic shells are constructed that use p-type interpolation along the director. The formulation is exact, resulting in nonlinear elements showing better characteristics in comparison to other such elements.

The orbital invariance problem is analyzed from the tensor theory point of view, with an emphasis on multireference coupled cluster methods. Using the transformation properties of second-quantized operators, we discuss the orbital invariance properties of various methods by examining the tensor properties of the residual equations. A simple self-consistency-checking algorithm is proposed. We first establish the orbital invariance properties for the Hartree–Fock, single reference configuration interaction, single reference coupled cluster, complete-active-space self-consistent-field, and multireference configuration interaction methods, and then discuss the invariance properties of the complete-active-space coupled cluster and CCSDt methods. Finally, we demonstrate theoretically the lack of orbital invariance for Jeziorski–Monkhorst ansatz based methods. It appears necessary to modify the ansatz to achieve orbital invariance, and internal contraction serves as one possible solution. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010

The appropriate thermodynamic setting for the combined configurational and deformational motion of standard continua is discussed in this paper. A key ingredient is an absolute (fixed) reference configuration, relative to which configurational and deformational changes (rates) with respect to the material (undeformed) and spatial (deformed) configurations, respectively, can be described in a unified fashion. In particular, we are interested in formulating the local as well as global measures of the energy dissipation due to configurational changes of a given physical system. It is believed that the presentation in this paper provides the following advantages: a unified kinematic and thermodynamic setting of the configurational and deformational motions, in particular the generic balance law accounting for configurational flux, increases the general clarity; the separation of the total dissipation in terms of the intrinsic change in elastic energy and in terms of the material dissipation that is induced by configurational changes becomes transparent. All results are obtained without any restrictions on dynamics, thermomechanical couplings, etc.

This papers addresses the behaviour of hypoplastic equations near the reference configuration. By an approxi- mation process, a general small strain hypoplastic equation is derived. Two particular equations are examined. It is shown that they can represent solids exhibiting different Young's moduli in compression and in extension.

As an initial step to investigate stimulusresponserelations in growth and remodeling (G&R) of cardiac tissue, this study aims to develop a method to simulate 3D inhomogeneous volumetric growth. Growth is regarded as a deformation that is decomposed into a plastic component which describes unconstrained growth and an elastic component to satisfy continuity of the tissue after growth. In current growth models, a single reference configuration is used that remains fixed throughout the entire growth process.However, considering continuous turnover to occur together with growth, such a fixed reference is unlikely to exist in reality. Therefore, we investigated the effect of tissue turnoveron growth by incrementally updating the reference configuration. With both a fixed reference and an updated reference, strain-induced cardiac growth in magnitude of 30% could be simulated. However, with an updated reference, the amplitude of the stimulus for growth decreased over time, whereas with a fixed reference this amplitude increased. We conclude that, when modeling volumetric growth, the choice of the reference configuration is of great importance for the computed growth.

Three cuts of the H 2 S ( 1 A ′ ) potential energy surface, which correspond to the dissociation of a single S–H bond [cut (i)], the simultaneous, C 2 v -symmetric, dissociation of both S–H bonds [cut (ii)], and the C 2 v -symmetric minimum energy dissociation pathway leading to H 2 ( X 1 Σ g + ) and S ( 3 p 4 1 D ) [cut (iii)], are examined with the conventional and completely renormalized (CR) coupled-cluster (CC) methods, and the multi-reference configuration interaction approach [MRCI(Q)]. The size extensive CR-CC method with singles, doubles, and non-iterative triples, termed CR-CC(2,3), provides the results of the MRCI(Q) quality for cuts (i) and (iii). To obtain a similar quality for cut (ii), the CR-CC(2,3) energy must be corrected for the effect of quadruply excited clusters.

A systematic procedure to extract a projected first-grade constitutive equation from a given second-grade one is proposed and proven to be independent of the reference configuration used. The symmetry group of the projected material is shown to contain the first-grade projection of the symmetry group of the original material. The proposed method is illustrated by means of an example.

