Displacement Regime Research Articles

Localization for the Random Displacement Model at Weak Disorder

This paper is devoted to the study of the random displacement model on \({\mathbb{R}^d}\) . We prove that, in the weak displacement regime, Anderson and dynamical localization hold near the bottom of the spectrum under a generic assumption on the single-site potential and a fairly general assumption on the support of the possible displacements. This result follows from the proof of the existence of Lifshitz tails and of a Wegner estimate for the model under scrutiny.

Mixed convection in a ventilated enclosure

This paper presents analysis, visualizations and differential pressure measurements of the flow within a confined ventilated space resulting from a buoyant turbulent 2D plume originating at the bottom of the enclosure with initial source volume flux, Q 0 and buoyancy flux, B 0. The enclosure is ventilated through lower and upper openings of heights H E and H S separated by a vertical distance H. Simple analysis shows that flow regimes between the interior and the exterior of the enclosure depends on a densitometric Froude number Fr ¯ H = Q 0 2 / ( Δ ρ ¯ H / ρ ) gH ( C S A S ) 2 related to the source flow rate, the density inside the enclosure and the area of the upper opening. For Fr ¯ H < 2 , a displacement regime is observed with inflow at the lower opening and outflow at the higher opening. For Fr ¯ H > 2 , the regime is blocked with two outflows. When the enclosure is well mixed the value Fr ¯ H = 2 corresponds to the criteria given by Woods et al. (2003). Experiments show that the natural regime is observed for Fr ¯ H < 2 while the blocked regime appears when Fr ¯ H > 2.6 . There is an intermediate regime for 2 > Fr ¯ H > 2.6 . This last regime where inflow and outflow are both present through the lower opening is due to the non negligible size of this opening not taken into account in the analysis.

Simulation of a flow of a “Sedate” reaction mass in a screw reactor with a thin wall layer

A transition to a flow virtually non-gradient in a screw reactors of heavy sedate liquid with thin wall layer is considered. The graphs of the differential response functions of the known models based on the ideal gas law for structures of flows (ideal mixture, ideal displacement, laminar and turbulent flows) in comparison with the response function of the sedate reaction mass were presented. The flow structure corresponds to the regime of the ideal displacement in the screw reactor at a treatment of the sedate reaction mass when air, water or other thin liquid are fed as lubricant in the wall layer.

Reduction in the field-dependent microwave surface resistance in YBa2Cu3O7−δ with submicrometric BaZrO3 inclusions as a function of BaZrO3 concentration

In order to study the vortex pinning determined by artificially introduced pinning centers in the small-vortex displacement regime, we measured the microwave surface impedance at 47.7 GHz in the mixed state of YBa2Cu3O7−δ thin films, where submicrometric BaZrO3 particles have been incorporated. As a function of the BaZrO3 content, we observed that the absolute losses slightly decrease up to a BaZrO3 content of 5%, and then increase. We found that the magnetic-field-induced losses behave differently in that they are not monotonic with increasing BaZrO3 concentration. At small concentration (2.5%) the field-induced losses increase, but large reduction in the losses themselves, by factors up to 3, is observed upon further increasing the BaZrO3 concentration in the target up to 7%. Using measurements of both surface resistance and surface reactance, we estimate vortex pinning-related parameters. We found that BaZrO3 inclusions introduce deep and steep pinning wells. In particular, the minimum height of the energy barrier for single vortices is raised. At larger BaZrO3 content (5% and 7%) the phenomenon is at its maximum, but it is unclear whether it shows a saturation or not, leaving room for further improvements.

Computer simulations of the collective displacement of self-propelled agents

We report extensive computer simulations of the Vicsek model [V.M. Vicsek, et al., Phys. Rev. Lett. 75 (1995) 1226], aimed to describe the onset of ordering within the low-velocity regime of the collective displacement of self-driven agents. The VM assumes that each agent adopts the average direction of movement of its neighbors, perturbed by an external noise. The existence of a phase transition between a state of ordered collective displacement (low-noise limit) and a disordered regime (high-noise limit) is most likely the most distinctive feature of the VM. In this paper, after briefly discussing the critical nature of the transition we focus our attention on the behavior of the VM in the low-velocity ( v 0 → 0 ) regime for the displacement of the agents. In fact, while the XY model, which could somewhat be considered as the equilibrium counterpart of the VM, does not exhibit order in d = 2 dimensions, an intriguing feature of the VM is precisely the onset of order. Since in the XY model the particles remain fixed in the lattice, we show that the understanding of the v 0 → 0 limit is relevant in order to explain the different behavior of both models.

