Quasi-static Changes Research Articles

Classical and quantum thermodynamics described as a system-bath model: The dimensionless minimum work principle.

We formulate a thermodynamic theory applicable to both classical and quantum systems. These systems are depicted as thermodynamic system-bath models capable of handling isothermal, isentropic, thermostatic, and entropic processes. Our approach is based on the use of a dimensionless thermodynamic potential expressed as a function of the intensive and extensive thermodynamic variables. Using the principles of dimensionless minimum work and dimensionless maximum entropy derived from quasi-static changes of external perturbations and temperature, we obtain the Massieu-Planck potentials as entropic potentials and the Helmholtz-Gibbs potentials as free energy. These potentials can be interconverted through time-dependent Legendre transformations. Our results are verified numerically for an anharmonic Brownian system described in phase space using the low-temperature quantum Fokker-Planck equations in the quantum case and the Kramers equation in the classical case, both developed for the thermodynamic system-bath model. Thus, we clarify the conditions for thermodynamics to be valid even for small systems described by Hamiltonians and establish a basis for extending thermodynamics to non-equilibrium conditions.

Three-dimensional quasi-static displacement of human middle-ear ossicles under static pressure loads: Measurement using a stereo camera system

The time delay and/or malfunctioning of the Eustachian tube may cause pressure differences across the tympanic membrane, resulting in quasi-static movements of the middle-ear ossicles. While quasi-static displacements of the human middle-ear ossicles have been measured one- or two-dimensionally in previous studies, this study presents an approach to trace three-dimensional movements of the human middle-ear ossicles under static pressure loads in the ear canal (EC). The three-dimensional quasi-static movements of the middle-ear ossicles were measured using a custom-made stereo camera system. Two cameras were assembled with a relative angle of 7° and then mounted onto a robot arm. Red fluorescent beads of a 106–125 µm diameter were placed on the middle-ear ossicles, and quasi-static position changes of the fluorescent beads under static pressure loads were traced by the stereo camera system. All the position changes of the ossicles were registered to the anatomical intrinsic frame based on the stapes footplate, which was obtained from µ-CT imaging. Under negative ear-canal pressures, a rotational movement around the anterior-posterior axis was dominant for the malleus-incus complex, with small relative movements between the two ossicles. The stapes showed translation toward the lateral direction and rotation around the long axis of the stapes footplate. Under positive EC pressures, relative motion between the malleus and the incus at the IMJ became larger, reducing movements of the incus and stapes considerably and thus performing a protection function for the inner-ear structures. Three-dimensional tracing of the middle-ear ossicular chain provides a better understanding of the protection function of the human middle ear under static pressured loads as immediate responses without time delay.

Periodic dynamics in superconductors induced by an impulsive optical quench

A number of experiments have evidenced signatures of enhanced superconducting correlations after photoexcitation. Initially, these experiments were interpreted as resulting from quasi-static changes in the Hamiltonian parameters, for example, due to lattice deformations or melting of competing phases. Yet, several recent observations indicate that these conjectures are either incorrect or do not capture all the observed phenomena, which include reflectivity exceeding unity, large shifts of Josephson plasmon edges, and appearance of new peaks in terahertz reflectivity. These observations can be explained from the perspective of a Floquet theory involving a periodic drive of system parameters, but the origin of the underlying oscillations remains unclear. In this paper, we demonstrate that following incoherent photoexcitation, long-lived oscillations are generally expected in superconductors with low-energy Josephson plasmons, such as in cuprates or fullerene superconductor K3C60. These oscillations arise from the parametric generation of plasmon pairs due to pump-induced perturbation of the superconducting order parameter. We show that this bi-plasmon response can persist even above the transition temperature as long as strong superconducting fluctuations are present. Our analysis offers a robust framework to understand light-induced superconducting behavior, and the predicted bi-plasmon oscillations can be directly detected using available experimental techniques.

