Relaxed Counterparts Research Articles

Iterative convex relaxation of unbalanced power distribution system integrated multi-energy systems

This study describes a multi-period, multi-energy operation of a three-phase unbalanced Electric Distribution System (EDS) that coordinates with a District Heating System (DHS) and a Natural Gas (NG) distribution system. The electrical subsystem problem is formulated as a bi-level programming problem, with levels 1 and 2 solving the subsystem’s linearized and relaxed nonlinear versions, respectively. Second-Order Cone Programming (SOCP) and polyhedral relaxations are availed to circumvent the non-convexities involved in the subsystems. The SOCP relaxation for an unbalanced power distribution network is inexact; also, the subsystems applying polyhedral relaxation may not generate a meaningful solution as the relaxations are not tight. Therefore, a solution recovery algorithm is developed for each subsystem to recover a feasible solution from their relaxed counterparts. The successive bound tightening algorithm employing a solution recovery procedure is proposed for each subsystem, improving solution quality and strengthening the relaxations with the desired computational efficiency. The proposed solution strategy to optimize the Multi-Energy System (MES) operation cost is verified on the three-phase IEEE-13 and IEEE-123 bus systems, each coordinating with a 30-node DHS and a 6-bus NG network. The results analyses demonstrate that the proposed solution strategy efficiently achieves an optimal solution, reducing maximum relaxation error below 0.1% for each subsystem. The proposed strategy delivered a 14.58% reduction in real power losses and a 12.73% decrease in phase voltage unbalance rate for the EDS in MES. Furthermore, a 1.96% decrease in operational cost demonstrates the techno-economic benefits of the proposed strategy.

Optimizing Path-Planning Solutions Obtained by Using Petri Nets Models

This paper addresses the multirobot path planning problem using Petri net (PN) models, integrating insights from linear integer programming with a focus on totally unimodular matrices. Initially, we establish theoretical foundations linking optimal solutions of linear integer problems to their relaxed counterparts. Subsequently, we adapt these findings to robot path planning. The core contribution lies in the introduction of an innovative algorithm designed to iteratively converge on the optimal solution by solving successive continuous linear problems. A key feature of this algorithm is its proven efficiency, which converges to the optimal solution of the integer problem within a theoretically established finite number of iterations. Empirical validation is achieved through the resolution of 300 different path planning scenarios, which include varying numbers of robots, maps, and missions. These cases, solved using both the proposed method and existing techniques, demonstrate the superiority of the proposed method in performance.

MAXIMUM PRINCIPLE FOR SINGULAR CONTROL PROBLEMS OF SYSTEMS DRIVEN BY MARTINGALE MEASURES

We provide necessary optimality conditions for singular controlled stochastic differential equations driven by an orthogonal continuous martingale measure. The control is allowed to enter both the drift and diffusion coefficient and has two components, the first being relaxed and the second singular, the domain of the first control does not need to be convex, and for the relaxing method, we show by a counter-example that replacing the drift and diffusion coefficients by their relaxed counterparts does not define a true relaxed control problem. The maximum principle for these systems is established by means of spike variation techniques on the relaxed part of the control and a convex perturbation on the singular one. Our result is a generalization of Peng's maximum principle to singular control problems.

On the relaxed mean-field stochastic control problem

This paper is concerned with optimal control problems for systems governed by mean-field stochastic differential equation, in which the control enters both the drift and the diffusion coefficient. We prove that the relaxed state process, associated with measure valued controls, is governed by an orthogonal martingale measure rather than a Brownian motion. In particular, we show by a counter example that replacing the drift and diffusion coefficient by their relaxed counterparts does not define a true relaxed control problem. We establish the existence of an optimal relaxed control, which can be approximated by a sequence of strict controls. Moreover, under some convexity conditions, we show that the optimal control is realized by a strict control.