Investigation of a large collapse sinkhole affecting a multi-storey building by means of geophysics and the trenching technique (Zaragoza city, NE Spain)

An active sinkhole around 100 m long has been investigated in the city of Zaragoza (NE Spain). Subsidence activity on this depression, including the sudden occurrence of a collapse sinkhole 5 m across, led to the abandonment of a factory in the 1990s. At the present time, a building with 100 flats and shallow pad foundations partially built on the sinkhole, is affected by rapid differential settlement. The development of the sinkhole results from the karstification of the halite- and glauberite- bearing bedrock and the sagging and collapse of the overlying bedrock and alluvium, more than 30 m thick. GPR and electrical resistivity profiles have provided information on the distribution and geometry of the subsidence structure. The application of the trenching technique and geochronological methods (AMS and OSL dating) has allowed us to infer objective and practical data on the sinkhole including (1) Limits of the subsidence structure, (2) subsidence mechanisms, (3) cumulative subsidence (>408 cm), (4) subsidence rates on specific failure planes (>1.8 cm/year), (5) episodic displacement regime of some fault planes. The available information indicates that the progressive deformation recorded in the building will continue and might be punctuated by events of more rapid displacement. This work illustrates the practicality of the trenching technique for the study of sinkholes in mantled karst areas.

Electromigration of microspheres in ferroelectric smectic liquid crystals

When an electric field is applied to microspheres which are dispersed in a ferroelectric smectic liquid crystal, particle translation along the smectic layer plane, i.e., in a direction nearly perpendicular to that of the director, can be observed. Under certain electric field conditions the translation is shown to be linear in time. We have determined the stability regime of linear particle displacement in the parameter space of amplitude and frequency for various applied wave forms. This regime enlarges for increasing electric field amplitude and frequency, with a threshold behavior observed for small parameters. The upper stability boundary is related to the reciprocal ferroelectric switching time. The microspheres translational velocity is independent of the applied electric field amplitude, but increases linearly with applied frequency. The microsphere velocity also increases with increasing temperature, which is indicative of the respective decrease in liquid crystal viscosity. Possible mechanisms of electric-field-induced particle motion are discussed.

Path integral Monte Carlo study of the interacting quantum double-well model: Quantum phase transition and phase diagram

The discrete time path integral Monte Carlo with a one-particle density matrix approximation is applied to study the quantum phase transition in the coupled double-well chain. To improve the convergence properties, the exact action for a single particle in a double-well potential is used to construct the many-particle action. The algorithm is applied to the interacting quantum double-well chain for which the zero-temperature phase diagram is determined. The quantum phase transition is studied via finite-size scaling, and the critical exponents are shown to be compatible with the classical two-dimensional Ising universality class--not only in the order-disorder limit (deep potential wells), but also in the displacive regime (shallow potential wells).

South Variscan terrane accretion: Sardinian constraints on the intra-Alpine Variscides

Structural data are presented that show that the Sardinian Variscides form the boundary of the Variscan intra-Alpine terrane, thrust onto a Gondwana foreland. This model replaces the currently held hypothesis that the south Armorican suture zone continues into the Sardinian Variscides. The orogenic activity propagated toward the foreland in two distinct waves: (1) thrusting, burial and Barrovian type metamorphism that reached the internal orogen in Late Devonian times and lasted in the external orogen until Early Carboniferous times. Transpressional strain partitioning is suggested by frontal thrusting in the external orogen and lateral displacement in the internal orogen. (2) Normal faulting, exhumation and local Buchan type metamorphism were superimposed on the internal orogen probably since Early Carboniferous times and reached the external orogen contemporaneously with the Late Carboniferous emplacement of voluminous granitic intrusions. Extensional doming and lateral displacement indicate a transtensional regime. The sense of orogen-parallel displacement during both stages was left-lateral on inward dipping movement planes and right-lateral on outward dipping movement planes. The resulting left-lateral displacement between the intra-Alpine terrane and the Gondwana foreland is due to the bending of the Variscan belt, during which the Sardinian segment underwent a bookshelf type movement within an overall right-lateral displacement regime.

Flexural–torsional bifurcations of a cantilever beam under potential and circulatory forces II. Post-critical analysis

The post-critical behavior of a cantilever beam with rectangular cross-section, under simultaneous action of conservative and non-conservative loads, is analyzed. An internally constrained Cosserat rod model is adopted to describe the dynamics of the beam in finite displacement regime. The bifurcation equations for simple buckling (divergence), simple flutter (Hopf) and double-zero (Takens–Bogdanova–Arnold) bifurcations are derived by means of the multiple time scales method. Due to the nilpotent eigenvalue at the double-zero critical point, the evaluation of the generalized Keldysh's eigenfunctions is required. Finally, some numerical results are shown and the bifurcation scenario of the beam is discussed.

