Dual Cone Research Articles

On dual cone theory for Euclidean Bosonic equations

On dual cone theory for Euclidean Bosonic equations

A Soft Mimic Robotic Arm Powered by Dielectric Elastomer Actuator

AbstractGiven the great importance of human‐robot collaboration (HRC), the development of robotic arms tends to prioritize high flexibility, safety as well as low energy consumption. Dielectric elastomer actuators (DEAs), with their high energy density and lightweight characteristics, present a promising alternative for the design of soft robotic arms suitable for HRC setting. Hence, a soft mimic robotic arm powered by dual cone DEA (DCDEA) driver unit is developed that demonstrates high energy density and low energy consumption. The resultant elaborate DCDEA driver unit exhibits a significant bi‐direction actuation stroke with a high load‐to‐weight ratio up to 1,300, ensuring sufficient mechanical power output for powering the robotic arm. The well‐designed efficient transmission mechanism and control system together with DCDEA allow the robotic arm to conduct lifting and twisting action, mimicking the movements of a human arm. During the transportation of a 10 g weight, the robotic arm consumes only ≈35 mJ of energy, while achieving an energy density of 42.1 J kg−1. Encased in soft outer shells, the robotic arm displays full flexibility, high safety, and excellent impact resistance, underscoring its potential as a next‐generation soft robotic arm for HRC setting.

A generalization of Riesz* homomorphisms on order unit spaces

Riesz homomorphisms on vector lattices have been generalized to Riesz* homomorphisms on ordered vector spaces by van Haandel using a condition on sets of finitely many elements. Van Haandel attempted to prove that it suffices to take sets of two elements. We show that this is not true, in general. The description by two elements motivates to introduce mild Riesz* homomorphisms. We investigate their properties on order unit spaces, where the geometry of the dual cone plays a crucial role. Hereby, we mostly focus on the finite-dimensional case.

Large deformation of cable networks with fiber sliding as a second-order cone programming

A new model for irreversible large deformations of fiber networks is developed. The fibers are considered as inextensible cables that slide relative to each other in the frictional junctions. This sliding is constituted by a rate-independent flow rule. The nonsmooth dissipation potential for each sliding system is defined as a product of the yield strength and the absolute value of the fiber sliding. The response of the cable segments is nonsmooth as well, since it shows asymmetry with respect to tension and compression. A principle of minimum incremental potential and a pure complementary energy principle are derived for the equilibrium incremental loading of the network at large deformations. They form a pair of primal and dual second-order cone programming problems with matching sets of displacement-based and force-based variables. These problems can be effectively solved by interior point methods that have many advantages compared to the gradient-based methods or dynamic relaxation. The model is extended by a simple mechanism of fiber pull-out resulting from fiber sliding at the free unconstrained ends. This can be used for the microstructural analysis of failure of needle-punched nonwoven materials.

A dual mapping associated to a closed convex set and some subdifferential properties

In this paper, we establish some properties of the multivalued mapping (x, d) ⇒ DC (x; d) that associates to every element x of a linear normed space X the set of linear continuous functionals of norm d ≥ 0 and which separates the closed ball B (x; d) from a closed convex set C ⊂ X. Using this mapping we give links with other important concepts in convex analysis (ε-approximation element, ε-subdifferential of distance function, duality mapping, polar cone). Thus, we establish a dual characterization of ε-approximation elements with respect to a nonvoid closed convex set as a generalization of a known result of Garkavi. Also, we give some properties of univocity and monotonicity of mapping DC. Mathematics Subject Classification (2010): 32A70, 41A65, 46B20, 46N10. Received 18 May 2023; Accepted 27 November 2023

Performance Evaluation of Square Cyclone Separator with Cone Geometry Variations

Rapid industrial development with intensive operations increases exhaust emissions that are polluting the environment and human health. Efforts to overcome the problem are urgent to be realized, one of which is by using a particle separator such as a cyclone separator. Along with that, the design of a cyclone separator with the best performance is very important. Therefore, it is necessary to innovate and analyze the design of the cyclone separator by varying the cone geometry of the cyclone. This study aimed to determine the best square cyclone separator among square cyclone separators with various cone geometries, including single cone, dual inverse cone 1, and dual inverse cone 2. It was conducted by Computational Fluid Dynamics (CFD) simulation and experiments and then continued by comparing pre-determined aspects comprising pressure drop, collection efficiency, static pressure contours, tangential velocity contours in the cyclone body, tangential velocity vectors in the cone geometry, and tangential velocity vectors at the cyclone inlet. The single cone is the best among all cone variations since it fulfils more aspects better than the dual inverse cones, namely: dominantly lowest pressure drop of 188.5 Pa, static pressure contour of 10.42 Pa, tangential velocity contour of 3.06 m/s, flow direction of the tangential velocity vector in the cyclone geometry was at the centre of the bin, and flow direction of the tangential velocity vector at the cyclone inlet was parallel.

