Conic Form Research Articles

Elliptical modelling of hysteresis operating characteristics in a dielectric elastomer tubular actuator

A dielectric elastomer (DE) tubular actuator, based on compliant metal electrode technology, exhibits hysteresis-like characteristics when driven with a low power rated high voltage power supply (HVPS). This behavior occurs mainly because the DE actuator acts as a capacitive load compromising the ‘slew rate’ of the HVPS during the actuator’s operation. The motivation of this contribution is to investigate the use of elliptical modelling approaches for capturing the hysteresis characteristics exhibited by the DE tubular actuator when it is driven by a low cost low power rated HVPS. The DE tubular actuator considered in this work demonstrates asymmetric hysteresis behaviour due to the nonlinear voltage–strain behaviour of the actuator. A linearization filter placed in series with the actuator (during its operation) ensures a symmetric hysteresis characteristic that can then be modelled using an ellipse-based approach. Elliptical models come in many forms with the two most popular being the constrained general conic form and the general parametric form. Elliptical-based hysteresis model fits are carried out on experimental data obtained from the application of periodic input voltages, at a number of different low-frequencies, to the tubular actuator. The range of frequencies used is related to the possible use of the tubular actuator for attenuating low frequency vibration during DE actuator-based load positioning applications. Constrained conic and general parametric forms of elliptical model are used for modelling the hysteresis characteristics of the DE actuator and rate dependent models developed based on both approaches. The sensitivity of both of these rate dependent models to small inaccuracies in model parameters was then investigated. The general parametric form was found to be more robust in this respect.

Two-term disjunctions on the second-order cone

Balas introduced disjunctive cuts in the 1970s for mixed-integer linear programs. Several recent papers have attempted to extend this work to mixed-integer conic programs. In this paper we study the structure of the convex hull of a two-term disjunction applied to the second-order cone and develop a methodology to derive closed-form expressions for convex inequalities describing the resulting convex hull. Our approach is based on first characterizing the structure of undominated valid linear inequalities for the disjunction and then using conic duality to derive a family of convex, possibly nonlinear, valid inequalities that correspond to these linear inequalities. We identify and study the cases where these valid inequalities can equivalently be expressed in conic quadratic form and where a single inequality from this family is sufficient to describe the convex hull. In particular, our results on two-term disjunctions on the second-order cone generalize related results on split cuts by Modaresi, Kılınç, and Vielma, and by Andersen and Jensen.

Development of a souvenir bell with use of modeling

The articles presents approaches to extract of parts of conic form from positions of analysis of technological deformability of modern non-ferrous metals. Use of modeling on research of process of multitransitional sheet extract for products not only improves the quality of process development, but also allows to predict technology and behavior of workpiece metal before production start. For modeling finite element AUTOFORM system is used. Basic data and results of modeling are given.

Vertices of Spectrahedra arising from the Elliptope, the Theta Body, and Their Relatives

Utilizing dual descriptions of the normal cone of convex optimization problems in conic form, we characterize the vertices of semidefinite representations arising from the Lovasz theta body, generalizations of the elliptope, and related convex sets. Our results generalize vertex characterizations due to Laurent and Poljak in the 1990s. Our approach, focused on the dimension of the normal cone, also leads us to nice characterizations of strict complementarity and to connections with some of the related literature.

Application axicons in a large-aperture focusing system

We consider the application of axicons in large-aperture focusing systems with different polarization. The aim is to increase the longitudinal extent of the focal spot and decrease its transversal size. Unlike conventional circular diaphragms, supplementing a high-aperture lens with an axicon is more efficient from the energetic point of view. The gain is proportional to the area of the masked part of the lens. Using an axicon we reduce the size of the central light spot from 0.51? to 0.3? for radial polarization. When we deal with linear polarization, which is the case for most laser beams, it is possible to produce a light spot narrowed in one direction to 0.32?. For circular and azimuthal polarization it is efficient to use spiral axicons for producing compact distributions. When a large-aperture lens is supplemented even with a "weak" converging axicon, the focal area gets the conic form whose vertex has a smaller transverse dimension than the focal spot of a single lens. By choosing the axicon parameters we can vary the extent and "sharpness" of the cone. Moreover, by adding vortex phase we can control the contribution of different components of the electromagnetic field in the core and vertex of the cone. It can be useful in interaction of the electromagnetic field with the materials that have selective sensitivity to either longitudinal or transverse components of the field.

