Narrow Results

With on-demand access to compute resources, pay-per-use, and elasticity, the cloud evolved into an attractive execution environment for High Performance Computing (HPC). Whereas elasticity, which is often referred to as the most beneficial cloud-specific property, has been heavily used in the context of interactive (multi-tier) applications, elasticity-related research in the HPC domain is still in its infancy. Existing parallel computing theory as well as traditional metrics to analytically evaluate parallel systems do not comprehensively consider elasticity, i.e., the ability to control the number of processing units at runtime. To address these issues, we introduce a conceptual framework to understand elasticity in the context of parallel systems, define the term elastic parallel system, and discuss novel metrics for both elasticity control at runtime as well as the ex-post performance evaluation of elastic parallel systems. Based on the conceptual framework, we provide an in-depth analysis of existing research in the field to describe the state-of-the-art and compile our findings into a research agenda for future research on elastic parallel systems.

It is demonstrated that the apex of a circular biconcave vesicle of fluid membrane can shift toward to (or away from) the center depending on the increase (or decrease) of the osmotic pressure.

Spider silk exhibits excellent mechanical features in both toughness and extensibility. In recent years considerable investigations have focused on it. The understanding of spider silk protein is important for the development bionic silk. In this paper, we study by Monte Carlo simulation the force-of-extension property of spider silk proteins as a function of the residue composition for major and minor ampullate glands of typical Araneid orb weaver as well as that for one artificial spider silk. The results are also compared with those from a designed protein whose amino acid composition is uniform. The results clearly show that the major and minor ampullate gland proteins are much tougher than the designed protein, whereas the artificial protein, as a model of a nature spider silk, does have good mechanical properties. Our simulation reveals that mechanical property of a spider silk protein is dependent on its amino acid composition and that an excellent result of natural evolution is manifest in the composition of the spider silk protein.

The Cauchy stress theory has been shown to be profoundly at variance with the principles of the theory of potentials. Thus, a new physical approach to deformation theory is presented, which is based on the balance of externally applied forces and material forces. The equation of state is generalized to apply to solids, and transformed into vector form. By taking the derivatives of an external potential and the material internal energy with respect to the coordinates, two vector fields are defined for the forces exerted by surrounding the system, subject to the boundary conditions, and vice versa, subject to the material properties. These vector fields are then merged into a third one that represents the properties of the loaded state. Through the work function, the force field is then directly transformed into the displacement field. The approach permits fully satisfactory prediction of all geometric and energetic properties of elastic and plastic simple shear. It predicts the existence of a bifurcation at the transition from reversible to irreversible behavior whose properties permit correct prediction of cracks in solids. It also offers a mechanism for the generation of sheath folds in plastic shear zones and for turbulence in viscous flow. Finally, an example is given on how to apply the new approach to deformation of a discrete sample as a function of loading configuration and sample shape.

The systematics of energetic terms as they are taught in continuum mechanics deviate seriously from the standard doctrine in physics, resulting in a profound misconception. It is demonstrated that the First Law of Thermodynamics has been routinely reinterpreted in a sense that would make it subordinate to Bernoulli's energy conservation law. Proof is given to the effect that the Cauchy stress tensor does not exist. Furthermore, it is shown that the attempt by Gibbs to find a thermodynamic understanding for elastic deformation does not sufficiently account for all the energetic properties of such a process.

In an exhaustive presentation of the linear theory of elasticity by Gurtin [The Linear Theory of Elasticity (Springer-Verlag, 1972)], the author included a chapter on the relation of the theory of elasticity to the theory of potentials. Potential theory distinguishes two fundamental physical categories: divergence-free and divergence-involving problems. From the criteria given in the source quoted by the author, it is evident that elastic deformation of solids falls into the latter category. It is documented in this short note that the author presented volume-constant elastic deformation as a divergence-free physical process, systematically ignoring all the information that was available to him that this is not so.

The purpose of this study is to obtain some information about the viscoelastic properties of the material and to see the effect of the addition of plasticizer on these properties. In particular, we try to study the loss of plasticizer, caused by ageing under conditions of utilization, on the properties of material at the neighborhood of vitreous transition.

Using a viscoelastimeter, the study of a polyamide-11 (PA11) at the neighborhood of its temperature of vitreous transition Tv has shown that the increase of the plasticizer rate clearly improves the properties of the material by decreasing its Tv temperature. The comparison of the curves giving the modulus of elasticity E' of the various samples showed that the mechanical properties of the material improve with the increase of the concentration of plasticizer, but ageing reduces this improvement by causing the loss of plasticizer, thus, the temperature range of utilization of material is reduced.

