scholarly journals A Principled Approach Towards Symbolic Geometric Constraint Satisfaction

1996 ◽  
Vol 4 ◽  
pp. 419-443 ◽  
Author(s):  
S. Bhansali ◽  
G. A. Kramer ◽  
T. J. Hoar
Keyword(s):  
Constraint Satisfaction ◽  
First Principles ◽  
Degrees Of Freedom ◽  
Geometric Reasoning ◽  
Geometric Constraint ◽  
And Topology

An important problem in geometric reasoning is to find the configuration of a collection of geometric bodies so as to satisfy a set of given constraints. Recently, it has been suggested that this problem can be solved efficiently by symbolically reasoning about geometry. This approach, called degrees of freedom analysis, employs a set of specialized routines called plan fragments that specify how to change the configuration of a set of bodies to satisfy a new constraint while preserving existing constraints. A potential drawback, which limits the scalability of this approach, is concerned with the difficulty of writing plan fragments. In this paper we address this limitation by showing how these plan fragments can be automatically synthesized using first principles about geometric bodies, actions, and topology.

scholarly journals Constraint and Mobility Change Analysis of Rubik’s Cube-inspired Reconfigurable Joints and Corresponding Parallel Mechanisms

2020 ◽  
Vol 33 (1) ◽  
Author(s):  
Duanling Li ◽  
Pu Jia ◽  
Jiazhou Li ◽  
Dan Zhang ◽  
Xianwen Kong
Keyword(s):  
Parallel Mechanism ◽  
Unique Feature ◽  
Theoretical Method ◽  
Geometric Constraint ◽  
Parallel Mechanisms ◽  
Change Analysis ◽  
Application Range ◽  
And Topology ◽  
Physical Experiments ◽  
Underlying Principle

Abstract The current research of reconfigurable parallel mechanism mainly focuses on the construction of reconfigurable joints. Compared with the method of changing the mobility by physical locking joints, the geometric constraint has good controllability, and the constructed parallel mechanism has more configurations and wider application range. This paper presents a reconfigurable axis (rA) joint inspired and evolved from Rubik's Cubes, which have a unique feature of geometric and physical constraint of axes of joint. The effectiveness of the rA joint in the construction of the limb is analyzed, resulting in a change in mobility and topology of the parallel mechanism. The rA joint makes the angle among the three axes inside the groove changed arbitrarily. This change in mobility is completed by the case illustrated by a 3(rA)P(rA) reconfigurable parallel mechanism having variable mobility from 1 to 6 and having various special configurations including pure translations, pure rotations. The underlying principle of the metamorphosis of this rA joint is shown by investigating the dependence of the corresponding screw system comprising of line vectors, leading to evolution of the rA joint from two types of spherical joints to three types of variable Hooke joints and one revolute joint. The reconfigurable parallel mechanism alters its topology by rotating or locking the axis of rA joint to turn all limbs into different phases. The prototype of reconfigurable parallel mechanism is manufactured and all configurations are enumerated to verify the validity of the theoretical method by physical experiments.

Novel algorithm for geometric constraint satisfaction

1996 ◽  
Author(s):  
Liping Chen ◽  
Hao Luo ◽  
Chongbin Tu ◽  
Xingfang Zhang ◽  
Ji Zhou ◽  
...  
Keyword(s):  
Constraint Satisfaction ◽  
Geometric Constraint ◽  
Novel Algorithm

Solid molecular phases of Hydrogen via constant-pressure first-principles Molecular Dynamics

1997 ◽  
Vol 499 ◽  
Author(s):  
Jorge Kohanoff ◽  
Sandro Scandolo
Keyword(s):  
Molecular Dynamics ◽  
First Principles ◽  
Degrees Of Freedom ◽  
Constant Pressure ◽  
Phase Iii ◽  
Orthorhombic Structure ◽  
Lattice Constants ◽  
Symmetry Phase ◽  
Dynamics Simulations ◽  
Zone Sampling