Linear Hookean elasticity formulated in terms of linear strain measures is the simplest way of modeling deformation in self-gravitating terrestrial bodies.

The first author gratefully acknowledges the hospitality and the support provided by the Insti- tut de Mathématiques de Marseille during the completion of this work.; International audience; We first consider an elastic thin heterogeneous cylinder of radius of order ε: the interior of the cylinder is occupied by a stiff material (fiber) that is surrounded by a soft material (matrix). By assuming that the elasticity tensor of the fiber does not scale with ε and that of the matrix scales with ε2, we prove that the one dimensional model is a nonlocal system.We then consider a reference configuration domain filled out by periodically distributed rods similar to those described above. We prove that the homogenized model is a second order nonlocal problem.In particular, we show that the homogenization problem is directly connected to the 3D–1D dimensional reduction problem.

This chapter gives a short introduction to the continuum mechanics applied to the uni-axial stress state.

In this paper, we determine numerically a large class of equilibrium configurations of an elastic two-dimensional continuous pantographic sheet in three-dimensional deformation consisting of two families of fibers which are parabolic prior to deformation. The fibers are assumed (1) to be continuously distributed over the sample, (2) to be endowed of bending and torsional stiffnesses, and (3) tied together at their points of intersection to avoid relative slipping by means of internal (elastic) pivots. This last condition characterizes the system as a pantographic lattice (Alibert and Della Corte in Zeitschrift fur angewandte Mathematik und Physik 66(5):2855–2870, 2015; Alibert et al. in Math Mech Solids 8(1):51–73, 2003; dell’Isola et al. in Int J Non-Linear Mech 80:200–208, 2016; Int J Solids Struct 81:1–12, 2016). The model that we employ here, developed by Steigmann and dell’Isola (Acta Mech Sin 31(3):373–382, 2015) and first investigated in Giorgio et al. (Comptes rendus Mecanique 2016, doi: 10.1016/j.crme.2016.02.009 ), is applicable to fiber lattices in which three-dimensional bending, twisting, and stretching are significant as well as a resistance to shear distortion, i.e., to the angle change between the fibers. Some relevant numerical examples are exhibited in order to highlight the main features of the model adopted: In particular, buckling and post-buckling behaviors of pantographic parabolic lattices are investigated. The fabric of the metamaterial presented in this paper has been conceived to resist more effectively in the extensional bias tests by storing more elastic bending energy and less energy in the deformation of elastic pivots: A comparison with a fabric constituted by beams which are straight in the reference configuration shows that the proposed concept is promising.

Atomistic modeling and simulations have become an invaluable tool for both the Materials Science and Mechanics communities to study and understand the nanoscale structure–property relationships in materials. Many of these studies focus specifically on the nanomechanics and fundamental deformation mechanisms that influence materials properties. However, the usefulness and impact of these simulations to influence the scientific community and materials design are ultimately hinged on the information extracted from the model or simulation. As such, a new and emerging focus in the atomistic modeling community is to develop more innovative avenues to produce more meaningful data. It is this goal that motivates the current chapter. This chapter presents an overview of a novel toolset for atomistic modeling and simulations to more effectively quantify the fundamental kinematics of atomistic structures. These new metrics are based on well-established theory from continuum mechanics, but provide unique insight into atomic-level processes that underly the nanomechanics of materials.

We present some novel equilibrium shapes of a clamped Euler beam (Elastica from now on) under uniformly distributed dead load orthogonal to the straight reference configuration. We characterize the properties of the minimizers of total energy, determine the corresponding Euler-Lagrange conditions and prove, by means of direct methods of calculus of variations, the existence of curled local minimizers. Moreover, we prove some sufficient conditions for stability and instability of particular solutions of the Euler-Lagrange conditions that can be applied to numerically found curled shapes.

We provide a quantitative description of the helicoid--to--spiral transition in thin ribbons of nematic elastomers using an elementary calculation based on a Koiter-type plate with incompatible reference configuration. Our calculation confirms that such transition is ruled by the competition between stretching energy and bending energy.