Phenotypic variation in shell form in the intertidal acorn barnacle Chthamalus montagui: distribution, response to predators and life history trade-offs

The acorn barnacle Chthamalus montagui can present strong variation in shell morphology, ranging from flat conic to a highly bent form, caused by a substantial overgrowth of the rostrum plate. Shell shape distribution was investigated between January and May 2004 from geographical to microhabitat spatial scales along the western coast of Britain. Populations studied in the north (Scotland and Isle of Man) showed a higher degree of shell variation compared to those in the south (Wales and south-west England). In the north, C. montagui living at lower tidal levels and in proximity to the predatory dogwhelk, Nucella lapillus, were more bent in profile. Laboratory experiments were conducted to examine behavioural responses, and vulnerability of bent and conic barnacles to predation by N. lapillus. Dogwhelks did not attack one morphotype more than the other, but only 15 % of attacks on bent forms were successful compared to 75 % in conic forms. Dogwhelk effluent reduced the time spent feeding by C. montagui (11 %), but there was no significant difference between conic and bent forms. Examination of barnacle morphology indicated a trade-off in investment in shell structure and feeding appendages associated with being bent, but none with egg or somatic tissue mass. These results are consistent with C. montagui showing an induced defence comparable to that found in its congeners Chthamalus anisopoma and Chthamalus fissus on the Pacific coast of North America, but further work to demonstrate inducibility is required.

Stability assessment of a failed artificial embankment slope

This paper presents the stability problems of an artificial cohesion-less embankment slope supported on a saturated silty clay layer.In June 2011, an embankment about 9.00 m high started to be constructed in the Energetic Park of Porto Romano, in Durres city, Albania, as part of Preloading to Mitigate Seismic Risk project. The embankment, foreseen to be built in a conic trunk shape form, was to be used as a preload during the consolidation process of the site.Eighteen days after starting the construction process, when the embankment reached the height of 6.35 m, a soil stability failure of the embankment occurred. The calculations include the embankment slope stability analysis, during the design phase, considering the total height of the embankment (9.00 m) and at the moment of failure when the embankment height reached 6.35 m. The paper also presents the results of a back calculation of shear strength parameters at the moment of failure. Probability Based Design Method and Eurocode 7 Design Approaches a...

Dose optimization with first‐order total‐variation minimization for dense angularly sampled and sparse intensity modulated radiation therapy (DASSIM‐RT)

A new treatment scheme coined as dense angularly sampled and sparse intensity modulated radiation therapy (DASSIM-RT) has recently been proposed to bridge the gap between IMRT and VMAT. By increasing the angular sampling of radiation beams while eliminating dispensable segments of the incident fields, DASSIM-RT is capable of providing improved conformity in dose distributions while maintaining high delivery efficiency. The fact that DASSIM-RT utilizes a large number of incident beams represents a major computational challenge for the clinical applications of this powerful treatment scheme. The purpose of this work is to provide a practical solution to the DASSIM-RT inverse planning problem. The inverse planning problem is formulated as a fluence-map optimization problem with total-variation (TV) minimization. A newly released L1-solver, template for first-order conic solver (TFOCS), was adopted in this work. TFOCS achieves faster convergence with less memory usage as compared with conventional quadratic programming (QP) for the TV form through the effective use of conic forms, dual-variable updates, and optimal first-order approaches. As such, it is tailored to specifically address the computational challenges of large-scale optimization in DASSIM-RT inverse planning. Two clinical cases (a prostate and a head and neck case) are used to evaluate the effectiveness and efficiency of the proposed planning technique. DASSIM-RT plans with 15 and 30 beams are compared with conventional IMRT plans with 7 beams in terms of plan quality and delivery efficiency, which are quantified by conformation number (CN), the total number of segments and modulation index, respectively. For optimization efficiency, the QP-based approach was compared with the proposed algorithm for the DASSIM-RT plans with 15 beams for both cases. Plan quality improves with an increasing number of incident beams, while the total number of segments is maintained to be about the same in both cases. For the prostate patient, the conformation number to the target was 0.7509, 0.7565, and 0.7611 with 80 segments for IMRT with 7 beams, and DASSIM-RT with 15 and 30 beams, respectively. For the head and neck (HN) patient with a complicated target shape, conformation numbers of the three treatment plans were 0.7554, 0.7758, and 0.7819 with 75 segments for all beam configurations. With respect to the dose sparing to the critical structures, the organs such as the femoral heads in the prostate case and the brainstem and spinal cord in the HN case were better protected with DASSIM-RT. For both cases, the delivery efficiency has been greatly improved as the beam angular sampling increases with the similar or better conformal dose distribution. Compared with conventional quadratic programming approaches, first-order TFOCS-based optimization achieves far faster convergence and smaller memory requirements in DASSIM-RT. The new optimization algorithm TFOCS provides a practical and timely solution to the DASSIM-RT or other inverse planning problem requiring large memory space. The new treatment scheme is shown to outperform conventional IMRT in terms of dose conformity to both the targetand the critical structures, while maintaining high delivery efficiency.