The hardness properties of materials are tracked from early history until the present time. Emphasis is placed on the hardness test being a useful probe for determining the local elastic, plastic and cracking properties of single crystal, polycrystalline, polyphase or amorphous materials. Beginning from connection made between individual hardness pressure measurements and the conventional stress–strain properties of polycrystalline materials, the newer consideration is described of directly specifying a hardness-type stress–strain relationship based on a continuous loading curve, particularly, as obtained with a spherical indenter. Such effort has received impetus from order-of-magnitude improvements in load and displacement measuring capabilities that are demonstrated for nanoindentation testing. Details of metrology assessments involved in various types of hardness tests are reviewed. A compilation of measurements is presented for the separate aspects of Hertzian elastic, dislocation-mechanics-based plasticity and indentation-fracture-mechanics-based cracking behaviors of materials, including elastic and plastic deformation rate effects. A number of test applications are reviewed, most notably involving the hardness of thin film materials and coatings.

The mechanical and thermodynamic properties of intermetallic compounds in the Ni–Ti system are studied by first-principles calculations. All phases show anisotropic elasticity in different crystallographic directions, in which Ni₃Ti and NiTi₂ are approaching the isotropy structure. The elastic moduli and Vicker’s hardness of Ni–Ti system intermetallic compounds decrease in the following order: Ni₃Ti $>$ B2_NiTi $>$ B19${}^{\prime }$_NiTi $>$ NiTi₂, and Ni₃Ti shows the best mechanical properties. The intrinsic ductile nature of Ni–Ti compounds is confirmed by the obtained $B$/$G$ ratio. The temperature dependence of linear thermal expansion coefficients (LTECs) of the compounds is estimated by the quasi-harmonic approximation (QHA) method. Ni₃Ti shows the largest values among all Ni–Ti intermetallic compounds. At room temperature, the LTEC for Ni₃Ti is 8.92 × 10${}^{-6}$ K${}^{-1}$, which falls in between the LTEC of zirconia toughened alumina (ZTA) (7.0–9.5 × 10⁶ K${}^{-1}$) and iron matrix (9.2–16.9 × 10⁶ K${}^{-1}$); i.e., the thermal matching of the ZTA/iron composite will be improved by introducing Ni₃Ti intermetallic compound into their interface. Other thermodynamic properties such as sound velocity and Debye temperature are also obtained.

We derive the general shape equations in terms of Euler angles for an elastic model of uniform ribbon with noncircular cross section and vanishing spontaneous curvatures. We show that it has in general not a planar solution for a closed ribbon free of external force and torque. We study the conditions to form a helix with the axis along the direction of the applied force for a ribbon under external force and twisting. We find that if the bending rigidity is greater than the twisting rigidity, then no such helical rod can exist. Our stability analysis shows that a helical ribbon is in general stable or at least metastable under arbitrary force and torque. We find that the extension of the ribbon may undergo a discontinuous transition from a twisted straight rod to a helical ribbon. The intrinsic asymmetric elasticity of a helical ribbon under external torque is also studied.

We derive the shape equations in terms of Euler angles for a uniform elastic rod with isotropic bending rigidity and spontaneous curvature, and study within this model the elasticity and stability of a helical filament under uniaxial force and torque. We find that due to the special requirements on the boundary conditions, a static slightly distorted helix cannot exist in this system except in some special cases. We show analytically that the extension of a helix may undergo a one-step sharp transition. This agrees quantitatively with experimental observations for a stretched helix in a chemically-defined lipid concentrate (CDLC). We predict further that under twisting, the extension of a helix in CDLC may also exhibit similar behavior. We find that a negative twist tends to destabilize a helix.

In this paper, we have measured the elastic and vibrational properties of CuMnPt₆ with embedded-atom method in three states of chemical order: as a disordered FCC (face-centered cubic) solid solution and as the equilibrium L1₂ and ABC₆ ordered structures. Our results agree quite well with the comparable experimental values. The present calculations indicate that the ABC₆ and L1₂ phases are energetically more stable than FCC phase. Numerical estimates of a set of elastic parameters, including aggregate elastic modulus, Poisson's ratio, and elastic anisotropy are performed, and the results demonstrate that the FCC phase is much softer than other two phases. Further analysis from the point of view of vibrational properties such as phonon density of states and vibrational entropy difference are also presented in this study.

The structural determination, thermodynamic, mechanical, dynamic and electronic properties of 4d transitional metal diborides MB₂ (M = Y–Ag) are systematically investigated by first-principles within the density functional theory (DFT). For each diboride, five structures are considered, i.e. AlB₂-, ReB₂-, OsB₂-, MoB₂- and WB₂-type structures. The calculated lattice parameters are in good agreement with the previously theoretical and experimental studies. The formation enthalpy increases from YB₂ to AgB₂ in AlB₂-type structure (similar to MoB₂- and WB₂-type). While the formation enthalpy decreases from YB₂ to MoB₂, reached minimum value to TcB₂, and then increases gradually in ReB₂-type structure (similar to OsB₂-type), which is consistent with the results of the calculated density of states. The structural stability of these materials relates mainly on electronegative of metals, boron structure and bond characters. Among the considered structures, TcB₂–ReB₂ (TcB₂–ReB₂ represents TcB₂ in ReB₂-type structure, the same hereinafter) has the largest shear modulus (248 GPa), and is the hardest compound. The number of electrons transferred from metals to boron atoms and the calculated densities of states (DOS) indicate that each diboride is a complex mixture of metallic, ionic and covalent characteristics. Trends are discussed.