Global competitiveness and increasing performance requirements have placed facilities management (FM) under constraints of limited resources, particularly in non‐core aspects of facilities, such as maintenance and operations. The hypothesis applied in this research is that the actual service life of buildings, their occupancy and their ambient environmental conditions affect the required maintenance resources of these facilities. The objective was to develop a facility coefficient aiming to adjust the allocation of maintenance resources to prevailing service conditions in healthcare facilities. The research uses deterioration patterns and predicted service lives of building components and systems under moderate, standard and intensive occupancy and under two categories of environment: marine and inland. In total, five configurations combining occupancy and environmental conditions were investigated through simulations and compared to a reference configuration defined as standard occupancy and inland envir...

First we briefly review our covariant Hamiltonian approach to quasi-local energy, noting that the Hamiltonian-boundary-term quasi-local energy expressions depend on the chosen boundary conditions and reference configuration. Then we present the quasi-local energy values resulting from the formalism applied to homogeneous Bianchi cosmologies. Finally we consider the quasi-local energies of the FRW cosmologies. Our results do not agree with certain widely accepted quasi-local criteria., Contributed to International Symposium on Cosmology and Particle Astrophysics (CosPA 2006), Taipei, Taiwan, 15-17 Nov 2006

A method for the numerical simulation of residual stresses occurring in arterial walls without blood pressure is proposed. It is quite well established in the literature that a sliced artery may be considered as a “stress-free” reference configuration, in some sense. In order to close the gap between the opened transmural surfaces of a sliced artery, a displacement-driven procedure is applied which is formulated in the relative displacement of associated nodal points, similar as in the framework of interface elements. Subsequently, a new mesh is considered, representing the eigenstress state without these interface elements. This is advantageous for further numerical simulations as e.g., applying an internal pressure. Finally, the proposed method is applied to an atherosclerotic artery in order to provide a numerical example for the simulation of residual stresses in arteries.

There are a number of situations where the deformed configuration of a body is known and it is necessary to determine the reference state. Previous methods developed to calculate the reference state involve the formulation of the finite elasticity equations in terms of the deformed configuration. This paper demonstrates that the undeformed reference state can be accurately determined from a deformed configuration and the associated loading conditions, by using conventional finite elasticity balance equations together with a solution procedure that treats the reference configuration as the unknowns. The mathematical theory behind the solution method is described, validated with an analytical solution, and verified using experimental studies on gel phantoms. The practical utility of this method is then demonstrated in the field of breast biomechanics. Copyright © 2007 John Wiley & Sons, Ltd.

The implementation of a regional ensemble data assimilation and forecasting system requires the specification of appropriate perturbations of lateral boundary conditions (LBCs), in order to simulate associated errors. The sensitivity of analysis and 6-h forecast ensemble spread to these perturbations is studied here formally and experimentally by comparing three different LBC configurations for the ensemble data assimilation system of the ALADIN-France limited-area model (LAM). While perturbed initial LBCs are provided by the perturbed LAM analyses in each ensemble, the three ensemble configurations differ with respect to LBCs used at 3- and 6-h forecast ranges, which respectively correspond to: (1) perturbed LBCs provided by the operational global ensemble data assimilation system (GLBC), which is considered as a reference configuration; (2) unperturbed LBCs (ULBC) obtained from the global deterministic model; (3) perturbed LBCs obtained by adding random draws of an error covariance model (PLBC) to the global deterministic system. A formal analysis of error and perturbation equations is first carried out, in order to provide an insight of the relative effects of observation perturbations and of LBC perturbations at different ranges, in the various ensemble configurations. Horizontal variations of time-averaged ensemble spread are then examined for 6-h forecasts. Despite the use of perturbed initial LBCs, the regional ensemble ULBC is underdispersive not only near the lateral boundaries, but also in approximately one-third of the inner area, due to advection during the data assimilation cycle. This artefact is avoided in PLBC through the additional use of non-zero LBC perturbations at 3- and 6-h ranges, and the sensitivity to the amplitude scaling of the covariance model is illustrated for this configuration. Some aspects of the temporal variation of ensemble spread and associated sensitivities to LBC perturbations are also studied. These results confirm the importance of LBC perturbations for regional ensemble data assimilation. They also indicate that perturbing initial LBC is not sufficient to obtain realistic ensemble spread, whereas this can be achieved approximately by using random covariance draws for simulating LBC errors during the forecast and associated data assimilation cycling. Keywords: lateral boundary conditions, regional ensemble, data assimilation, ensemble spread (Published: 15 December 2015) Citation: Tellus A 2015, 67, 28502, http://dx.doi.org/10.3402/tellusa.v67.28502

