Relative Rigidity Research Articles

Does the Choice between Wage Inequality and Unemployment Affect Productivity Growth?

Abstract We present a non-scale continuous-time overlapping-generations growth model that provides an explanation for why economies with relative wage rigidity feature higher unemployment, but not slower productivity growth, than economies with flexible wages. The compression of the wage distribution associated with relative wage rigidity slows down human capital accumulation and growth ceteris paribus. But unemployment among the low-skilled workers strengthens the incentives to invest in human capital and, hence, growth. The two effects are offsetting, and growth is independent of the prevailing degree of relative wage rigidity. This knife-edge result is robust with respect to some modifications of the model.

On the duality of the solution of the problem of finding the relative rigidity of the elastic edge edges of a cylindrical shell with respect to two eigenfrequencies of its axisymmetric oscillations

We consider the inverse problem of finding the relative rigidity of elastic edge edges of a cylindrical shell that is inaccessible to visual inspection, by two natural frequencies of its axisymmetric vibrations. A theorem on the duality of the solution of this inverse problem is proved. The corresponding counterexamples are given.

Nonlinear waves in porous media saturated with live oil

A nonlinear equation is obtained for waves propagating in porous media of arbitrary consolidation (relative rigidity) saturated with live (i.e., air-bearing) oil. The equation describes the evolution of fast and slow Biot-Frenkel longitudinal acoustic waves propagating in both directions and allows one to analyze the reflected waves and their interaction. For a wave of the second kind, the diffusion coefficient is determined. The dependences of the dispersion and dissipation parameters on the rigidity of the oil pool structure and on the depth of the oil pool occurrence are analyzed.

Kinematics of the southwestern U.S. deformation zone inferred from GPS motion data

We have estimated the surface deformation field of the southwestern U.S. deformation zone in terms of the velocity gradient field and surface creep simultaneously by inversion of 497 geodetic velocities. The model shows aseismic fault motion consistent with aseismic creep measurements and a sense of motion consistent with geological observations. We deduce that our surface deformation field shows distributed deformation in a zone around the faults containing shear strains and rotations. The eastern California shear zone acts as a distinct fault zone bounded by more rigid blocks. The faults within the zone partition the shear motion, while right‐lateral shear strain rates and clockwise rotations are concentrated between the bounding faults. In the same way, the San Jacinto and southern San Andreas faults act as bounding faults of a fault zone. The Mojave Desert is dominated by right‐lateral shear, whereas the western Transverse Ranges (WTR) is subjected to contraction. We find significant localization of deformation east of the San Andreas fault between the Transverse Ranges and the San Francisco Bay. We attribute this to a relative rigidity contrast across the fault of ∼1.8. Finally, a moment deficit analysis shows an accumulation of moment deficit between 1973 and 2000 corresponding to a Mw = 6.1–6.3 earthquake along the San Andreas fault just north of the Big Bend, around the Imperial and southern San Andreas faults, and in the San Francisco Bay area along the Hayward and southern Calaveras faults.

The Glass Transition Temperature of Polymer Melts

We develop an analytic theory to estimate the glass transition temperature T(g) of polymer melts as a function of the relative rigidities of the chain backbone and side groups, the monomer structure, pressure, and polymer mass. Our computations are based on an extension of the semiempirical Lindemann criterion of melting to locate T(g) and on the use of the advanced mean field lattice cluster theory (LCT) for treating the thermodynamics of systems containing structured monomer, semiflexible polymer chains. The Lindemann criterion is translated into a condition for T(g) by expressing this relation in terms of the specific volume, and this free volume condition is used to calculate T(g) from our thermodynamic theory. The mass dependence of T(g) is compared to that of other characteristic temperatures of glass-formation. These additional characteristic temperatures are determined from the temperature variation of the LCT configurational entropy, in conjunction with the Adam-Gibbs model for long wavelength structural relaxation. Our theory explains generally observed trends in the variation of T(g) with polymer microstructure, and we find that T(g) can be tuned either upward or downward by increasing the length of the side chains, depending on the relative rigidities of the side groups and the chain backbone. The elucidation of the molecular origins of T(g) in polymer liquids should be useful in designing and processing new synthetic materials and for understanding the dynamics and controlling the preservation of biological substances.

Korn’s Inequalities for Junctions of Elastic Bodies with Thin Plates

We prove the anisotropic Korn inequalities for an elastic junction of a massive body with thin plates clamped along parts of the lateral surfaces. The distribution of the weight factors in the norms under consideration depends essentially on the disposition of the plates, the way they are clamped to the body, and their relative rigidity (as compared with the body).