Identification of weathered troughs in granites for tunneling at Daya Bay reactor-neutrino experiment site

Abstract: Weathered troughs are frequently encountered in granites. They can cause problems to tunneling in the rocks and have to be properly addressed. The structures or spatial shapes of weathered troughs were seldom clarified in the past. In this paper, four weathered troughs are identified by means of geophysical exploration, core drilling, logging, and in-situ stress measurement at Daya Bay reactor-neutrino experiment site in Shenzhen, China. The weathered troughs are exposed on the ground or partially covered by grass and soils, which will threaten the safety of horizontal tunneling at a shallow depth. High electrical resistivity (HER) method is adopted for its feasibility and practicality, in combination with field geological observation, ultrasonic televiewer in boreholes and in-situ stress measurement. By comparing the HER values of completely decomposed to fresh rocks, it is indicated that the HER values of weathered troughs in natural state are 0.4–100 Ω · m, and the in-situ stress is abnormally lower than those at upper and lower layers. Field investigations show that the depths of the four weathered troughs are 30–182 m, with bottom elevation over 10 m. The volume of each weathered trough is mostly over 1 × 106 m3 in inverted conic form. The weathered troughs often occur in various kinds of landforms, such as ridges, gullies or gently dipping dish-like depression areas. Faults and boundaries of different granitic plutons as well as joints govern the formation, locations and strikes of these troughs under development.

A cell‐based smoothed finite element method for kinematic limit analysis

AbstractThis paper presents a new numerical procedure for kinematic limit analysis problems, which incorporates the cell‐based smoothed finite element method with second‐order cone programming. The application of a strain smoothing technique to the standard displacement finite element both rules out volumetric locking and also results in an efficient method that can provide accurate solutions with minimal computational effort. The non‐smooth optimization problem is formulated as a problem of minimizing a sum of Euclidean norms, ensuring that the resulting optimization problem can be solved by an efficient second‐order cone programming algorithm. Plane stress and plane strain problems governed by the von Mises criterion are considered, but extensions to problems with other yield criteria having a similar conic quadratic form or 3D problems can be envisaged. Copyright © 2010 John Wiley & Sons, Ltd.

Sperm ultrastructure in representatives of six bivalve families from Peter the Great Bay, Sea of Japan

The ultrastructure of sperm in seven species of bivalves, the representatives of six families, Arcidae (Anadara broughtonii, Arca boucardi), Anomiidae (Pododesmus macrochisma), Tellinidae (Macoma tokyoensis), Ostreidae (Crassostrea gigas), Myidae (Mya japonica) and Trapezidae (Trapezium liratum) is described. All the studied sperm were typical tail sperm, adapted to external insemination, which, however, had a specific structure. Differences were revealed in the form of head, acrosome structure and number of mitochondria. The studied species of the above families had their specific morphology, the Arcidae species had a bullet- or barrel-shaped head with four or five mitochondria in the middle part; the Anomiidae had conic head, the acrosome with periacrosome material and four mitochondria (a basic feature of sperm is the axial core entering periacrosome material and consisting of bundle of actin filaments); the Myidae had a curved conic head and four mitochondria; in the Tellinidae the head was bullet-shaped, the periacrosome material contained a fibril component and four mitochondria; the Trapezidae had sperm of a conic form with spherical acrosome. The spherical sperm of C. gigas were similar to sperm of Saccostrea commercialis and Crassostrea virginica, but with some distinctions in the acrosome substructure. The morphology of sperm testified to the correct attribution of the Crassostreidae family as a synonym to the Ostreidae family.

