Updating constraint preconditioners for KKT systems in quadratic programming via low-rank corrections

This work focuses on the iterative solution of sequences of KKT linear systems arising in interior point methods applied to large convex quadratic programming problems. This task is the computational core of the interior point procedure and an efficient preconditioning strategy is crucial for the efficiency of the overall method. Constraint preconditioners are very effective in this context; nevertheless, their computation may be very expensive for large-scale problems, and resorting to approximations of them may be convenient. Here we propose a procedure for building inexact constraint preconditioners by updating a "seed" constraint preconditioner computed for a KKT matrix at a previous interior point iteration. These updates are obtained through low-rank corrections of the Schur complement of the (1,1) block of the seed preconditioner. The updated preconditioners are analyzed both theoretically and computationally. The results obtained show that our updating procedure, coupled with an adaptive strategy for determining whether to reinitialize or update the preconditioner, can enhance the performance of interior point methods on large problems.Comment: 22 page

Effect of flow choking on experimental average friction factor of gas microflows

Pressure drop experiments are performed for a rectangular channel having a hydraulic diameter of 295\u3bcm (w=360\u3bcm, h=250\u3bcm) up to Re 16000. A validated numerical model is used to gain insight of flow physics inside employed microchannel test assembly. Comparison of numerical and experimentally calculated flow properties considering two different data reduction methodologies show that adiabatic treatment of gas results in a better agreement of average friction factor values with conventional theory in turbulent regime. Minor loss coefficients available in literature are not valid for microflows as they change from one assembly to other. This necessitates an estimation of minor loss coefficients as a priori which can be established using a validated numerical model of the experimental test rig. However, such a treatment of minor loss coefficients adds an additional step of establishing a well posed numerical model before each experiment and hence is not convenient at all from experimentalist point of view. An adiabatic treatment of the gas along the length of the channel coupled with isentropic flow assumption from manifold to microchannel inlet results in a self-sustained experimental data reduction and therefore should be followed in consequent gas flow studies. Furthermore, assumption of perfect expansion and wrong estimation of average gas temperature between inlet and outlet results in an apparent increase of experimental friction factor in highly turbulent choked regime. Literature has been divided into two main approaches for establishing experimental average frictional characteristics in micro channels (MCs). When a total pressure drop and inlet temperature are available, a classical methodology is to invoke minor loss coefficients and subtract pressure losses associated to inlet/outlet manifold. Resulting pressure difference is then utilized along with measured temperature at manifold inlet to calculate average isothermal fanning friction factor. Such a treatment is quite realistic when an incompressible liquid working fluid is utilized but has been applied to compressible flows as well in the past [1]. In reality, a gas microflow does not stay isothermal and shows a strong temperature decrease close to outlet for adiabatic walls. For an adiabatic flow, temperature estimation at MC outlet can be done using a quadratic equation proposed by [2]. Data reduction methodology where minor losses are utilized along with the temperature estimation at outlet, is referred to as M1 in the subsequent text. An alternative methodology (M2), originally proposed by [2] is to estimate MC inlet flow properties by assuming isentropic flow between inlet manifold and MC inlet. This automatically caters for a reduction in MC inlet pressure and hence inlet coefficient is not required. Main aim of current study is to investigate underlying differences and their effects on experimental average friction factor between above stated methodologies in the presence of flow choking. An establishment of a unique methodology for future compressible gas experimentalists is also intended

DEL British Dashboard October 2020

Overall, the profile of public engagement with development has not changed significantly since June 2020. Changes in overall engagement between June and October with the 10 actions DEL tracks are small and/or insignificant

Data reduction of average friction factor of gas flow through adiabatic micro-channels

This paper presents data reduction of average friction factor of gas flow through adiabatic microchannels. In the case of micro-channel gas flow at high speed, the large expansion occurs near the outlet and the pressure gradient along the length is not constant with a significant increase near the outlet. This results in flow acceleration and a decrease in gas temperature. Therefore the friction factor of microchannel gas flow should be obtained with measuring both the pressure and temperature. The data reductions on friction factors were carried out under the assumption of isothermal flow for numerous experimental and numerical studies since temperature measurement of micro-channel gas flow at high speed is quite difficult due to the measurement limitations. In the previous study, it was found that the gas temperature can be determined by the pressure under the assumption of one dimensional flow in an adiabatic channel (Fanno flow). Therefore in the present study data reduction to estimate friction factors between two relatively distant points considering the effect of a decrease in temperature is introduced with the temperature determined by the measured pressure at a specific location. The Friction factors obtained by using the present data reduction are examined with the available literature and the results are compared with empirical correlations on Moody chart