Bifurcation structures and bursting dynamics in a two degrees of freedom quasi-zero stiffness system with elastic constrain

In this manuscript, bifurcation structures and bursting patterns involving grazing phenomena are discussed based on a nonsmooth quasi-zero stiffness vibration isolation system. Within the selected parameter zone, analysis about stability and bifurcations of equilibria belonging to two sub-systems in phase space show that, equilibria of both sub-systems lose their stability through supercritical Hopf bifurcations. Numerical continuation performed on two sub-systems indicates that, the sub-system S− presents bi-stability consisting of small amplitude cycle branch circling around the S-shape equilibrium curve and large amplitude cycle branch, while the sub-system S+ presents mono-stability. Meanwhile, both cycle branches are terminated by fold bifurcations of cycle. Furthermore, as the quasi-static external force changes, periodic motions governed by the small amplitude branch of S− and cycle branch of S+ may touch the nonsmooth boundary and enter the other side of the boundary, which indicates the grazing bifurcations. By computing the bifurcation diagrams of the overall system, it is shown that grazing bifurcations result in complex distribution of cycle attractors as well as the occurrence of chaos. Based on these, multiple patterns of periodic and aperiodic bursting and the corresponding generation mechanisms are obtained. Besides, it is found that increasing the damping in coupling parts can improve the isolation efficiency.

Research on material selection of force-sensitive element for high-frequency dynamic piezoelectric pressure sensor

The high-frequency dynamic piezoelectric pressure sensor has the advantages of simple structure, long service life, high natural frequency, excellent signal-to-noise ratio and great sensitivity. It is appropriate for measuring high dynamic, dynamic or quasi-static pressure changes and pressure fluctuations. And this kind of sensor is widely utilized in the shock wave testing. The force-sensitive element is one of the main factors affecting the static and dynamic performance of piezoelectric pressure sensors. Basing on the piezoelectric equation and coupling effect between mechanics and electricity, in this paper, the finite element model of the high-frequency dynamic piezoelectric pressure sensor is established. The influences of the force-sensing element on the sensitivity of the sensor are analysed. Referential suggestions for choosing force-sensitive element of high-frequency dynamic piezoelectric pressure sensor are provided.

In situ monitoring and 3D geomechanical numerical modelling to evaluate seismic and aseismic rock deformation in response to deep mining

In this work we investigated seismic and aseismic rock mass behaviors in response to deep underground mining. For this purpose, an area under production of the metal mine of Garpenberg (Sweden) was instrumented with a geophysical and geotechnical monitoring network. In situ monitoring data were analyzed and interpreted considering mining operations and the local geological setting. In addition, a 3D elasto-plastic numerical model was built to better understand the interactions between quasi-static stress changes due to mining and the generation of the induced seismicity. Results of this multiparameter approach show a complex rock mass response. We observed two main types of seismic behaviors: one local and temporally short, directly induced by production, the other long-lasting over time and remote from excavations being mainly controlled by geological heterogeneities. In addition to seismicity, we also observed creep-like phenomena induced by mining. In turn, these time-dependent strains appear to be a third mechanism driving seismicity. All these findings underline the importance of considering both seismic and aseismic deformations when one wants to characterize the rock mass response to mining. This significantly enhances our understanding of the phenomena involved, as well as their interactions, for an improved hazard assessment in deep mining operations.

The effect of stress changes on time-dependent earthquake probabilities for the central Wasatch Fault Zone, Utah, USA.

