Natural Stability Conditions Research Articles

ANÁLISIS DE ESTABILIDAD DE TALUDES MEDIANTE EL EMPLEO DE ELEMENTOS FINITOS: UN CASO DE ESTUDIO EN LA PAZ – BOLIVIA

The geomechanically analysis of slopes is one important application within the geotechnical engineering scope; this fact comprehends the evaluation of natural or artificial slope stability conditions. Such evaluation process can be optimized by means of modelling combined with engineer criteria. It is important to apply a mathematical model that focuses in the analysis objective and expected results; stress-strain methods allow determining the resistant and deformational parameters in a slope, being capable to reproduce its natural behavior [1]. The present research applies to a specific sector of La Paz city, named Villa Exaltacion. The objective of this study is the performing of slope stability analysis through finite elements, in order to determine the areas that need remediation. The evaluation of stability alternatives it is also included. These alternatives go from simple remediation techniques (unstable material removal, slope undercut, inclination reduction, toe counterweight) to complex stabilization works such as pile curtains. The results reveal that a head slope undercut technique can bring stable conditions and minimal strain generation, being a satisfactory and feasible answer with low complexity works. Finally, verification was performed by means of limit equilibrium analysis. Both methodologies show satisfactory results, demonstrating that numerical methods are more representative and conservative. The calibration process of soil parameters plays a key role for the generation of a reliable model; critical conditions were simulated in order to determine minimal parameters needed for a stable slope.

Nonabelianization of Higgs bundles

The character varieties of representations of a surface group into the Lie groups SL(m,H), SO(2m,H) and Sp(m,m) have a holomorphic description in terms of the moduli space of Higgs bundles. We show that the fibres of the integrable system in these cases are not abelian varieties, but are instead moduli spaces of rank 2 bundles on a spectral curve, satisfying natural stability conditions.

Effects of Heater Orientations on the Natural Circulation and Heat Transfer in a Supercritical CO2 Rectangular Loop

Supercritical fluid based heat transfer loop (NCL) has become a hot topic in energy conversion systems. In such systems, supercritical natural convection stability and heat transfer conditions are crucial for design and safe operation. In the present study, numerical simulations were performed to investigate the influences of heater orientations on the performance of supercritical CO2 based circulation loops. The numerical model is based on Navier-Stokes equations with supercritical turbulence effects considered. It is found that the heat source location has significant influence on the flow pattern and system heat transfer. Vertical heating cases are found stable in a wide range of heat flux conditions due to the changes of buoyancy force torques across the NCLs, while horizontal heating cases show transition heat flux and oscillations are still seen. However, the influence of heat source location is less significant on the heat transfer characteristics. The effect of cooler heat transfer is found of special importance for the heat transfer and system stability behaviors. The NCL flow and heat transfer correlations are also compared in this study, and it is recommended that more numerical and experimental studies be made in the future.

Asymptotic Irrelevance of Initial Conditions for Skorohod Reflection Mapping on the Nonnegative Orthant

A reflection map, induced by the deterministic Skorohod problem on the nonnegative orthant, is applied to a vector-valued function X on the nonnegative real line and then to a + X, where a is a nonnegative constant vector. A question that was posed over 15 years ago is, under what conditions does the difference between the two resulting regulated functions converge to zero for any choice of a as time diverges. This, in turn, implies that if one imposes enough stochastic structure that ensures that the reflection map applied to a multidimensional process X converges in distribution, then it will also converge in distribution when it is applied to η + X, where η is any almost surely finite-valued random vector that may even depend on the process X. In this paper we obtain a useful equivalent characterization of this property. As a result, we are able to identify a natural sufficient condition in terms of the given data X and the constant routing matrix. A similar necessary condition is also indicated. A particular implication of our analysis is that under additional stochastic assumptions, asymptotic irrelevance of the initial condition does not require the existence of a stationary distribution. As immediate corollaries of our (and earlier) results we conclude that under the natural stability conditions, a reflected Lévy process as well as a Markov additive process has a unique stationary distribution and converges in distribution to this stationary distribution for every initial condition. Extensions of the sufficient condition are then developed for reflection maps with drift and routing coefficients that may be time- and state-dependent; some implications to multidimensional insurance models are briefly discussed.

Active force-torque robot control without using wrist force-torque sensors

A method of active force-torque control of manipulator robots is considered; in this method it is proposed to use signals proportional to elastic deformations of flexible elements of the manipulators as feedback signals, rather than conventional forces and moments of reactions arising under the contact of the gripper and the moved object. It is proposed to construct control laws which are the functions of these feedback constraints in such a way that they generate artificial potential control forces. Due to it, unlike conventional approaches, simple and natural stability conditions are provided, as well as the weak dependence of dynamic properties of the control system on the variation of its parameters, i.e., the parametric robustness of the system.

Analysis of stochastic fluid queues driven by local-time processes

We consider a stochastic fluid queue served by a constant rate server and driven by a process which is the local time of a reflected Lévy process. Such a stochastic system can be used as a model in a priority service system, especially when the time scales involved are fast. The input (local time) in our model is typically (but not necessarily) singular with respect to the Lebesgue measure, a situation which, in view of the nonsmooth or bursty nature of several types of Internet traffic, is nowadays quite realistic. We first discuss how to rigorously construct the (necessarily) unique stationary version of the system under some natural stability conditions. We then consider the distribution of performance steady-state characteristics, namely, the buffer content, the idle period, and the busy period. These derivations are much based on the fact that the inverse of the local time of a Markov process is a Lévy process (a subordinator), hence making the theory of Lévy processes applicable. Another important ingredient in our approach is the use of Palm calculus for stationary random point processes and measures.