Galaxy Cluster Mass Reconstruction Project – III. The impact of dynamical substructure on cluster mass estimates

With the advent of wide-field cosmological surveys, we are approaching samples of hundreds of thousands of galaxy clusters. While such large numbers will help reduce statistical uncertainties, the control of systematics in cluster masses is crucial. Here we examine the effects of an important source of systematic uncertainty in galaxy-based cluster mass estimation techniques: the presence of significant dynamical substructure. Dynamical substructure manifests as dynamically distinct subgroups in phase-space, indicating an ‘unrelaxed’ state. This issue affects around a quarter of clusters in a generally selected sample. We employ a set of mock clusters whose masses have been measured homogeneously with commonly used galaxy-based mass estimation techniques (kinematic, richness, caustic, radial methods). We use these to study how the relation between observationally estimated and true cluster mass depends on the presence of substructure, as identified by various popular diagnostics. We find that the scatter for an ensemble of clusters does not increase dramatically for clusters with dynamical substructure. However, we find a systematic bias for all methods, such that clusters with significant substructure have higher measured masses than their relaxed counterparts. This bias depends on cluster mass: the most massive clusters are largely unaffected by the presence of significant substructure, but masses are significantly overestimated for lower mass clusters, by ∼ 10 per cent at 1014 and ≳ 20 per cent for ≲ 1013.5. The use of cluster samples with different levels of substructure can therefore bias certain cosmological parameters up to a level comparable to the typical uncertainties in current cosmological studies.

Multi-region relaxed Hall magnetohydrodynamics with flow

The recent formulations of multi-region relaxed magnetohydrodynamics (MRxMHD) have generalized the famous Woltjer-Taylor states by incorporating a collection of “ideal barriers” that prevent global relaxation and flow. In this paper, we generalize MRxMHD with flow to include Hall effects, and thereby obtain the partially relaxed counterparts of the famous double Beltrami states as a special subset. The physical and mathematical consequences arising from the introduction of the Hall term are also presented. We demonstrate that our results (in the ideal MHD limit) constitute an important subset of ideal MHD equilibria, and we compare our approach against other variational principles proposed for deriving the partially relaxed states.

Influence of heat treatment on the mechanical properties, corrosion behavior, and biocompatibility of Zr56Al16Co28 bulk metallic glass

This paper reports the influence of heat treatment on the mechanical properties, corrosion behavior and biocompatibility of Zr56Al16Co28 bulk metallic glass (BMG) investigated by dynamic mechanical analysis (DMA), electrochemical analysis in vitro hemocompatibility and in vivo experiments. Zr56Al16Co28 alloys with amorphous, semi-crystalline and fully crystallized microstructures were obtained by thermal treatment of as-cast Zr56Al16Co28 BMG below or above glass transition temperature (Tg). The modulus slightly decreased with increasing temperature below Tg whereas the modulus dramatically increased treated above Tg due to the appearance of crystalline phase. The passivation potential did not change for samples heat-treated below Tg but decreased significantly above Tg, which indicated that Zr56Al16Co28 BMG possessed better corrosion resistance than crystallized Zr56Al16Co28 alloys. Zr56Al16Co28 alloys showed good hemolytic resistance regardless of the microstructural condition and presented lower hemolytic rate than their crystallized counterparts. In vivo test revealed that as-cast Zr56Al16Co28 BMG presented similar biocompatibility to the structurally relaxed BMG and better biocompatibility than the crystallized counterparts. Mice implanted with Zr56Al16Co28 BMGs showed lower degree of inflammatory infiltration response compared to mice implanted with the crystallized counterparts. The results showed that the properties of as-cast Zr56Al16Co28 BMG were generally comparable to its structurally relaxed counterpart and superior to the crystalline samples.