Summary Static and quasi-static Coulomb stress changes produced by large earthquakes can modify the probability of occurrence of subsequent events on neighboring faults. This approach is based on physical (Coulomb stress changes) and statistical (probability calculations) models, which are influenced by the quality and quantity of data available in the study region. Here, we focus on the Wasatch Fault Zone (WFZ), a well-studied active normal fault system having abundant geologic and paleoseismological data. Paleoseismological trench investigations of the WFZ indicate that at least 24 large, surface-faulting earthquakes have ruptured the fault's five central, 35–59-km long segments since ∼7 ka. Our goal is to determine if the stress changes due to the youngest paleoevents have significantly modified the present-day probability of occurrence of large earthquakes on each of the segments. For each segment, we modeled the cumulative (coseismic + postseismic) Coulomb stress changes (∆CFScum) due to earthquakes younger than the most recent event on the segment in question and applied the resulting values to the time-dependent probability calculations. Results from the Coulomb stress modeling suggest that the Brigham City, Salt Lake City, and Provo segments have accumulated ∆CFScum larger than 10 bars, whereas the Weber segment has experienced a stress decrease of 5 bars, in the scenario of recent rupture of the Great Salt Lake fault to the west. Probability calculations predict high probability of occurrence for the Brigham City and Salt Lake City segments, due to their long elapsed times (> 1–2 ka) when compared to the Weber, Provo, and Nephi segments (< 1 ka). The range of calculated coefficients of variation (CV) has a large influence on the final probabilities, mostly in the case of the Brigham City segment. Finally, when the Coulomb stress and the probability models are combined, our results indicate that the ∆CFScum resulting from earthquakes postdating the youngest events on each of the five segments substantially affects the probability calculations for three of the segments: Brigham City, Salt Lake City, and Provo. The probability of occurrence of a large earthquake in the next 50 years on these three segments may therefore be underestimated if a time-independent approach, or a time-dependent approach that does not consider ∆CFS, is adopted.

The effect of NaOCl and heat treatment on static and dynamic mechanical properties and chemical changes of dentine

ObjectivesTo determine the effect of heat on flexural strength (FS), maximum strain (MS), storage modulus (SM), tan delta (TD) and chemical changes through micro-Raman spectroscopy of dentine exposed to 2.5% NaOCl or saline. Methodology: Dentine bars were randomly allocated to 8 test groups. Half (groups 2,4,6,8) were treated with NaOCl for 20 min; the rest (groups 1,3,5,7) remained in saline. FS/MS were measured in groups 1–4 (n = 15) (3/4 were also heated to 200 °C & re-hydrated in saline). Micro-Raman spectroscopy was performed on bars from groups 1–4. SM/TD were measured in 5–8: in 5/6 (n = 10), repeated after heating (200 °C), then following re-hydration; in 7/8 (n = 3) after heating to 25–185 °C. ResultsIncrease in MS on heat and FS/MS on heat + NaOCl was not significant (P > 0.05). SM increased (P = 0.06) after heat treatment but reduced to initial state after rehydration (P = 0.03). TD did not change (P = 0.4) after heat (200 °C) treatment but rehydration increased it compared with pre-treatment state (P = 0.001). For dentine bars pre-treated with NaOCl, SM did not change (P = 0.6) after heat (200 °C) treatment or rehydration but TD significantly increased (P = 0.02) upon re-hydration compared with pre- (P=0.007), or post- (P = 0.03) heat-treatment states. SM and TD varied between 25–185 °C with no consistent trend amongst the NaOCl pre-treated bars. Micro-Raman only detected chemical changes following NaOCl treatment in the mineral phase. ConclusionsExposure of dentine bars to heat and NaOCl produced only moderate changes to quasi-static but marked changes to viscoelastic properties, which may be explained by chemical alterations.

Specific Features of the Deformation and Fracture of Low-Alloy Steels in Hydrogen-Containing Media: Influence of Hydrogen Concentration in the Metal

We establish basic regularities of the influence of hydrogen concentration in metals on the fracture strength of low-alloy pipe steels. In particular, we determine the characteristic value of hydrogen concentration for which the mechanism of its influence on the deformation of specimens by uniaxial quasistatic tension changes, namely, below this concentration, hydrogen enhances the plasticity of the material and, above this concentration, promotes its embrittlement. For the first time, we detected an ambiguous relationship between fatigue crack-growth rate and the volume hydrogen concentration in these steels under cyclic loading in hydrogen-containing media and established its value for which the cyclic crack growth resistance of steel increases. We revealed a correlation between the intensity of hydrogenation of steels and the strength of passive film at the crack tip, which gives us an instrument for the development of efficient barriers against hydrogen penetration into the materials.