International audience; The classification of rainfall fields has mainly focused on the split between convective and stratiform rainfall fields. In the present case study, the wavelet-based scattering transform is used to classify rainfall events observed by a weather radar. This very recent method has, to the best of the authors’ knowledge, not yet been applied for such a purpose. This method considers the spatial properties of rainfall radar images. This case study regroups 34 rainfall periods recorded over the Nantes region (western France) during 23 days in both 2009 and 2012. These periods display different characteristics in terms of duration and type of rainfall field. A reference configuration of the scattering transform has been evaluated and compared to various configurations in order to approximate the application conditions most appropriate to this case study. This evaluation is performed by a leave-one-out cross validation. A global accuracy of 93.5% of well classified images is obtained in the reference conditions which is an encouraging result. The temporal sampling of the rainfall fields is an important aspect of the classification process.

International audience; Even when entirely unloaded, biological structures are not stress-free, as shown by Y.C. Fung's seminal opening angle experiment on arteries and the left ventricle. As a result of this prestrain, subject-specific geometries extracted from medical imaging do not represent an unloaded reference configuration necessary for mechanical analysis, even if the structure is externally unloaded. Here we propose a new computational method to create physiological residual stress fields in subject-specific left ventricular geometries using the continuum theory of fictitious configurations combined with a fixed-point iteration. We also reproduced the opening angle experiment on four swine models, to characterize the range of normal opening angle values. The proposed method generates residual stress fields which can reliably reproduce the range of opening angles between 8.7±1.8 and 16.6 ± 13.7 as measured experimentally. We demonstrate that including the effects of prestrain reduces the left ventricular stiffness by up to 40%, thus facilitating the ventricular filling, which has a significant impact on cardiac function. This method can improve the fidelity of subject-specific models to improve our understanding of cardiac diseases and to optimize treatment options.

A possible procedure is proposed, which basically refers to tribological variables commonly used in engineering screen tests and in principle allows extended use of experimental wear data from the ball on disc standard system when the reference configuration has different geometry (e.g. flat pin on disc pairs) or nominal sliding conditions. The method is approximated and has been conceived to simplify comparative analysis of wear behaviour, in particular at equal nominal pressure. Expressing the ratio of wear constants on the basis of geometrical experimental variables for sphere and disc, it also aims to reduce time consumption in profilometry sessions and to split real-time linear wear curves for mating members from the overall approach pattern. An experimental example illustrates the proposed procedure, although full validation needs additional testing.

In this paper we analyze some aspects of the mechanics of anisotropic non-linearly elastic solids for which the anisotropy is associated with two preferred directions, thereby modelling the effect of two families of fiber reinforcement. Particular attention is focused on the role of the invariant I 8 , which couples the fiber kinematics in the constitutive law, and results are illustrated for a model strain–energy function that includes this invariant. The distinctive effects of this invariant on the stress–strain behaviour of the material and on the failure of ellipticity are discussed separately for pure homogeneous deformation and for a simple shear deformation. For pure homogeneous deformation it is shown that ellipticity fails with an associated weak surface of discontinuity that bisects the fiber directions. Moreover, ellipticity fails close to the reference configuration in either tension or compression. For simple shear it is found that loss of ellipticity occurs both for positive and negative shearing, and the orientation of the weak surface relative to the fiber directions is characterized in each case. Again ellipticity fails close to the reference configuration, and inclusion of the invariant I 8 in the constitutive law therefore has a pronounced destabilizing influence.