The Synthesis of Novel p‐Quinone Methides: O‐Dealkylation of5‐(p‐Alkyloxyaryl)‐10,11‐dihydrodibenzo[a,d]cyclohepten‐5‐ols and Related Compounds

AbstractThe synthesis of a series of novel tricyclic p‐quinone methides (p‐QMs) from 5‐(p‐alkyloxyaryl)‐10,11‐dihydrodibenzo[a,d]cyclohepten‐5‐ol and related substrates in moderate‐to‐good yields is reported. The reaction is proposed to proceed under mild acidic conditions by O‐dealkylation of the p‐alkoxy group on the p‐position of the pendant 5‐aryl ring on the B‐ring of the tricyclic system.The effect of different alkyl groups on the oxygen atom, as well as substituent groups on the phenyl ring flanking the O‐alkyl group has also been investigated The mechanism of the reaction is discussed in terms of the relatively high intermediate cation stabilities, the possible intermediacy of a hemiketal, as well as conformational effects. Various modifications to the central seven‐membered B‐ring to introduce more rigidity to the tricyclic system have been made and the scope of the reaction further elaborated. Furthermore, the single crystal structure of dienone 14 has been determined and the p‐quinone methide shown to be non‐planar, which would account for the relative conformational rigidity of these systems and their ability to accommodate the planar cyclohexa‐2,5‐dienone moiety and thus explain the stability of these systems relative to their 5‐ and six‐membered B‐ring counterparts. These compounds may be useful for the synthesis of novel dyes or compounds which may exhibit photochromic and thermochromic properties. (© Wiley‐VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2005)

Comparative Ab Initio Study of Point Defect Energies and Atom Migration Profiles in the L1<sub>2</sub>-Ordered Intermetallic Compounds Ni<sub>3</sub>Al, Ni<sub>3</sub>Ga, Pt<sub>3</sub>Ga, Pt<sub>3</sub>In

aFormation energies of antisite defects and vacancies were derived for the L12-ordered intermetallic Ni3Al, Ni3Ga, Pt3Ga, and Pt3In by a supercell ab initio approach. A thermodynamic treatment of point-like defects was then used for the calculation of temperature-dependent defect properties. For all compounds antisite formation requires less energy than vacancy formation, the difference being larger (by 1.2 - 2 eV) for the Ni compounds than for the Pt compounds (by ~0.7-1.1 eV). Some of the tendencies observed can be made plausible by arguments of atom size and relative rigidity of the lattice. Energy profiles for atom jumps were calculated by statically displacing the jumping atom and relaxing the surrounding neighbours. The influence of variable atomic neighbourhoods on the migration barrier and the stability of the initial and final states were studied by systematically exchanging nearest and next nearest neighbour atoms.

Synthesis, Characterization, and Photophysical Properties of a Free Base and a Biszinc(II) Complex of 1,3-Bisporphyrincalix[4]arene: Evidence for “Tunable Intramolecular Open and Closed Conformations”

The bismacrocycle 5,17-bis[5-(2,8,13,17-tetraethyl-3,7,12,18-tetramethylporphyrinyl)]-25,26,27,28-tetrapropoxycalix[4]arene (4) was synthesized in three steps from the corresponding bisaldehyde 5,17-diformyl-25,26,27,28-tetrapropoxycalix[4]arene. The biszinc(II) complex (5) was prepared as well, and the photophysical properties were measured using 2-MeTHF as solvent at 298 and 77 K. While computer modeling for 5 predicts that both pinched cone conformers, closed (porphyrins near each other) and open (porphyrins away from each other), may exist in the "gas phase", the experimental data indicate clearly that no zinc porphyrin...zinc porphyrin interactions are present in solution at 298 K, favoring the open conformer, where the two macrocycles are placed away from each other. On the other hand, clear evidence for a closed conformer is observed at 77 K. Variable-temperature (1)H NMR experiments show that 5 is fluxional between 298 and 183 K, while 4 keeps the open conformation for the whole temperature range. This behavior is unprecedented for calix[4]areneporphyrin compounds, and the relative porphyrin ring rigidity is postulated to explain this difference.