Data reduction of average friction factor of gaseous flow in micro-channels with adiabatic wall

This study focuses on data reduction of average friction factor of gaseous flow through microchannels. In the case of microchannel gas flow at high speed, the large expansion occurs near the outlet and the pressure gradient along the length is not constant and increases near the outlet. This results in flow acceleration and a decease in bulk temperature. Therefore both pressure and temperature are required to obtain the friction factor of the microchannel gas flow. In the past data reduction of many experiments, the friction factors have been obtained under the assumption of isothermal flow since temperature measurement of compressible flow in micro-channels is quite difficult due to the experimental technique limitations. Kawashima and Asako [1] found that the gas temperature can be determined by the pressure under the assumption of one dimensional flow in an adiabatic channel (Fanno flow) to obtain the friction factor considering the effect of a decrease in gas temperature

Hyperplastic cholangitis in a naturally Toxoplasma gondii-infected cat.

Toxoplasma gondii can cause in cats a multisystemic disease involving the liver, lungs, central nervous system and other organs. The liver generally shows multifocal necrotizing hepatitis with possible panlobular extension, with histological evidence of free tachyzoites and/or cysts containing bradyzoites within necrotic foci. Very rarely, toxoplasmosis is expressed by cholangitis, the latter being much more frequently caused in cats by bacteria of intestinal origin. We report here a case of cholangitis/cholangiohepatitis in a young cat, where cytology of the liver showed multiple maturational stages of protozoa in the cytoplasm of cells of the bile ducts. On the basis of the cytological, histological, ultrastructural and molecular details, the microorganisms were identified as belonging to the species Toxoplasma gondii

Experimental Investigation on Latent Thermal Energy Storages (LTESs) Based on Pure and Copper-Foam-Loaded PCMs

In this work, a commercial paraffin PCM (RT35) characterized by a change range of the solid-liquid phase transition temperature Ts−l=29–36 °C and the low thermal conductivity λSL=0.2 W/m K is experimentally tested by submitting it to thermal charging/discharging cycles. The paraffin is contained in a case with a rectangular base and heated from the top due to electrical resistance. The aim of this research is to show the benefits that a 95% porous copper metal foam (pore density PD=20PPI) can bring to a PCM-based thermal storage system by simply loading it, due to the consequent increase in the effective thermal conductivity of the medium (λLOAD=7.03 W/m K). The experimental results highlight the positive effects of the copper foam presence, such as the heat conduction improvement throughout the system, and a significant reduction in time for the complete melting of the PCM. In addition, the experimental data highlight that in the copper-foam-loaded PCM the maximum temperature reached during the heating process is lower than 20K with respect to the test with pure PCM, imposing the same heat flux on the top (P=3.5 W/m2)

Modelling of an intersubband quantum confined Stark effect in Ge quantum wells for mid-infrared photonics

: In this work we theoretically investigate quantum confined Stark effect of intersubband transitions in asymmetric Ge/SiGe quantum wells for intensity modulation in the mid-infrared. Our calculations show that extinction ratios up to 1 dB and modulation speeds of several tens of GHz could be obtained in 100 µm long waveguides

A second order minimality condition for the Mumford-Shah functional

A new necessary minimality condition for the Mumford-Shah functional is derived by means of second order variations. It is expressed in terms of a sign condition for a nonlocal quadratic form on $H^1_0(\Gamma)$, $\Gamma$ being a submanifold of the regular part of the discontinuity set of the critical point. Two equivalent formulations are provided: one in terms of the first eigenvalue of a suitable compact operator, the other involving a sort of nonlocal capacity of $\Gamma$. A sufficient condition for minimality is also deduced. Finally, an explicit example is discussed, where a complete characterization of the domains where the second variation is nonnegative can be given.Comment: 30 page

Effect of Electron Correlation on the Bragg Reflection

We study the effect of correlation on the Bragg reflection in the 3D electron gas, the 1D Luttinger liquid, and the 1D Hubbard model in an alternating periodic potential at half-filling. In the last system, we suggest a Luttinger-liquid-type quasi-metallic state in the crossover region from the band insulator to the Mott insulator. We explain the appearance of this state in terms of the incompatibility of the Bragg reflection with the concept of Luttinger liquids.Comment: 4 pages, 3 figure