The role of major mergers in the size growth of intermediate-mass spheroids

We study of the role of major mergers (mass ratios >1:4) in driving size growth in high-redshift (1<z<2) spheroidal galaxies (SGs) with stellar masses between 10^9.5 MSun and 10^10.7 MSun. This is a largely unexplored mass range at this epoch, containing the progenitors of more massive SGs on which the bulk of the size-evolution literature is based. We visually split our SGs into systems that are relaxed and those that exhibit tidal features indicative of a recent merger. Numerical simulations indicate that, given the depth of our images, only tidal features due to major mergers will be detectable at these epochs (features from minor mergers being too faint), making the disturbed SGs a useful route for estimating major-merger-driven size growth. The disturbed SGs are offset in size from their relaxed counterparts, lying close to the upper envelope of the local size -- mass relation. The mean size ratio of the disturbed SGs to their relaxed counterparts is ~2. Combining this observed size growth with empirical major-merger histories from the literature suggests that the size evolution of a significant fraction (around two-thirds) of SGs in this mass range could be driven by major mergers. If, as is likely, our galaxies are progenitors of more massive M > 10^10.7 MSun SGs at z<1, then major mergers are also likely to play an important role in the size growth of at least some massive SGs in this mass range.

Peculiar early-type galaxies in the Sloan Digital Sky Survey Stripe82

We explore the properties of `peculiar' early-type galaxies (ETGs) in the local Universe, that show (faint) morphological signatures of recent interactions such as tidal tails, shells and dust lanes. Standard-depth (51s exposure) multi-colour galaxy images from the Sloan Digital Sky Survey (SDSS) are combined with the significantly (2 mags) deeper monochromatic images from the public SDSS Stripe82 to extract, through careful visual inspection, a robust sample of nearby, luminous ETGs, including a subset of ~70 peculiar systems. 18% of ETGs exhibit signs of disturbed morphologies (e.g. shells), while 7% show evidence of dust lanes and patches. The peculiar ETG population is found to preferentially inhabit low-density environments (outskirts of clusters, groups or the field). An analysis of optical emission-line ratios indicates that the fraction of peculiar ETGs that are Seyferts or LINERs (19.4%) is twice the corresponding values in their relaxed counterparts (10.1%). LINER-like emission is the dominant type of nebular activity in all ETG classes, plausibly driven by stellar photoionisation associated with recent star formation. An analysis of UV-optical colours indicates that, regardless of the luminosity range being considered, the fraction of peculiar ETGs that have experienced star formation in the last Gyr is a factor of ~1.5 higher than that in their relaxed counterparts. The spectro-photometric results strongly suggest that the interactions that produce the morphological peculiarities also induce low-level recent star formation which, based on the recent literature, are likely to contribute a few percent of the stellar mass over the last 1 Gyr. The catalogue of galaxies that forms the basis of this paper can be obtained at: http://www.mssl.ucl.ac.uk/~ska/stripe82/skaviraj_stripe82.dat or on request from the author.

Plastic deformation in a partially crystallized Zr-based BMG under Vickers indenter

Vickers indentations were carried out on an anneal-introduced partially crystallized Zr 41Ti 14Cu 12.5Ni 10Be 22.5 bulk metallic glass (BMG), and the evolution of the shear bands in this sample was investigated and compared to the as-cast, as well as the structurally relaxed counterparts. The results indicate that the plastic deformation in the partially crystallized BMG was accommodated by the semi-circular (primary) and radial (secondary) shear bands. A full crack or flake that was produced due to the spring back during the load removal was observed. The shear band density in the annealed alloy which was dispersed with crystallites was significantly lower than that of the as-cast alloy. The difference of the shear band features among the three kinds of alloy status, i.e., partially crystallized, structurally relaxed and as-cast alloys was discussed in terms of the free volume in the BMGs and the characteristics of nano-composites. It has been demonstrated that the plasticity for the three statuses of alloys queues in the descending order as the as-cast, annealed with partial crystallization, and annealed without crystallization.