ABSTRACTBy performing constant pressure ab initio molecular dynamics simulations we analyse the high pressure phases of molecular solid hydrogen. We use a gradient corrected LDA, and a freshly implemented efficient technique for Brillouin zone sampling. An extremely good k-point sampling turns out to be crucial for obtaining the correct ground state. Our constant pressure approach allows us to optimize simultaneously the ori-entational degrees of freedom, the lattice constants, and the space group. This can be done either by a local optimization tehcnique, or by running molecular dynamics (MD) trajectories. The MD allows for the system to undergo structural transformations spontaneously. In the lower pressure, namely for the broken symmetry phase (BSP or phase II), we find a quadrupolar orthorhombic structure, of Pca21 symmetry. By means of an MD investigation, we find, at higher pressures, a slightly distorted orthorhombic structure of Cmc21 symmetry. This structure cannot be straightforwardly identified with the H-A phase (or phase III) because: 1) it is metallic, and 2) the Raman vibron discontinuity would be far too large compared to experiment. In fact, we argue that this phase is the first metallic molecular phase of hydrogen. Metallization would happen then, not via a band-overlap mechanism, but due to a structural transformation. By comparing total enthalpies, we also give suggestions for the structure of phase III.

Derivation of Topological Graphs of Some Planar 4DOF Redundant Closed Mechanisms by Contracted Graphs and Arrays

2010 ◽  
Vol 2 (3) ◽  
Author(s):  
Yi Lu ◽  
Ling Ding ◽  
Shuyan Li ◽  
Jianping Yu
Keyword(s):  
Degrees Of Freedom ◽  
Visual Basic ◽  
Topological Graphs ◽  
And Topology ◽  
Singular Configuration ◽  
Topology Graph

Some planar redundantly closed mechanisms (RCMs) have better dexterity, less singular configuration, and higher stiffness. In this paper, the derivation of valid topology graphs (TGs) of some planar four degrees of freedom (4DOF) RCMs is studied based on the contracted graph (CG), arrays, and topology graph with digits (DTG). First, some CGs without any binary links are constructed for the planar 4DOF RCMs, some curves with only binary links are distributed over CGs, and some valid TGs of the planar 4DOF RCMs are derived. Second, a complicated derivation of TG is transformed into an easy derivation of array and DTG, and some programs are compiled in VISUAL BASIC; all valid arrays corresponding to nonisomorphic TGs are derived, and some invalid arrays corresponding to the isomorphic TGs and invalid TGs are determined and removed by the compiled programs. Third, many valid TGs of the planar 4DOF RCMs with various basic links are derived from valid arrays and DTGs. Finally, some application examples are illustrated.

scholarly journals Universality of the SAT-UNSAT (jamming) threshold in non-convex continuous constraint satisfaction problems

2017 ◽  
Vol 2 (3) ◽  
Author(s):  
Silvio Franz ◽  
Giorgio Parisi ◽  
Maxime Sevelev ◽  
Pierfrancesco Urbani ◽  
Francesco Zamponi
Keyword(s):  
Constraint Satisfaction ◽  
Disordered Systems ◽  
Statistical Physics ◽  
Degrees Of Freedom ◽  
Universality Class ◽  
Constraint Satisfaction Problems ◽  
Worst Case ◽  
Average Case ◽  
Soft Spheres ◽  
Scaling Solution

Random constraint satisfaction problems (CSP) have been studied extensively using statistical physics techniques. They provide a benchmark to study average case scenarios instead of the worst case one. The interplay between statistical physics of disordered systems and computer science has brought new light into the realm of computational complexity theory, by introducing the notion of clustering of solutions, related to replica symmetry breaking. However, the class of problems in which clustering has been studied often involve discrete degrees of freedom: standard random CSPs are random (aka disordered Ising models) or random coloring problems (aka disordered Potts models). In this work we consider instead problems that involve continuous degrees of freedom. The simplest prototype of these problems is the perceptron. Here we discuss in detail the full phase diagram of the model. In the regions of parameter space where the problem is non-convex, leading to multiple disconnected clusters of solutions, the solution is critical at the SAT/UNSAT threshold and lies in the same universality class of the jamming transition of soft spheres. We show how the critical behavior at the satisfiability threshold emerges, and we compute the critical exponents associated to the approach to the transition from both the SAT and UNSAT phase. We conjecture that there is a large universality class of non-convex continuous CSPs whose SAT-UNSAT threshold is described by the same scaling solution.