We build explicitly an infinite number of equilibrium solutions of unloaded Marguerre–von Karman membrane shells. This construction is based upon the existence of three elementary solutions, together with the solution of a Monge–Ampere equation associated with a partition of the reference configuration of the shell. These solutions are characterized as stationary points of energy functionals depending on the partition.

The existence of a deformation and magnetization minimizing the magnetostrictive free energy is given. Mathematical challenges are presented by a free energy that includes elastic contributions defined in the reference configuration and magnetic contributions defined in the spatial frame. The one-to-one a.e. and orientation-preserving property of the deformation is demonstrated, and the satisfaction of the nonconvex saturation constraint for the magnetization is proven.

The coupled-cluster corrections to multi-reference configuration interaction method with singles and doubles (MR-CISD) are applied to describe the N 2 dissociation process which is a prototypical case of the triple-bond breaking. The exact solvability of the double-zeta N 2 model used in the calculation permits comparison of results obtained within approximate schemes with the exact ones thus allows us to evaluate their performance. In our approach the MR-CISD method is corrected to improve description of the dynamic correlation thus an adequate selection of the MR-CISD reference space becomes an important factor for the successful application of the method. Several different reference spaces are tested.

Inelastic materials that form dislocation cells on being deformed are modeled as a "constrained-mixture" of plastically hard and soft regions by associating different natural states with these regions. The deformation gradient from the reference configuration to the natural configuration is identified as the plastic deformation tensor and the stress is measured from a changing set of natural configurations. Two sets of natural configurations are introduced: one for the hard phase and the other for the soft phase. The full elastic response of the body is determined by elastic responses from different natural configurations. The energy stored in the dislocation networks is explicitly accounted for in the Helmholtz potential. Within a specialized constitutive set up, the soft phase is assumed to be non-hardening while the hardening response of the hard phase is dependent upon the response of both the hard and soft phases. These special forms are used to model the response of the material that forms cellular structures when subjected to cyclic loading.

We consider the plane stress unloading waves emanating from a suddenly punched circular hole in a thin elastic sheet, subjected to an initial finite deformation simple tension. The sheet is assumed to be hyperelastic, isotropic, incompressible and thin enough that the generalized plane stress approximation is valid. It is further assumed that the plugging of the hole is due to normal impact of a cylindrical projectile and that the impact velocity of the projectile is sufficiently high that the plugging can be assumed instantaneous. The governing equations of the problem are obtained in Lagrangian form with respect to a reference configuration that is the initial stretched configuration. A numerical scheme is proposed for the solution of the governing equations, and numerical results are obtained for the neo-Hookean strain energy function. However with some additional complication other isotropic strain energy functions can be considered.

An algorithm to optimise the fuel loading pattern (LP) in nuclear reactors was developed using an artificial neural network (ANN) to generate arrangements for the fuel in the core. The core parameters were calculated with the WIMS-D4 and CITATION-LDI2 codes, and the minimization of the maximum power peaking factor (FP max ) was used to choose the best arrangements. To verify the algorithm a PWR reactor with approximately 1/3 reprocessed fuel loaded was considered. The neutronic performance of the obtained arrangements and the efficiency of the implemented method were analysed. Several configurations were found for the core presenting better characteristics than the reference configuration adopted, so indicating the viability of the developed methodology. The algorithm was applied to a core considering part of the loading with reprocessed fuels, however this technique can be used for standard loadings.

A method to obtain localized orbitals of CAS-SCF quality has been applied to model systems composed of linear Hydrogen chains. Both large distance (‘magnetic’) and short distance (‘metallic’) geometries have been investigated. Several possibilities of truncation of the complete active space have been tested. The orbitals obtained in this way have been used to perform multi-reference configuration interaction with single and double excitations (MR-CISD). It is shown that the proposed formalism permits a great reduction of the dimensions of the problem, without affecting significantly the quality of the results.