Short-circuit diffusion in an ultrafine-grained copper–zirconium alloy produced by equal channel angular pressing

Many unusual properties of ultrafine grain materials obtained by equal channel angular pressing (ECAP) are commonly attributed to non-equilibrium grain boundaries. Such grain boundaries are expected to exhibit higher values of energy, higher amplitude of strain fields, a larger free volume and a higher diffusivity than their relaxed counterparts. In the present study, the diffusivity of 63Ni radiotracer in ECAP-processed Cu–0.17 wt.% Zr alloy was measured in the low-temperature range of 150–350 °C under conditions at which no bulk diffusion occurs. The microstructure observations after annealing indicate that alloying with Zr is essential for stabilizing the ECAP-processed alloys against grain growth and recrystallization. In all samples studied the experimentally measured diffusion profiles exhibited two distinct slopes, which are associated with “slow” and “fast” short-circuit diffusion paths. The diffusivity of “slow” diffusion paths in the ECAP-processed samples coincides with the diffusivity via relaxed grain boundaries in the coarse grain Cu measured by the same radiotracer method at similar temperatures. We associate the “fast” diffusion paths observed in this study with the non-equilibrium grain boundaries produced by ECAP.

Tractable Approximations to Robust Conic Optimization Problems

In earlier proposals, the robust counterpart of conic optimization problems exhibits a lateral increase in complexity, i.e., robust linear programming problems (LPs) become second order cone problems (SOCPs), robust SOCPs become semidefinite programming problems (SDPs), and robust SDPs become NP-hard. We propose a relaxed robust counterpart for general conic optimization problems that (a) preserves the computational tractability of the nominal problem; specifically the robust conic optimization problem retains its original structure, i.e., robust LPs remain LPs, robust SOCPs remain SOCPs and robust SDPs remain SDPs, and (b) allows us to provide a guarantee on the probability that the robust solution is feasible when the uncertain coefficients obey independent and identically distributed normal distributions.

Characterization of a wide range base-damage-endonuclease activity of mammalian rpS3

Mammalian rpS3, a ribosomal protein S3 with a DNA repair endonuclease activity, nicks heavily UV-irradiated DNA and DNA containing AP sites. RpS3 calls for a novel endonucleolytic activity on AP sites generated from pyrimidine dimers by T4 pyrimidine dimer glycosylase activity. This study revealed that rpS3 cleaves the lesions including AP sites, thymine glycols, and other UV damaged lesions such as pyrimidine dimers. This enzyme does not have a glycosylase activity as predicted from its amino acid sequence. However, it has an endonuclease activity on DNA containing thymine glycol, which is exactly overlapped with UV-irradiated or AP DNAs, indicating that rpS3 cleaves phosphodiester bonds of DNAs containing altered bases with broad specificity acting as a base-damage-endonuclease. RpS3 cleaves supercoiled UV damaged DNA more efficiently than the relaxed counterpart, and the endonuclease activity of rpS3 was inhibited by MgCl 2 on AP DNA but not on UV-irradiated DNA.

The effect of strain on gas–surface reactivity in group-IV heteroepitaxial systems

Supersonic molecular beam techniques have been employed to examine the dissociative adsorption of GeH 4 and Si 2H 6 on strained Si 1− x Ge x (0≤ x≤1) epitaxial overlayers deposited on Si(100). Low-energy ion scattering spectrometry (LEISS) has been utilized to quantify in situ the topmost Ge surface composition of the Si 1− x Ge x films. Through the measurements of reaction probability we find that these ultrathin strained semiconducting overlayers, both alloy and pure component (i.e., Ge/Si(100)), exhibit enhanced gas–surface reactivity when compared to their bulk (relaxed) counterparts, reflecting the critical role played by strain in these epitaxial overlayers.

Improving the efficiency of discrete time scheduling formulation

The problem of production scheduling in multipurpose plants can be formulated as a mixed integer linear programming (MILP) problem based on a discrete representation of time. The mathematical difficulties associated with solving integer programs are well established, and combining this factor with the increasing complexity and size of scheduling problems, there exists a strong requirement for efficient solution algorithms. This paper attempts to address this requirement by looking at two ways to reduce the gap between the optimal solution and the solution of its relaxed LP counterpart. The first method involves generating cut constraints in problems where the presence of changeover activities tends to widen the relaxation gap. The second method uses an established reformulation technique based on variable disaggregation which exploits the lot sizing problem found embedded in many scheduling instances. The reformulation is applied to a general scheduling framework and its performance evaluated. Test examples are described for both methods, along with their numerical results.