Transient response of a spherical cavity with a partially sealed shell embedded in viscoelastic saturated soil

Based on Biot's wave equation, this paper discusses the transient response of a spherical cavity with a partially sealed shell embedded in viscoelastic saturated soil. The analytical solution is derived for the transient response to an axisymmetric surface load and fluid pressure in Laplace transform domain. Numerical results are obtained by inverting the Laplace transform presented by Durbin, and are used to analyze the influences of the partial permeable property of boundary and relative rigidity of shell and soil on the transient response of the spherical cavity. It is shown that the influence of these two parameters is remarkable. The available solutions of permeable and impermeable boundary without shell are only two extreme cases of this paper.

Elastohydrodynamic analysis of double-layered journal bearings lubricated with couple-stress fluids

Elastohydrodynamic (EHD) analysis of a journal bearing with a realistic model for the bearing made of two distinct layers is extended to include couple-stress effects in lubricants blended with polymer additives. Based on the Stokes microcontinuum theory, a transient pressure differential equation (modified Reynolds' equation) is derived from the fluid motion equations and solved numerically. The elegant and powerful semi-analytical approach based on the complex variable theory developed in an earlier work is extended to solve linear elastostatics problems for a double-layered journal bearing. The EHD solution in isothermal conditions is obtained numerically by means of an iterative procedure. By the finite perturbation technique, the eight fluid-film stiffness and damping coefficients are determined. At the threshold of instability, the dynamic coefficients are used as input data for studying the linear stability of the rotor-bearing system. According to the results obtained, the influence of couple-stress parameter on the static and dynamic performance characteristics of the compliant journal-bearing system is physically apparent and not negligible. Compared with the Newtonian lubricants case, lubricants with couple-stresses provide an increase in the load-carrying capacity and stability, a reduction in the attitude angle and the friction factor. It is also found that the fluid-solid interaction effect on the performance characteristics is more important, especially for high values of couple-stress parameter and relative rigidity of liner-bush assembly.

DISCHARGE FROM CYLINDRICAL SLENDER STEEL SILOS: FINITE ELEMENT SIMULATION AND COMPARISON WITH EUROCODE 1

This study presents a model for the analysis of silo discharge with the finite element method. The proposed modelincorporates the Drucker-Prager plasticity model, a metal wall, and surface-to-surface contact using a dynamic analysis.This study reports the results obtained for discharge from a silo with a flexible wall and compares these results with the newversion of Eurocode 1. The mean overpressure coefficients obtained were 1.23 on the vertical wall and 1.28 on the hopper.The analysis of different silo geometries reveals a strong dependence of the value of the overpressure coefficient on silo height.A study of the relative rigidity of the wall and the grain showed that rigidity did not affect the dynamic pressures clearly.

MODULUS OF CORE REACTION APPROACH TO BUCKLING OF SANDWICH PLATES

This paper deals with the linear stability analysis of sandwich plates modeled as thin plates resting on elastic media. To compute the elastic buckling coefficient of sandwich plates, equations have been presented in the literature by using a coefficient R, which relates the rigidity of facing to the core. In the finite element analysis, if the sandwich plates are to be modeled as plates supported by Winkler elastic springs, the relative rigidity R cannot be directly used to represent the stiffness of the Winkler springs. Instead, the stiffness of the core has to be expressed as a modulus of subgrade/core reaction. Furthermore, the R value cannot be directly used in a finite element postbuckling analysis of sandwich plates. In this study, an empirical relation between modulus of core reaction and the R value is established. This is then used in the finite element computation of buckling loads of sandwich panels. This modulus of core reaction can be directly used in the linear buckling analysis of sandwich plates as well as the postbuckling analysis using finite elements.

On the Concepts of Frame of Reference and Connection in Space-Time Bundles of Classical Mechanics.

The definition of frame of reference in classical space–time bundles is investigated, in the general case of bundles whose fibres are not euclidean and of frames without the rigidity requirement. The enriching of the geometry of the bundle following from the presence of a frame of reference, viewed as a particular time–like vector field, is analyzed. Space–like tensor fields, unless totally contravariant, are proved to be correctly defined only if a frame of reference H is assigned. The connection associated to H is introduced and the selection of special covariant and time derivatives associated to H is soundly motivated. The usual kinematic quantities relative to H are defined. The relationships between pairs of frames are examinated and the concepts of relative rigidity, relative spin and relative acceleration are defined and investigated. The main results of Relative Kinematics are shown to fit readily into this geometric context.