Robust portfolio selection based on a multi-stage scenario tree

The aim of this paper is to apply the concept of robust optimization introduced by Bel-Tal and Nemirovski to the portfolio selection problems based on multi-stage scenario trees. The objective of our portfolio selection is to maximize an expected utility function value (or equivalently, to minimize an expected disutility function value) as in a classical stochastic programming problem, except that we allow for ambiguities to exist in the probability distributions along the scenario tree. We show that such a problem can be formulated as a finite convex program in the conic form, on which general convex optimization techniques can be applied. In particular, if there is no short-selling, and the disutility function takes the form of semi-variance downside risk, and all the parameter ambiguity sets are ellipsoidal, then the problem becomes a second order cone program, thus tractable. We use SeDuMi to solve the resulting robust portfolio selection problem, and the simulation results show that the robust consideration helps to reduce the variability of the optimal values caused by the parameter ambiguity.

An interior-point smoothing technique for Lagrangian relaxation in large-scale convex programming†

An interior-point smoothing technique for Lagrangian relaxation in large-scale convex programming is discussed. We consider the general convex program formulated in the conic form. For the problem, we define the perturbed Lagrangian relaxation by using the self-concordant barriers, and show the basic properties of the perturbed problems. Based on the properties, we present a conceptual method which numerically traces the trajectory that leads to the optimal solution of the original problem. †Dedicated to H. Th. Jongen on the occasion of his 60th birthday.

Invariance and efficiency of convex representations

We consider two notions for the representations of convex cones G-representation and lifted-G-representation. The former represents a convex cone as a slice of another; the latter allows in addition, the usage of auxiliary variables in the representation. We first study the basic properties of these representations. We show that some basic properties of convex cones are invariant under one notion of representation but not the other. In particular, we prove that lifted-G-representation is closed under duality when the representing cone is self-dual. We also prove that strict complementarity of a convex optimization problem in conic form is preserved under G-representations. Then we move to study efficiency measures for representations. We evaluate the representations of homogeneous convex cones based on the “smoothness” of the transformations mapping the central path of the representation to the central path of the represented optimization problem.

Upper bound limit analysis using simplex strain elements and second‐order cone programming

AbstractIn geomechanics, limit analysis provides a useful method for assessing the capacity of structures such as footings and retaining walls, and the stability of slopes and excavations. This paper presents a finite element implementation of the kinematic (or upper bound) theorem that is novel in two main respects. First, it is shown that conventional linear strain elements (6‐node triangle, 10‐node tetrahedron) are suitable for obtaining strict upper bounds even in the case of cohesive‐frictional materials, provided that the element sides are straight (or the faces planar) such that the strain field varies as a simplex. This is important because until now, the only way to obtain rigorous upper bounds has been to use constant strain elements combined with a discontinuous displacement field. It is well known (and confirmed here) that the accuracy of the latter approach is highly dependent on the alignment of the discontinuities, such that it can perform poorly if an unstructured mesh is employed. Second, the optimization of the displacement field is formulated as a standard second‐order cone programming (SOCP) problem. Using a state‐of‐the‐art SOCP code developed by researchers in mathematical programming, very large example problems are solved with outstanding speed. The examples concern plane strain and the Mohr–Coulomb criterion, but the same approach can be used in 3D with the Drucker–Prager criterion, and can readily be extended to other yield criteria having a similar conic quadratic form. Copyright © 2006 John Wiley & Sons, Ltd.

Fine spatiotemporal structure of phase in human intracranial EEG

Objective To transfer to the clinic for humans the technology and theory for high-resolution EEG analysis that have been developed in the laboratory with animals. Methods EEGs were recorded at high spatial resolution from a 1×1 cm 8×8 electrode array on the right inferior temporal gyrus of a patient undergoing preoperative monitoring for epilepsy surgery. Cosines were fitted to EEG segments to measure frequency and phase and compute location, size, latency, phase velocity, duration, and recurrence rate of radially symmetric spatial patterns called phase cones. The Hilbert transform was also used to get high temporal resolution. Results In the awake state, the power spectral density (PSD) showed power-law decrease in log power with log frequency at 1/ f α , α∼2, but with peaks in the standard empirical ranges. The phase in beta and gamma ranges had spatial gradients in conic form. Resetting of these stable spatial patterns of phase cones was spatially coincident at intermittent discontinuities (‘phase slip’) recurring at theta rates. Cones had half power diameters from 2 to 50+ mm; their durations had power-law distributions with values ranging from 6 to 300+ ms depending on length of the analysis window. In slow wave sleep PSD decreased at 1/ f α , α∼3,with loss of beta–gamma spectral peaks and diminished or absent oscillations and spatiotemporal phase structure. Conclusions Spatiotemporal structures in awake human and rabbit EEG showed striking similarities. The only clear differences were ascribable to differing scales of measurement. These fine spatiotemporal structures of EEG were diminished or lost in slow wave sleep. Significance The fine structure indicates that neocortical stability is sustained at self-organized criticality; that synaptic input in the awake state drives neocortex away from criticality causing beta–gamma oscillations in re-stabilizing ‘neural avalanches’; and that diminished input in slow wave sleep allows return toward criticality but with some added risk of instability and seizure.