A dual cone actuator with high energy density and long fatigue life by developing a nano-silica reinforced dielectric elastomer composite

Dielectric elastomer actuator (DEA) is considered as one of the most promising soft actuators due to its light weight, good flexibility, high actuated strain and energy density. Herein, a novel DEA material is developed by introducing a kind of SiO2 nanoparticles with strong interfacial polarizability into polydimethyl(methylvinyl) siloxane (PMVS). The 7.5 SiO2/PMVS DEA exhibits a high actuated strain of 31.3 % and blocked stress of 68.4 kPa, 2.4 and 2.9 times of pure PMVS DEA. A dual cone DEA (DCDEA) device was self-designed by using 7.5 SiO2/PMVS films, which possesses a high actuated displacement of 1.3 mm, output force of 0.3 N and energy density of 4.7 J/kg. More importantly, because of the high elasticity and strong interfacial interaction, the 7.5 SiO2/PMVS DCDEA exhibits a long fatigue life of 500,000 times, resulting in a full-life energy density of 2.3 × 106 J/kg, 39 times higher than that of the VHB based DCDEA.

Techniques to Remove Press-Fit Osseointegration Implants.

Techniques to Remove Press-Fit Osseointegration Implants.

Best approximation with geometric constraints

In this paper, we consider a finite family of sets (geometric constraints) F1,F2,…,Fr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F_{1}, F_{2},\\ldots , F_{r}$$\\end{document} in the Euclidean space Rn.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {R}}^n.$$\\end{document} We show under mild conditions on the geometric constraints that the “perturbation property” of the constrained best approximation from a nonempty closed set K∩F\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K \\cap F$$\\end{document} is characterized by the “convex conical hull intersection property” (CCHIP in short) at a reference feasible point in F. In this case, F is the intersection of the geometric constraints F1,F2,…,Fr,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F_{1}, F_{2},\\ldots , F_{r},$$\\end{document} and K is a nonempty closed convex set in Rn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {R}}^n$$\\end{document} such that K∩F≠∅.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K \\cap F \ e \\emptyset .$$\\end{document} We do this by first proving a dual cone characterization of the contingent cone of the set F. Finally, we obtain the “Lagrange multiplier characterizations” of the constrained best approximation. Several examples are given to illustrate and clarify our results.

Unravelling the nuclear dust morphology of NGC 1365: a two-phase polar–RAT model for the ultraviolet to infrared spectral energy distribution

ABSTRACT We present a 3D radiative transfer model for the spectral energy distribution (SED) of NGC 1365, which is a ‘changing look’ Seyfert 1.8 type active galactic nucleus (AGN). The SED from the ultraviolet (UV) to the infrared (IR) is constructed using archival data from the Ultra-Violet Imaging Telescope (UVIT) onboard AstroSat, along with IR data from the literature. The skirt radiative transfer code is used to model the SED and derive the geometry and composition of dust in this AGN. Similar to our earlier SED model of NGC 4151, the nuclear region of NGC 1365 is assumed to contain a ring or disc-like structure concentric to the accretion disc, composed of large (0.1–1 $\mu$m) graphite grains in addition to the two-phase dusty torus made up of interstellar-medium-type grains (Ring And Torus or RAT model). We also include, for the first time, an additional component of dusty wind in the form of a bipolar cone. We carry out a detailed analysis and derive the best-fitting parameters from a χ2 test to be Rin, r = 0.03 pc, σ = 26°, and τtotal = 20 for the assumed ring–torus–polar wind geometry. Our results suggest the presence of hot dust at a temperature T ∼ 1216 K at the location of the ring that absorbs and scatters the incident UV radiation and emits in the near-IR. In the mid-IR, the major contributors are the polar cone and warm dust with T ∼ 914 K at Rin, t = 0.1 pc. Not only are our model radii in agreement with IR interferometric observations, but also our study reiterates the role of high-resolution UV observations in constraining the dust grain size distribution in the nuclear regions of AGN.