A new way to manage displacements in zones of active faults

The objective of this paper was to perform the complex study of features of force and deformation response of interfaces between structural tectonic blocks in the Earth's crust (active faults), which are under complex stress. The research was based on consideration of contacting geoblocks as typical friction pairs. This allowed authors to suggest investigation of influence of vibrations and also of lubrication induced change of physico-mechanical properties of the contact zone (this was realized by watering) on the maximum value of sliding resistance force and regime of relative tangential block displacement (slip). It was found that combined use of watering and “high-frequency” vibration fundamentally changes response regime of interface region and can initiate extensive but seismically safe “smooth” displacements of geo-blocks along the fault. Analysis of investigation results on the basis of Tomlinson model shown that revealed change of response character (including sliding regime) of boundaries between structural elements is general for friction pairs of various natures. Analysis of research results allows authors to propose the new approach to manmade control of displacements along seismically active faults. This approach seems to be an important tool in the management of seismic hazards in the future.

Electromigration of microspheres in nematic liquid crystals

Application of an electric field to microspheres, dispersed in a nematic liquid crystal host material, causes particle translation along the direction of the average long molecular liquid crystal axis, i.e., the director. We have determined the stability regime of linear particle displacement in the parameter space of electric field amplitude and frequency for various applied electric wave forms and demonstrate a linear relationship between microsphere velocity and applied electric field amplitude. For increasing frequency the particle velocity exhibits a maximum before motion slowly vanishes. Addition of a small amount of an ionic dopant is shown to largely increase the stability region of linear microsphere motion, with particle velocities increasing until saturation is observed for increasing ion dopant concentration. It is presumed that the particle velocity is related to the surface charges adsorbed on the dispersed particles. Also the dynamics of occasionally observed two- and three-particle clusters is discussed.

Factors Affecting Cleanup of Water Blocks: A Laboratory Investigation

Summary Water-blocked low-permeability gas formations with drawdown pressures comparable to capillary entry pressures can take a very long time to clean up. This work aims to study the effect of permeability, wettability, temperature, and drawdown on the cleanup of cores containing brine. Gas displacement experiments were conducted on cores fully saturated with brine. Addition of methanol, increasing temperature, and increasing core permeability by changing rock type resulted in faster cleanup after approximately 50 to 100 pore volumes (PV, the volume of vacant pores in the dry sample) of gas flow. The change of wettability of the rock from water-wet to oil-wet also resulted in faster recoveries in gas relative permeability. The cleanup of water blocks in gas wells occurs in two regimes: displacement of the fluids from the formation, followed by vaporization by the flowing gas, which becomes undersaturated as the pressure decreases. Our observations show that the cleanup of water blocks can be improved by: (a) Influencing the displacement regime (i.e., by changing the wettability) and (b) increasing the rate of vaporization by introducing volatile solvents such as methanol. The study quantifies the effects of factors such as rock type (permeability), wettability, surface tension/volatility, and temperature on gas relative permeability. The results of this study will help in selecting strategies for cleanup of water blocks created by various operations such as drilling, acidizing, and fracturing, as well as making recommendations for the use of surfactants or solvents for well treatments to remove water blocks.

Motive Forces in a Complex Model Involving a Direct Flow and Mixing of a Liquid

The influence of liquid mixing on mean logarithmic and arithmetic forces as well as the numbers of transfer units in direct flow has been studied. The extreme cases where liquid on the plate is entirely mixed and where it moves in a regime of perfect displacement are considered. The interrelationship between the mean arithmetic forces and numbers of transfer units in the case of complete liquid mixing and without it has been found. Dependences of the efficiency on the numbers of transfer units are determined.

Classification and quantification of microstructures in steels

The International Institute of Welding (IIW) microstructure classification scheme for ferrous weld metals has been investigated as a basis for the quantification of complex microstructures in steels. The aim has been to cover the full range of microstructures observed in plain carbon and low alloy steel products, as well as ferritic weld metals and parent plate heat affected zones. The mechanisms of formation of the principal structures and the characteristic ferrite morphologies produced in the reconstructive and displacive transformation regimes of ferrous materials have been briefly reviewed. The classification and terminology used for intragranular as well as austenite grain boundary microstructural constituents have been considered, and also the way in which transformation products are orientated in space. Problems encountered in relating microstructural constituents to principal structures have been discussed in detail and solutions proposed. The microstructure classification and terminology used in the IIW scheme have been built upon and new terminology incorporated into a table providing descriptions of the principal structures and sub-category components. A new classification scheme has been defined in the form of flow charts with guidelines for identifying the principal structures. Evaluation exercises have been carried out with the new scheme. These have shown that a reasonable degree of consistency may be obtained between operators in identifying primary ferrite, pearlite, martensite and the transformation products constituting ferrite sideplate and acicular ferrite structures, notably Widmanstätten ferrite and bainite. A means is thus provided of obtaining database information for developing microstructure–property relationships, or generating data for calibrating physical models, which have the principal structures as their output.