8] Supercoiled DNA and cruciform structures

Publisher Summary The sequence-dependent rearrangement of DNA structure to adopt a new geometry involves a change in local DNA twist, and this is usually negative—that is, perturbed DNA structures are usually underwound relative to the normal B-form double helix. For this reason, such structures will be more stable in negatively supercoiled DNA circles than their relaxed counterparts, and DNA supercoiling is well known to stabilize a number of structural polymorphs, including left-handed Z-DNA, cruciform structures, and H-triplex structures. Cruciform structures are paired hairpin loop structures formed by intrastrand base pairing that is possible when a sequence possesses 2-fold symmetry. A cruciform structure comprises three components—namely, the loops, the stems, and the four-way junction. The structure of the four-way junction is of considerable interest and importance, because it is formally equivalent to the Holliday junction—the putative central intermediate of genetic recombination—and there is good evidence for the involvement of a four-way junction in the integrase class of site-specific recombination events.

RelA-independent (p)ppGpp accumulation and heat shock protein induction after salt stress inBacillus subtilis

Abstract Sodium chloride treatment triggered the accumulation of (p)ppGpp in the Bacillus subtilis relA+ strain IS58 as well as in its relaxed counterpart IS56. Besides this relA-independent (p)ppGpp induction the GTP and ATP pools decreased dramatically. In previous papers we found a direct correlation between (p)ppGpp accumulation and stress protein induction. In B. subtilis relA the (p)ppGpp accumulation was accompanied by the induction of general stress proteins whose synthesis rates were also enhanced by heat stress, amino acid limitation or oxygen starvation. Specific heat shock proteins were not induced by salt stress. We suggest that these general stress proteins are induced under non-growing conditions in general.

RelA-independent (p)ppGpp accumulation and heat shock protein induction after salt stress in Bacillus subtilis

Sodium chloride treatment triggered the accumulation of (p)ppGpp in the Bacillus subtilis relA+ strain IS58 as well as in its relaxed counterpart IS56. Besides this relA-independent (p)ppGpp induction the GTP and ATP pools decreased dramatically. In previous papers we found a direct correlation between (p)ppGpp accumulation and stress protein induction. In B. subtilis relA the (p)ppGpp accumulation was accompanied by the induction of general stress proteins whose synthesis rates were also enhanced by heat stress, amino acid limitation or oxygen starvation. Specific heat shock proteins were not induced by salt stress. We suggest that these general stress proteins are induced under non-growing conditions in general.

Role of relA mutation in the survival of amino acid-starved Escherichia coli.

Amino acid-starved cells of Escherichia coli relA+, which contain a large number of glycogen particles, are able to survive in phosphate buffer for a longer time period than their relaxed counterparts. With regard to NH4+ starvation differences in the survival of both strains were not found. NH4+ starved cells of E. coli relA are able to synthesize glycogen but amino acid-starved cells of the relA strain are not. We suggest that the synthesis of glycogen triggered by guanosine tetraphosphate during amino acid starvation is responsible for the prolonged viability of the E. coli relA+ strain.

Synthesis of alkaline phosphatase in a stringent and a relaxed strain of Escherichia coli under amino acid and phosphate limitation

Synthesis of alkaline phosphatase in Escherichia coli is derepressed under phosphate starvation in the stringent strain CP78 as well as in its relaxed counterpart CP79. During limitation of phosphate as well as of amino acids a decrease of enzyme activity is observed, especially in the relaxed strain, which can not produce ppGpp under this conditions. After phosphate limitation synthesis of ppGpp is not stimulated and the kinetics of RNA synthesis is similar in both strains. We suggest that ppGpp is not directly involved in the regulation of gene expression during phosphate starvation.