Steady-state thermodynamics for population growth in fluctuating environments.

We report that population dynamics in fluctuating environments is characterized by a mathematically equivalent structure to steady-state thermodynamics. By employing the structure, population growth in fluctuating environments is decomposed into housekeeping and excess parts. The housekeeping part represents the integral of the stationary growth rate for each condition during a history of the environmental change. The excess part accounts for the excess growth induced by environmental fluctuations. Focusing on the excess growth, we obtain a Clausius inequality, which gives the upper bound of the excess growth. The equality is shown to be achieved in quasistatic environmental changes. We also clarify that this bound can be evaluated by the "lineage fitness", which is an experimentally observable quantity.

INTERMEDIATE TERM EARTHQUAKE PREDICTION BASED ON INTEREVENT TIMES OF MAINSHOCKS AND ON SEISMIC TRIGGERING

Two models, which contribute to the knowledge on intermediate term earthquake prediction are further examined, improved and applied. The first of these models, called Time and Magnitude Predictable (TIMAP) regional model is based on repeat times of mainshocks generated by tectonic loading on a network of faults which are located in a certain seismic region (faults’ region). The second model, called Decelerating-Accelerating Strain (D-AS) model, is based on triggering of a mainshock by its preshocks. Parameters of the TIMAP model have been specified for the Aegean area and applied by a backward test in 86 circular faults’ regions of this area. The test shows the validity of this time dependent model with 29% false alarms. Data concerning decelerating and accelerating seismic (Benioff) strain, which preceded 46 strong (M≥6.3) recent mainshocks in a variety of global seismotectonic regimes, show that the generation of a mainshock is triggered by quasi-static stress changes due to accelerating preshocks which occur in a broad (critical) region and by static stress changes due to the large number (frequency of occurrence) of small preshocks generated in a narrow (seismogenic) region. Retrospective predictions (postdictions) of these 46 mainshocks by the D–AS model confirms previous results concerning the prediction uncertainties (2σ) of the model in the origin time (± 2.5 years), epicenter location (≤ 150 km) and magnitude (± 0.4) of an ensuing mainshock with a probability ~ 80%. Information is also given on the successful prediction by the D-AS model of: 1) the Cythera strong (M = 6.9) earthquake which occurred on 8 January 2006 in the southwestern part of the Hellenic Arc and 2) of the Rhodes strong (M = 6.4) earthquake which occurred on 15 July 2008 in the Eastern part of this Arc. A backward combined application of both models in the Aegean area shows an uncertainty ≤120km in the epicenter location of an ensuing mainshock.

HALO: Hop-by-Hop Adaptive Link-State Optimal Routing

We present HALO, the first link-state routing solution with hop-by-hop packet forwarding that minimizes the cost of carrying traffic through packet-switched networks. At each node $u$ , for every other node $t$ , the algorithm independently and iteratively updates the fraction of traffic destined to $t$ that leaves $u$ on each of its outgoing links. At each iteration, the updates are calculated based on the shortest path to each destination as determined by the marginal costs of the network's links. The marginal link costs used to find the shortest paths are in turn obtained from link-state updates that are flooded through the network after each iteration. For stationary input traffic, we prove that HALO converges to the routing assignment that minimizes the cost of the network. Furthermore, we observe that our technique is adaptive, automatically converging to the new optimal routing assignment for quasi-static network changes. We also report numerical and experimental evaluations to confirm our theoretical predictions, explore additional aspects of the solution, and outline a proof-of-concept implementation of HALO.

Parameters for novel incus replacement prostheses.