A generalizable new figure of merit for dose optimization in dual energy cone beam CT scanning protocols

Objective. This study proposes and evaluates a new figure of merit (FOMn) for dose optimization of Dual-energy cone-beam CT (DE-CBCT) scanning protocols based on size-dependent modeling of radiation dose and multi-scale image quality. Approach. FOMn was defined using Z-score normalization and was proportional to the dose efficiency providing better multi-scale image quality, including comprehensive contrast-to-noise ratio (CCNR) and electron density (CED) for CatPhan604 inserts of various materials. Acrylic annuluses were combined with CatPhan604 to create four phantom sizes (diameters of the long axis are 200 mm, 270 mm, 350 mm, and 380 mm, respectively). DE-CBCT was decomposed using image-domain iterative methods based on Varian kV-CBCT images acquired using 25 protocols (100 kVp and 140 kVp combined with 5 tube currents). Main results. The accuracy of CED was approximately 1% for all protocols, but degraded monotonically with the increased phantom sizes. Combinations of lower voltage + higher current and higher voltage + lower current were optimal protocols balancing CCNR and dose. The most dose-efficient protocols for CED and CCNR were inconsistent, underlining the necessity of including multi-scale image quality in the evaluation and optimization of DE-CBCT. Pediatric and adult anthropomorphic phantom tests confirmed dose-efficiency of FOMn-recommended protocols. Significance. FOMn is a comprehensive metric that collectively evaluates radiation dose and multi-scale image quality for DE-CBCT. The models and data can also serve as lookup tables, suggesting personalized dose-efficient protocols for specific clinical imaging purposes.

The Homogenization Cone: Polar Cone and Projection

The Homogenization Cone: Polar Cone and Projection

Rational dual certificates for weighted sums-of-squares polynomials with boundable bit size

In Davis and Papp (2022), the authors introduced the concept of dual certificates of (weighted) sum-of-squares polynomials, which are vectors from the dual cone of weighted sums of squares (WSOS) polynomials that can be interpreted as nonnegativity certificates. This initial theoretical work showed that for every polynomial in the interior of a WSOS cone, there exists a rational dual certificate proving that the polynomial is WSOS. In this article, we analyze the complexity of rational dual certificates of WSOS polynomials by bounding the bit sizes of integer dual certificates as a function of parameters such as the degree and the number of variables of the polynomials, or their distance from the boundary of the cone. After providing a general bound, we explore several special cases, such as univariate polynomials nonnegative over the real line or a bounded interval, represented in different commonly used bases. We also provide an algorithm which runs in rational arithmetic and computes a rational certificate with boundable bit size for a WSOS lower bound of the input polynomial.

Mixed and Nitsche’s discretizations of Coulomb frictional contact-mechanics for mixed dimensional poromechanical models

This work deals with the discretization of single-phase Darcy flows in fractured and deformable porous media, including frictional contact at the matrix–fracture interfaces. Fractures are described as a network of planar surfaces leading to so-called mixed-dimensional models. Small displacements and a linear poro-elastic behavior are considered in the matrix. One key difficulty to simulate such coupled poro-mechanical models is related to the formulation and discretization of the contact mechanical sub-problem. Our starting point is based on the mixed formulation using facewise constant Lagrange multipliers along the fractures representing normal and tangential stresses. This is a natural choice for the discretization of the contact dual cone in order to account for complex fracture networks with corners and intersections. It leads to local expressions of the contact conditions and to efficient semi-smooth nonlinear solvers. On the other hand, such a mixed formulation requires to satisfy a compatibility condition between the discrete spaces restricting the choice of the displacement space and potentially leading to sub-optimal accuracy. This motivates the investigation of two alternative formulations based either on a stabilized mixed formulation or on the Nitsche’s method. These three types of formulations are first investigated theoretically in order to enhance their connections. Then, they are compared numerically in terms of accuracy and nonlinear convergence. The sensitivity to the choice of the formulation parameters is also investigated. Several 2D test cases are considered with various fracture networks using both P1 and P2 conforming Finite Element discretizations of the displacement field and an Hybrid Finite Volume discretization of the mixed-dimensional Darcy flow model.