The possible structural changes of a non-sharp quaternary distillation configuration are considered. For the reference configuration composed of four columns, different alternatives are generated following the process intensification principle to reduce the number of equipment units. The intensified systems with three or two columns are obtained, including the dividing wall columns. Simulator Aspen Plus V8.0 was used to design and simulate all the systems for a hydrocarbon mixture. The intensified structures showed relevant energy savings compared to the reference case. The most promising alternatives were optimized by means of the differential evolution (DE) method minimizing the total annual cost (TAC). It was observed that the intensified systems were able to reduce both the energy consumption and the number of equipment units. The best intensified system has a TAC of 11.98% lower than the optimized reference case.

We study the asymptotic behavior of the discrete elastic energies in the presence of the prestrain metric G, assigned on the continuum reference configuration \(\Omega \). When the mesh size of the discrete lattice in \(\Omega \) goes to zero, we obtain the variational bounds on the limiting (in the sense of \(\Gamma \)-limit) energy. In the case of the nearest-neighbour and next-to-nearest-neighbour interactions, we derive a precise asymptotic formula, and compare it with the non-Euclidean model energy relative to G.

Many viral capsids undergo a series of significant structural changes following assembly, a process known as maturation. The driving mechanisms for maturation usually are chemical reactions taking place inside the proteins that constitute the capsid (“subunits”) that produce structural changes of the subunits. The resulting alterations of the subunits may be directly visible from the capsid structures, as observed by electron microscopy, in the form of a shear shape change and/or a rotation of groups of subunits. The existing thin shell elasticity theory for viral shells does not take account of the internal structure of the subunits and hence cannot describe displacement patterns of the capsid during maturation. Recently, it was proposed for the case of a particular virus (HK97) that thin shell elasticity theory could in fact be generalized to include transformations of the constituent proteins by including such a transformations as a change of the stress-free reference state for the deformation free energy. In this study, we adopt that approach and illustrate its validity in more generality by describing shape changes occurring during maturation across different T-numbers in terms of subunit shearing. Using phase diagrams, we determine the shear directions of the subunits that are most effective to produce capsid shape changes, such as transitions from spherical to facetted capsid shape. We further propose an equivalent stretching mechanism offering a unifying view under which capsid symmetry can be analyzed. We conclude by showing that hexamer shearing not only drives the shape change of the viral capsid during maturation but also is capable of lowering the capsid elastic energy in particular for chiral capsids (e.g., T = 7 ) and give rise to pre-shear patterns. These additional mechanisms may provide a driving force and an organizational principle for virus assembly.

Multi-reference configuration interaction (MRD–CI) calculations are required to compute the vertical electronic spectrum of HC 7 H, because two leading configurations resulting from the excitations 2π u →2π g (HOMO–SOMO) and 2π g →3π u (SOMO–LUMO) are almost equally important in the description of the states 1 3 Σ u − and 2 3 Σ u − . The electronic absorption spectrum is dominated by the dipole-allowed transitions to these two states from X 3 Σ g − . The lower 1 3 Σ u − is computed at 2.55 eV in reasonable agreement with experimental work of 505 nm (2.46 eV), whereas the upper 2 3 Σ u − is predicted close to 6.6 eV.

We report a new global potential energy surface (PES) for H 2 CO, based on precise fitting of roughly 67 000 MRCI/cc-pVTZ energies. This PES describes the global minimum, the cis - and trans -HCOH isomers, and barriers relevant to isomerization, formation of the molecular (H 2 +CO) and radical (H+HCO) products, and the loose so-called roaming transition-state saddle point. The key features of the PES are reviewed and compared with a previous PES, denoted by PES04, based on five local fits that are ‘stitched’ together by switching functions (Zhang et al. 2004 J. Phys. Chem. A 108 , 8980–8986 ( doi:10.1021/jp048339l )). Preliminary quasi-classical trajectory calculations are performed at the total energy of 36 233 cm −1 (103 kcal mol −1 ), relative to the H 2 CO global minimum, using the new PES, with a particular focus on roaming dynamics. When compared with the results from PES04, the new PES findings show similar rotational distributions, somewhat more roaming and substantially higher H 2 vibrational excitation. This article is part of the themed issue ‘Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces’.