Analysis of stochastic fluid queues driven by local-time processes

We consider a stochastic fluid queue served by a constant rate server and driven by a process which is the local time of a reflected Lévy process. Such a stochastic system can be used as a model in a priority service system, especially when the time scales involved are fast. The input (local time) in our model is typically (but not necessarily) singular with respect to the Lebesgue measure, a situation which, in view of the nonsmooth or bursty nature of several types of Internet traffic, is nowadays quite realistic. We first discuss how to rigorously construct the (necessarily) unique stationary version of the system under some natural stability conditions. We then consider the distribution of performance steady-state characteristics, namely, the buffer content, the idle period, and the busy period. These derivations are much based on the fact that the inverse of the local time of a Markov process is a Lévy process (a subordinator), hence making the theory of Lévy processes applicable. Another important ingredient in our approach is the use of Palm calculus for stationary random point processes and measures.

ON THE UNIQUENESS OF GIBBS STATES IN THE PIROGOV–SINAI THEORY

We consider models of classical statistical mechanics satisfying natural stability conditions: a finite spin space, translation-periodic finite potential of finite range, a finite number of ground states meeting Peierls or Gertzik–Pirogov–Sinai condition. The Pirogov–Sinai theory describes the phase diagrams of these models at low temperature regimes. By using the method of doubling and mixing of partition functions we give an alternative elementary proof of the uniqueness of limiting Gibbs states at low temperatures in ground state uniqueness region.

On a Class of Lévy Stochastic Networks

We consider a Levy stochastic network as a regulated multidimensional Levy process. The reflection direction is constant on each boundary of the positive orthant and the corresponding reflection matrix corresponds to a single-class network. We use the representation of the Levy process and Ito's formula to arrive at some equations for the steady-state process; the latter is shown to exist, under natural stability conditions. We specialize first to the class of Levy processes with non-negative jumps and then add the assumption of self-similarity. We show that the stationary distribution of the network corresponding the the latter process does not has product form (except in trivial cases). Finally, we derive asymptotic bounds for two-dimensional Levy stochastic network.

STABILITY OF POLIPHIMOS CAVE IN MARONEIA, THRACE

The Poliphimos cave is located in a distance of 5 km from Maronia Town, near Komotini City, in Thrace - Eastern Greece. The cave is an under development site for touristic purposes. The cave is full of beautiful stalactites and stalagmites and it is of great palaeontological and touristic interest. The cave is 2000 m long and covers an area of 10.000 m2 . The proposed visiting route is 355 m. The inside temperature is about 16 °C. For the development an integrated study was performed regarding to its geotechnical stability, together with speleological and ecological studies. In the present paper the stability conditions were studied regarding to wedge and planar failures.For this purpose, all the tectonic data were determined and recorded separately for each site in the cave and tectonic and stability diagrams were elaborated, in order to determine stability factors. A stress-strain analysis as performed in tunneling is not recommended in cases of natural caves because of the slow procedure of its formation which allows the full relief of the applied stresses. So the stability analysis of the natural cave is based only on the behavior of the blocks formed by the tectonic features. The geometry of the blocks formed by the combination of the vertical discontinuities sets with the horizontal bedding creates potential instability conditions. The instability conditions observed in situ are mainly unstable blocks falling from the roof. The main purpose, after determining any type of potential failure, was to propose the more appropriate stability methods. It is obvious that all the ordinary methods, used in underground construction, are not appropriate for use in caves.Supporting methods have to be adapted, taking into account the already existing natural stability conditions, the safety of visitors and the monumental character of the cave. According to the stability analysis of the cave, the main failure mechanism is the falling of wedges from the roof. The sides of the cave seem to be stable. For the reinforcement support of the roof, an arrangement of stainless pre-tensioned self-drilling rockbolts is suggested (2X2m and 2X2.5m, length 3m and 5m) as the optimum scenario of intervention.

Stochastic storage networks: stationarity and the feedforward case

We show that for a certain storage network the backward content process is increasing, and when the net input process has stationary increments then, under natural stability conditions, the content process has a stationary version under which the cumulative lost capacities have stationary increments. Moreover, for the feedforward case, we show that under some minimal conditions, two content processes with net input processes which differ only by initial conditions can be coupled in finite time and that the difference of two content processes vanishes in the limit if the difference of the net input processes monotonically approaches a constant. As a consequence, it is shown that for the natural stability conditions, when the net input process has stationary increments, the distribution of the content process converges in total variation to a proper limit, independent of initial conditions.

Stochastic storage networks: stationarity and the feedforward case

We show that for a certain storage network the backward content process is increasing, and when the net input process has stationary increments then, under natural stability conditions, the content process has a stationary version under which the cumulative lost capacities have stationary increments. Moreover, for the feedforward case, we show that under some minimal conditions, two content processes with net input processes which differ only by initial conditions can be coupled in finite time and that the difference of two content processes vanishes in the limit if the difference of the net input processes monotonically approaches a constant. As a consequence, it is shown that for the natural stability conditions, when the net input process has stationary increments, the distribution of the content process converges in total variation to a proper limit, independent of initial conditions.