Damping behavior of fibrous composites with viscous interface under longitudinal shear loads

Mechanical damping of fiber composites with viscous interface under longitudinal shear loads is analyzed. The specific damping capability is obtained explicitly by using the micromechanical model of composite cylinders assemble. The study indicates that the effective damping of the composite depends on several factors, including fiber volume fraction, the relative shear rigidity of fiber to matrix, and a dimensionless parameter composed of interface viscosity, fiber radius, vibration frequency and shear modulus of matrix. The respective influences of these factors are discussed in detail, and the results are expected helpful in tailoring microstructure of composites with desired damping behaviors.

Power flow paths in stiffened plates

The structural intensity of a rectangular plate with stiffeners attached is calculated using the finite element method. The power flow behaviors for the plate with stiffeners attached at various positions are investigated. The effects of geometrical properties of stiffeners on the changes of power flow are quantitatively analyzed by numerical integration for the structural intensities. A series of calculation results showed that the total amount of injected or transmitted power flow is dependent on the natural vibration frequency of the whole structure and the relative percentage of power flowing through the cross section of the plate or the stiffener depends on the ratio of their relative flexural rigidity.

Dynamic response of partially sealed circular tunnel in viscoelastic saturated soil

Based on Biot's wave equation, dynamic response of a circular tunnel with partially sealed liner in viscoelastic saturated soil is investigated. By introducing two scalar potential functions, the analytical solutions of stresses, displacements and pore pressure induced by axisymmetric gradually applied step load are derived in Laplace transform domain. Numerical results are obtained by inverting Laplace transform presented by Durbin and used to analyze the influences of partial permeable property of boundary and viscoelastic damping coefficient of soil on dynamic response of the tunnel. It is shown that the attenuation of radial displacement appeared with the increase of viscoelastic damping coefficient of soil, and relative rigidity of liner and soil, and the influence of partial sealing property of boundary on stresses, displacements and pore pressure is remarkable. The available solutions of permeable and impermeable boundary conditions are only two extreme cases of this paper.

Effects of Presentation Order on Product Evaluation: An Empirical Analysis

There are a number of consumer behaviour theories regarding the importance of the first stimulus and of a reference point in buying decision-making. However, there are not many empirical analyses, and they usually consider only hypothetical situations and payoffs. This paper aims to fill the gap by providing an empirical analysis for the effects of presentation order, using data collected in a natural setting. Two different personal computers are considered and evaluated along with the perceptions of price, quality, and price–quality relationship; evaluations are compared when the presentation order changes. The results confirm that the first alternative is more likely to be preferred; however, presentation order effects are not the same for all elements and show a relative rigidity for price perception. Managerial implications and issues for future research are highlighted.

Geometrical Changes and Their Energies in the Formation of Donor–Acceptor Complexes

We have mapped the energy demands of the geometrical changes in donor–acceptor complexes BH3⋅NH3 and AlCl3⋅NH3 and in the course of their formation from their monomers. We have varied the individual geometrical parameters systematically and performed ab initio quantum chemical calculations for these structures. We investigated the energy requirements to change bond lengths and bond angles in both the monomers and complexes and the angles of torsion in the complexes. The changes of bond lengths require more energy in the monomers than in the complexes. The energies to change the acceptor bond angles in the monomers are markedly higher than in the complexes. The changes in the geometrical parameters during the complexation process are more moderate in donors than in acceptors, in agreement with prior experimental observations. The geometry versus energy variations related to the process of complexation are in agreement with the notion of relative rigidity of the donor parts and the more compliant nature of the acceptor parts as well as with the notion of competing effects in the structures of the complexes.

On the potential performance of micro-fabricated subminiature microphones based on electron surface tunneling

The principle of electron tunneling across a vacuum potential energy barrier, as utilized in surface tunneling microscopy (STM), is a well known, highly sensitive, method for the detection of surface features and displacements in the subnanometer regime. In this paper, the basic properties of the surface tunneling principle and its possible utilization in acoustic sensors are discussed, with particular focus on the expected noise properties of a microphone based on tunneling in comparison to more conventional devices based on capacitive detection. It is found that the noise performance is largely limited by thermal noise due to the acoustical radiation impedance of the device in combination with electronic noise in the circuit used to establish and control the tunneling current. Finally, possible methods for sensor fabrication are discussed with special attention aimed at resolving the common problem of vibration sensitivity associated with STM. This problem stems from the relative large inertial mass and low flexural rigidity of the tunneling tip suspension system in most detector designs. Alternative approaches suitable for acoustic sensors in which the tunneling tip is fixed are described and it is shown that low vibration sensitivities comparable to capacitive devices can be achieved.