Intentional electromagnetic interference arises to be a threat to critical infrastructures. These infrastructures are increasingly reliant on the proper functioning of electronic systems. An interference of such systems can lead to a tremendous damage both physically and financially. For the protection and hardening of infrastructures, their subsystems and functions need to be assessed. However, each infrastructure is built specifically so that a comprehensive assessment is not possible. In order to enable an assessment of the infrastructures, in this paper, a basic reference configuration is derived based on existing standards. This reference configuration will be applied to chosen examples of critical infrastructures. The differences and similarities of the critical subsystems of the infrastructures will be pointed out.

We considered a nonlinear reduced Cosserat continuum: an elastic medium, whose translations and rotations are independent, the force stress tensor is asymmetric and the couple stress tensor is zero. We suggested the reduced Cosserat continuum as a possible model for granular medium. Granular materials are ubiquitous in our daily lives. They play an important role in many industries, such as mining, agriculture, and construction. We considered a nonlinear reduced Cosserat continuum for reference and current configurations and obtained the set of equations for each configuration.

The concept of the average of a family of related nuclear configurations, for example, the average of those configurations which are slightly distorted versions of a given stable conformer of a molecule, has a role as both interpretative tool and also as a reference configuration in practical, computational use. However, depending on the actual coordinates used along which the average is defined, the average of nuclear configurations is not necessarily a physically viable arrangement, a fact that has to be taken into account when generating the corresponding electron density averages. Some of the associated mathematical and computational problems are described and the validity of a macroscopically motivated approach to conformation averaging is discussed.

The notion of natural stress tensors is introduced, which are tensors obtained from Cauchy and Kirchhoff stress tensors by operations of mapping, half‐mapping, and mixed mapping of the actual configuration onto the reference configuration, and also onto two intermediate configurations. A complete class of natural stress tensors is obtained and analyzed.

We present a method for constructing a scalar-relativistic pseudopotential which provides exact agreement with relativistic Dirac-Slater all-electron eigenvalues at the reference configuration. All-electron wave functions are self-consistently computed in the valence region at the exact all-electron scalar relativistic eigenvalues. This method improves tr ansferability of the resulting pseudopotential and presents a better starting point for th e designed non-local pseudopotential approach {[Phys. Rev. B {\bf 59}, 12471 (1999)]}. We present calculations for the gold atom as an example of the new approach., Comment: 10 pages, 1 table, submitted to Physical Review B

Restrictions imposed on stress response functions by objectivity and material symmetry are usually obtained by appeal to both a reference configuration and a response function common to all observers. Here these restrictions are obtained by regarding the reference configuration to be observer-dependent in a natural manner, and without the need to assume the existence of a common response function. Remarks are made on the distinction which should be drawn between the notions of observer transformation and rigid deformation, the consequences of this distinction for the correct interpretation of ‘invariance under superposed rigid motions’, and on the domains of response functions.

We show a necessary and sufficient condition for the undistorted reference configuration y(x)=x, with ∇y=F=1, to be a minimizer of the total stored energy for an isotropic elastic body. Polyconvexity of the stored energy function is not sufficient, and we give an example which possesses two distinct natural (i.e., unstressed) states to illustrate this point.

The multi-reference configuration interaction method applies equally well to ground and excited states. However, a disadvantage of the MR-CI scheme is that its accuracy can be seriously affected by inadequate description of dynamical electron correlation effects. This problem can be alleviated to a large extent through an a posteriori correction based on the coupled-cluster (CC) expansion. Since our correction is derived within the single-reference CC formulation, its application to excited states is less obvious although possible and fully justified. In this Letter, we explore this possibility and study the performance of the correction for excited states.

Using the methods of rational mechanics, a new equation of the acoustics of inhomogeneous unsteadily moving media is derived. Its advantage over traditional approaches is demonstrated.