Laboratory-Based Evaluation of Gas Well Deliverability Loss Caused by Water Blocking

Summary Water blocking caused by invasion of completion fluids has been suspected to reduce gas well deliverability.1–5 However, this effect has not been quantified. We report results of a laboratory program to measure the water-blocking effect in core samples from a gas field. These data were mapped to a wellbore model to make deliverability predictions. The laboratory data consist of gas flow rate as a function of injected gas pore volume for various liquids (brine, methanol, toluene, isopropyl alcohol, and brine-methanol mixtures) at two saturation states (fully saturated with liquid, and containing liquid and trapped gas). We injected over 10,000 PV of gas in each test to mimic near-wellbore conditions. The data showed that the liquid displacement regime was followed by a mass transfer regime. The wellbore model had a time varying skin to account for the cleanup of the fluid invaded ("water-blocked") region. Cleanup occurs as gas flows past this high liquid-saturated region and removes liquid by displacement and mass transfer. We used the laboratory data to relate the reduced permeability of this region to pore volumes of gas throughput. We find that any loss in gas well deliverability recovers in two phases. The first phase corresponds to fluid displacement ("flowback period") and lasts for a few days at most. The second phase is slower and can last several months. Here, evaporation causes the deliverability to slowly increase. It is in this regime that adding volatile fluids, such as methanol, to the completion brines has advantages.

ON DISPERSION IN THE MATHEMATICAL MODEL OF POROELASTIC MATERIALS WITH THE BALANCE EQUATION FOR POROSITY

This article concerns the nonlinear asymptotic analysis of the mathematical model of a multi-component poroelastic medium with the porosity balance equation. It is proved that there exist soliton-like solutions for porosity and kink-like solutions for phase velocities under conditions similar to the entropy one. It is shown that solutions appear that describe a regime of stable displacement (so-called piston displacement) and a regime similar to the Saffman–Taylor instability. It is established that the diffusion force of interaction between phases of the inner friction type causes a decrease in the amplitudes of the discontinuities. This leads to the damping of initial perturbations of stable states. Such regimes have some properties similar to those of the pendulum model in the vicinity of a stable equilibrium point.

Dynamic crosswind fatigue of slender vertical structures

Wind-excited vibrations of slender structures can induce fatigue damage and cause structural failure without exceeding ultimate limit state. Unfortunately, the growing importance of this problem is coupled with an evident lack of simple calculation criteria. This paper proposes a mathematical method for evaluating the crosswind fatigue of slender vertical structures, which represents the dual formulation of a parallel method that the authors recently developed with regard to alongwind vibrations. It takes into account the probability distribution of the mean wind velocity at the structural site. The aerodynamic crosswind actions on the stationary structure are caused by the vortex shedding and by the lateral turbulence, both schematised by spectral models. The structural response in the small displacement regime is expressed in closed form by considering only the contribution of the first vibration mode. The stress cycle counting is based on a probabilistic method for narrow-band processes and leads to analytical formulae of the stress cycles histogram, of the accumulated damage and of the fatigue life. The extension of this procedure to take into account aeroelastic vibrations due to lock-in is carried out by means of ESDU method. The examples point out the great importance of vortex shedding and especially of lock-in concerning fatigue.

Cooperative dynamics in unentangled polymer fluids.

We present a generalized Langevin equation for the dynamics of interacting semiflexible polymer chains undergoing slow cooperative dynamics. The calculated Gaussian intermolecular center-of-mass and monomer potentials are in quantitative agreement with computer-simulation data. The experimentally observed short-time subdiffusive regime of the polymer mean-square displacement emerges from the competition between intra- and intermolecular mean-force potentials.

Dynamical properties of magnetization reversal in exchange-coupled NiO/Co bilayers

Real time dynamic magnetization reversal measurements at room temperature have been performed on polycrystalline exchange-coupled NiO/Co bilayers over 10 decades of applied field sweep rates. Domain wall displacement and domain nucleation regimes govern the magnetization reversal at low and high sweep rates, respectively. The crossover between the two regimes depends on the relative thickness of the two layers. Thicker Co favors propagation, whereas thicker NiO favors nucleation. The coupling energy at the interface was found to be inversely proportional to the square root of the area corresponding to the activation (Barkhausen) volume. These results are consistent with a model of exchange anisotropy in which a randomness of the coupling along the ferromagnetic (F)/antiferromagnetic (AF) interface is combined with a thermally activated switching process of the AF magnetization.