Prostheses replacing the incus in its normal position and equipped with two joints might transfer sound as effectively as the intact ossicular chain and allow adjustment to quasi-static pressure changes. A prerequisite for prostheses development is the access to dimensions and distances of the ossicular chain which are necessary to conceptualize shape and size. Fifteen cadaveric human temporal bone specimens were investigated by means of micro-CT followed by 3D analysis. Each specimen was scanned three times: after removal of incus, after additional removal of the malleus head, and after approaching the umbo to the promontory. Artificial umbo medialization as a surrogate for quasi-static pressure changes leads to relevant variations in the distance between the upper part of the malleus and the stapes. Prostheses replacing the incus in its normal position should be equipped with a sliding ball joint or similar construction to allow adjustment to quasi-static pressure changes.

Localized auxin peaks in concentration-based transport models of the shoot apical meristem

We study the formation of auxin peaks in a generic class of concentration-based auxin transport models, posed on static plant tissues. Using standard asymptotic analysis, we prove that, on bounded domains, auxin peaks are not formed via a Turing instability in the active transport parameter, but via simple corrections to the homogeneous steady state. When the active transport is small, the geometry of the tissue encodes the peaks' amplitude and location: peaks arise where cells have fewer neighbours, that is, at the boundary of the domain. We test our theory and perform numerical bifurcation analysis on two models that are known to generate auxin patterns for biologically plausible parameter values. In the same parameter regimes, we find that realistic tissues are capable of generating a multitude of stationary patterns, with a variable number of auxin peaks, that can be selected by different initial conditions or by quasi-static changes in the active transport parameter. The competition between active transport and production rate determines whether peaks remain localized or cover the entire domain. In particular, changes in the auxin production that are fast with respect to the cellular life cycle affect the auxin peak distribution, switching from localized spots to fully patterned states. We relate the occurrence of localized patterns to a snaking bifurcation structure, which is known to arise in a wide variety of nonlinear media, but has not yet been reported in plant models.

Instability of the magnetic fluid shape in the field of a line conductor with current

The static shape of the surface of a finite magnetic fluid volume between horizontal plates is investigated theoretically. The nonuniform magnetic field is generated by a horizontal line conductor with current, which is placed above the upper plate. The variational problem of minimum energy relative to plane surface perturbations is considered for a simply connected magnetic fluid volume. The problem is solved for arbitrary magnetic fields in the noninductive approximation with account for the gravity force and surface tension. Unstable solutions are found. The possibility of stepwise behavior in response to quasi-static changes of the current in the conductor is investigated for the surface shape of a finite magnetic fluid volume.

Elimination of harmonic induced viable bifurcations with TCSC for ac–fed electric arc furnaces

AC-fed electric arc furnaces (EAFs) are known with their unbalanced, excessively nonlinear and time varying load characteristics. The nonlinear oscillations produced by EAF operation cause several problems to interconnected feed system. Injection of harmonics/interharmonics and rising flicker effects on the feed system are two of major problems produced by EAF. These nonlinear effects result into quasistatic changes in the feed system parameters (L − R) . In last decade many studies have been reported that such quasistatic changes in the feed system parameters result in viable bifurcation formations which strictly cause sudden and drastic changes on system behaviors. This paper presents an analytical control procedure to eliminate viable bifurcation points on L − I and R − I curves that cause sudden resonant peak arc currents. After control procedure, stability margins of EAF are extended into larger levels and viable bifurcation points on the feed system parameter have been eliminated. During study, possible roles of small parameter changes of uncontrolled EAF around bifurcation points and controlled EAF have been traced over time series analysis, phase plane analysis and bifurcation diagrams. A wide collection of useful dynamic analysis procedures for the exploration of studied arc furnace dynamics have been handled through the AUTO open-source algorithms.