Lower bound limit analysis of cohesive‐frictional materials using second‐order cone programming

AbstractThe formulation of limit analysis by means of the finite element method leads to an optimization problem with a large number of variables and constraints. Here we present a method for obtaining strict lower bound solutions using second‐order cone programming (SOCP), for which efficient primal‐dual interior‐point algorithms have recently been developed. Following a review of previous work, we provide a brief introduction to SOCP and describe how lower bound limit analysis can be formulated in this way. Some methods for exploiting the data structure of the problem are also described, including an efficient strategy for detecting and removing linearly dependent constraints at the assembly stage. The benefits of employing SOCP are then illustrated with numerical examples. Through the use of an effective algorithm/software, very large optimization problems with up to 700 000 variables are solved in minutes on a desktop machine. The numerical examples concern plane strain conditions and the Mohr–Coulomb criterion, however we show that SOCP can also be applied to any other problem of lower bound limit analysis involving a yield function with a conic quadratic form (notable examples being the Drucker–Prager criterion in 2D or 3D, and Nielsen's criterion for plates). Copyright © 2005 John Wiley & Sons, Ltd.

Assessing surface area of coarse woody debris with line intersect and perpendicular distance sampling

Coarse woody debris (CWD) plays an important role in many terrestrial and aquatic ecosystem processes. In recent years, a number of new methods have been proposed to sample CWD. Of these methods, perpendicular distance sampling (PDS) is one of the most efficient methods for estimating CWD volume in terms of both estimator variance and field effort. This study extends the results for PDS to the estimation of the surface area of CWD. The PDS estimator is also compared to two line intersect sampling (LIS) estimators, where one of the LIS estimators requires the measurement of surface area on each log and the other estimates surface area using a single measurement of log circumference at the point of intersection between the log and the line. The first estimator approximates the true surface area by assuming either a conic or parabolic stem form and requires measurements of the end diameters of each log, which is more time consuming than a single measurement. The performance of the three estimators was compared using a computer simulation. The results of the simulation indicate that, given the same number of pieces of CWD sampled at each point, equal variances can be achieved with PDS using sample sizes that range from about 10% to in excess of 100% the size of a comparable LIS estimator. When the LIS estimators were compared, the estimator that required the measurement of surface area was only about 3%–6% more efficient than the alternative estimator, but the bias associated with assuming a conic or parabolic stem form ranged from roughly 5% to 15%. We conclude that PDS will generally outperform either of the LIS estimators. Another important conclusion is that the LIS estimator based on a measured surface area is likely to have a higher mean squared error than an LIS estimator that employs a single measurement of circumference. Thus, LIS sampling strategies that require the least amount of field work will often have the smallest mean square error.

On an Extension of Condition Number Theory to Nonconic Convex Optimization

The purpose of this paper is to extend, as much as possible, the modern theory of condition numbers for conic convex optimization: z* ≔ minx ct x, s.t. Ax−b ∈ CY, x ∈ CX, to the more general nonconic format: z* ≔ minx ctx, (GPd) s.t. Ax − b ∈ CY, x ∈ P, where P is any closed convex set, not necessarily a cone, which we call the ground-set. Although any convex problem can be transformed to conic form, such transformations are neither unique nor natural given the natural description of many problems, thereby diminishing the relevance of data-based condition number theory. Herein we extend the modern theory of condition numbers to the problem format (GPd). As a byproduct, we are able to state and prove natural extensions of many theorems from the conic-based theory of condition numbers to this broader problem format.

Using a Conic Formulation for Finding Steiner Minimal Trees

We present a new mathematical programming formulation for the Steiner minimal tree problem. We relax the integrality constraints on this formulation and transform the resulting problem (which is convex, but not everywhere differentiable) into a standard convex programming problem in conic form. We consider an efficient computation of an e-optimal solution for this latter problem using an interior-point algorithm.