Bone Mineral Density through DEXA and CBCT: A Systematic Review with Meta-Analysis

Dual-energy X-ray absorptiometry is used to determine bone density in several pathologies, namely osteoporosis and fracture risk in post-menopausal women. The aim of this study was to identify, appraise and synthesize all available evidence about the correlation between Dual Energy X-ray Absorptiometry (DEXA) and Cone Beam Computed Tomography (CBCT) techniques through a systematic review. A systematic literature search was conducted in the following databases: PubMed via MEDLINE, Cochrane Library, EMBASE and Web of Science Core Collection, along with several sources of grey literature. The Cochrane Risk of Bias Tools were used to perform the qualitative assessment of the selected studies. A total of 913 articles were initially scrutinized and 11 were included for qualitative analysis, of which 3 were included in a meta-analysis. Most of the included studies revealed a low risk of bias (7 out of 11). A strong correlation (min r = 0.46 max r = 0.62) between DEXA and CBCT values were found. Thus, opportunistic CBCT scans may be used to assess the bone mineral density and fracture risk, improving the ability to track disease progression and providing better care.

Robust trajectory tracking and control allocation of X-rudder AUV with actuator uncertainty

This paper proposes a robust trajectory tracking control method for an X-rudder autonomous underwater vehicle subject to imprecise model parameters, unknown disturbances, and actuator uncertainty. The control scheme consists of a kinematics controller, dynamics controller, and rudder allocator constructed using backstepping techniques. The kinematics controller employs a line-of-sight guidance law, while the dynamics controller uses integral sliding mode and a Radial Basis Function Neural Network to handle modeling errors and unknown disturbances. Finally, a Recursive Least Square Control Allocation method is developed to minimize the allocation error considering the uncertainty in the control effectiveness matrix by solving a dual second-order cone programming problem. Simulation results demonstrate that the RBFNN-based trajectory tracking method achieves satisfactory performance in the presence of time-varying environmental disturbances, and the Recursive Least Square Control Allocation method effectively deals with actuator uncertainty.

On the optional and orthogonal decompositions of supermartingales and applications

We consider a set Q of probability measures, which are absolutely continuous with respect to the physical probability measure P and at least one is equivalent to P. We investigate in the finite probability space case, necessary and sufficient conditions on Q, under which any Q-supermartingale can be decomposed into the sum of a Q-martingale and a decreasing process. We also provide an orthogonal decomposition of Q-super-martingales and apply this result to the orthogonal decomposition of the polar cone of Q.

Generalized Truncated Moment Problems with Unbounded Sets

This paper studies generalized truncated moment problems with unbounded sets. First, we study geometric properties of the truncated moment cone and its dual cone of nonnegative polynomials. By the technique of homogenization, we give a convergent hierarchy of Moment-SOS relaxations for approximating these cones. With them, we give a Moment-SOS method for solving generalized truncated moment problems with unbounded sets. Finitely atomic representing measures, or certificates for their nonexistence, can be obtained by the proposed method. Numerical experiments and applications are also given.

Symmetries of Calabi-Yau prepotentials with isomorphic flops

Calabi-Yau threefolds with infinitely many flops to isomorphic manifolds have an extended Kähler cone made up from an infinite number of individual Kähler cones. These cones are related by reflection symmetries across flop walls. We study the implications of this cone structure for mirror symmetry, by considering the instanton part of the prepotential in Calabi-Yau threefolds. We show that such isomorphic flops across facets of the Kähler cone boundary give rise to symmetry groups isomorphic to Coxeter groups. In the dual Mori cone, non-flopping curve classes that are identified under these groups have the same Gopakumar-Vafa invariants. This leads to instanton prepotentials invariant under Coxeter groups, which we make manifest by introducing appropriate invariant functions. For some cases, these functions can be expressed in terms of theta functions whose appearance can be linked to an elliptic fibration structure of the Calabi-Yau manifold.

On δ- character in symmetric tω-Δ- Banach-Algebra

The aim of this paper is to provide information on new results from studies of symmetric tω-Δ- Banach Algebra. A new function d- character has been defined and apparent to be symmetric tω-Δ- Banaich Algebra. tω- approach dual cone space is introduced, with its symmetry properties indicated tω- ∆- Banaich algebra. Some new definitions, results and properties are given and discussed in this field.