Phase transition in the Jarzynski estimator of free energy differences

The transition between a regime in which thermodynamic relations apply only to ensembles of small systems coupled to a large environment and a regime in which they can be used to characterize individual macroscopic systems is analyzed in terms of the change in behavior of the Jarzynski estimator of equilibrium free energy differences from nonequilibrium work measurements. Given a fixed number of measurements, the Jarzynski estimator is unbiased for sufficiently small systems. In these systems the directionality of time is poorly defined and the configurations that dominate the empirical average, but which are in fact typical of the reverse process, are sufficiently well sampled. As the system size increases the arrow of time becomes better defined. The dominant atypical fluctuations become rare and eventually cannot be sampled with the limited resources that are available. Asymptotically, only typical work values are measured. The Jarzynski estimator becomes maximally biased and approaches the exponential of minus the average work, which is the result that is expected from standard macroscopic thermodynamics. In the proper scaling limit, this regime change has been recently described in terms of a phase transition in variants of the random energy model. In this paper this correspondence is further demonstrated in two examples of physical interest: the sudden compression of an ideal gas and adiabatic quasistatic volume changes in a dilute real gas.

Ab initiostudy of pressure stabilized NiTi allotropes: Pressure-induced transformations and hysteresis loops

Changes in stoichiometric NiTi allotropes induced by hydrostatic pressure have been studied employing density functional theory. By modelling the pressure-induced transitions in a way that imitates quasi-static pressure changes, we show that the experimentally observed B19' phase is (in its bulk form) unstable with respect to another monoclinic phase, B19". The lower symmetry of the B19" phase leads to unique atomic trajectories of Ti and Ni atoms (that do not share a single crystallographic plane) during the pressure-induced phase transition. This uniqueness of atomic trajectories is considered a necessary condition for the shape memory ability. The forward and reverse pressure-induced transition B19'{$\leftrightarrow$}B19" exhibits a hysteresis that is shown to originate from hitherto unexpected complexity of the Born-Oppenheimer energy surface.

Preparation, microstructure and deformation behavior of Zr-based metallic glass/porous SiC interpenetrating phase composites

New Zr-based metallic glass/porous SiC interpenetrating phase composites were prepared by water quenching after pressure infiltration. Microstructural investigations conducted by scanning electron microscopy and X-ray diffraction show that the voids of the porous SiC preform were filled with the melt which was quenched into an amorphous state during subsequent solidification. Both the metallic glass and the porous SiC exhibit a three-dimensional interconnected net structure. The fracture mode of the composites under quasi-static compression changes from a shear mode to an axial splitting mode with the increase of the SiC volume fraction from 51% to 82%. The significant difference was present in the fracture morphologies of the composites with various volume fractions of the SiC preform. The stresses concentrated in the phase ahead the interface inflections are proposed to be responsible for the transformation of the compressive fracture mode. (C) 2011 Elsevier B.V. All rights reserved.

Mechanics of layered anisotropic poroelastic media with applications to effective stress for fluid permeability

The mechanics of vertically layered porous media has some similarities to and some differences from the more typical layered analysis for purely elastic media. Assuming welded solid contact at the solid–solid interfaces implies the usual continuity conditions, which are continuity of the vertical (layering direction) stress components and the horizontal strain components. These conditions are valid for both elastic and poroelastic media. Differences arise through the conditions for the pore pressure and the increment of fluid content in the context of fluid-saturated porous media. The two distinct conditions most often considered between any pair of contiguous layers are: (1) an undrained fluid condition at the interface, meaning that the increment of fluid content is zero ( i.e., δζ = 0), or (2) fluid pressure continuity at the interface, implying that the change in fluid pressure is zero across the interface ( i.e., δp f = 0). Depending on the types of measurements being made on the system and the pertinent boundary conditions for these measurements, either (or neither) of these two conditions might be directly pertinent. But these conditions are sufficient nevertheless to be used as thought experiments to determine the expected values of all the poroelastic coefficients. For quasi-static mechanical changes over long time periods, we expect drained conditions to hold, so the pressure must then be continuous. For high-frequency wave propagation, the pore-fluid typically acts as if it were undrained (or very nearly so), with vanishing of the fluid increment at the boundaries being appropriate. Poroelastic analysis of both these end-member cases is discussed, and the general equations for a variety of applications to heterogeneous porous media are developed. In particular, effective stress for the fluid permeability of such poroelastic systems is considered; fluid permeabilities characteristic of granular media or tubular pore shapes are treated in some detail, as are permeabilities of some of the simpler types of fractured materials.