The structural properties of Mo₂Ga₂C are simulated by first-principles under pressure. At 40 GPa, the axial compressibilities of $c$- and $a$-axes are 0.9763 and 0.9264, respectively, which are the known largest and smallest values in the $M_{n+1}A{X}_n(n=1)$ compounds. A phase transition at 48 GPa is observed with an abrupt increase of $c$-axis and a rapid decrease of $a$-axis. The elastic properties and phonon imaginary frequencies confirmed the structural transition at 48 GPa, which probably should be the lowest-pressure transition in the $M_{n+1}A{X}_n$ ($n=1,2,3$, etc.) phases. The anti-expansion of Mo–Mo bond length is responsible for the $c$-axis ultra-incompressibility as well as the structural transition at 48 GPa.

There is a class of complex problems where solutions must satisfy multiple subjective criteria, while meeting specific quantifiable constraints. Route planning for leisurely travel is an example of a problem in this class. Constraints including total available time, transit times, and one's budget and subjective interests determine whether a potential solution is acceptable to a prospective traveler.

In this paper we present a route planning (routing) interface that metaphorically leverages various elastic properties of a rubber band to allow for playful interaction with the relevant constraints. Each of these properties — attenuation, tension, and color — were integrated into an experimental system and then investigated in a series of task-based evaluations.

Our research shows this playful interaction enables potential travelers to explore the solution space in order to find a route that meets, not only the easily quantifiable constraints, but also their own subjective preferences.

If $M$ is an atomic monoid and $x$ is a nonzero non-unit element of $M$, then the set of lengths $L(x)$ of $x$ is the set of all possible lengths of factorizations of $x$, where the length of a factorization is the number of irreducible factors (counting repetitions). In a recent paper, F. Gotti and C. O’Neil studied the sets of elasticities ${ℛ}(P):=\{supL(x)/infL(x):x\in P\}$ of Puiseux monoids $P$. Here, we take this study a step further and explore the local $k$-elasticities of the same class of monoids. We find conditions under which Puiseux monoids have all their local elasticities finite as well as conditions under which they have infinite local $k$-elasticities for sufficiently large $k$. Finally, we focus our study of the $k$-elasticities on the class of primary Puiseux monoids, proving that they have finite local $k$-elasticities if either they are boundedly generated and do not have any stable atoms or if they do not contain $0$ as a limit point.

A cancellative commutative monoid is atomic if every non-invertible element factors into irreducibles. Under certain mild conditions on a positive algebraic number $\alpha$, the additive monoid $M_{\alpha }$ of the evaluation semiring ${\mathbb{N}}_0[\alpha ]$ is atomic. The atomic structure of both the additive and the multiplicative monoids of ${\mathbb{N}}_0[\alpha ]$ has been the subject of several recent papers. Here we focus on the monoids $M_{\alpha }$, and we study its omega-primality and elasticity, aiming to better understand some fundamental questions about their atomic decompositions. We prove that when $\alpha$ is less than $1$, the atoms of ${\mathbb{N}}_0[\alpha ]$ are as far from being prime as they can possibly be. Then we establish some results about the elasticity of ${\mathbb{N}}_0[\alpha ]$, including that when $\alpha$ is rational, the elasticity of $M_{\alpha }$ is full (this was previously conjectured by Chapman, Gotti and Gotti).

We study an optimization-based, non-overlapping, domain decomposition method for a bonded structure theoretically and numerically. The problem is restated as a constrained minimization problem for which the objective functional controls the normal component of stresses across the interface and the constraints are equlibrium equations in subdomains represented by adherents. We show that the minimization problem has a unique solution. We propose a domain decomposition method, based on the conjugate gradient minimization algorithm, which converges theoretically, in a finite number of steps.

We construct first-order, stable, nonconforming mixed finite elements for plane elasticity and analyze their convergence. The mixed method is based on the Hellinger–Reissner variational formulation in which the stress and displacement fields are the primary unknowns. The stress elements use polynomial shape functions but do not involve vertex degrees of freedom.

We study an optimization-based domain decomposition method for a nonlinear wall law in a coupled system. The problem is restated as a saddle-point problem by introducing as a new variable the displacement jump across the interface. Then the minimization step of the saddle-point problem corresponds to the equilibrium equations stated in each subdomain with Lagrange multiplier as interface force. The maximization step corresponds to maximizing a (nonlinear) strictly concave functional. This could have a lot of applications in geophysical flows such as coupling ocean and atmosphere, free surface and groundwater flows.