scholarly journals Computationally accelerated discovery of high entropy pyrochlore oxides

2021 ◽  
Author(s):  
Krishna Chaitanya Pitike ◽  
Antonio Macias ◽  
Markus Eisenbach ◽  
Craig Bridges ◽  
Valentino Cooper
Keyword(s):  
Monte Carlo ◽  
Oxygen Vacancy ◽  
First Principles ◽  
Degrees Of Freedom ◽  
Vacancy Concentration ◽  
Oxygen Vacancy Concentration ◽  
High Entropy ◽  
Impurity Phases ◽  
Wide Range ◽  
Pyrochlore Oxides

Abstract High entropy ceramics provide enhanced flexibility for tailoring a wide range of physical properties, emerging from the diverse chemical and configurational degrees of freedom. Expanding upon the endeavors of recently synthesized high entropy ceramics in rock salt, fluorite, spinel and perovskite structures, we explore the relative feasibility of formation of high entropy pyrochlore oxides, A2B2O7, with multi-cation occupancy of the B-site, estimated from first principles based thermodynamic descriptors. Subsequently, we used Monte Carlo simulations to estimate the phase composition, oxygen vacancy concentration and local ionic segregation as a function of temperature and oxygen partial pressure. In parallel, we have investigated the synthesis of several multicomponent oxides with a pyrochlore composition, related to our computational investigations, resulting in several high purity pyrochlore oxides, in some cases with minor impurity phases. Ultimately, our approach allows us to evaluate potential impurity phases, ionic disorder and oxygen vacancy concentration in response to the experimental variables, thereby making realistic predictions that can direct and accelerate experimental synthesis of novel multicomponent ceramics.

Solution of Topology Embryonic Graph and Topology Graph for Unified Planar-Spatial Mechanisms

2003 ◽  
Author(s):  
Lu Yi ◽  
Tatu Leinonen
Keyword(s):  
Degrees Of Freedom ◽  
Degree Of Freedom ◽  
Matrix Approach ◽  
Group Approach ◽  
Spatial Mechanism ◽  
Spatial Mechanisms ◽  
And Topology ◽  
Topology Graph ◽  
Relative Theory

An analysis matrix approach for solving an isomeric topology embryonic graph and a digital group approach for solving an isomeric topology graph of a unified planar-spatial mechanism are presented and the relative theory is discussed. Firstly, all binary links are removed from each acceptable linkage system with different degrees of freedom, many analysis matrixes are constructed, and many topology embryonic graphs of the mechanism are derived. Secondly, from an acceptable multi-element link combination of planar or spatial mechanisms, a rule for determining the isomeric topology embryonic graphs and an unreasonable topology embryonic graph is obtained. Thirdly, by considering the degree of freedom of the mechanism and the configuration of a planar or spatial mechanism, the number of binary links is determined. Finally, all removed binary links are rearranged systematically back into an isomeric topology embryonic graph, and the acceptable topology graphs of the mechanism are derived by using a digital group approach. Some illustrations show that the two approaches are simple and effective tools and can be employed to synthesize both planar and spatial mechanisms.

scholarly journals Gravity and quantum theory: Domains of conflict and contact

2019 ◽  
Vol 29 (01) ◽  
pp. 2030001
Author(s):  
T. Padmanabhan
Keyword(s):  
Thermal Properties ◽  
Cosmological Constant ◽  
First Principles ◽  
Degrees Of Freedom ◽  
Dynamical Variable ◽  
Quantum Structure ◽  
Cosmological Constant Problem ◽  
Metric Tensor ◽  
Long Wavelength ◽  
Thermodynamic Interpretation

There are two strong clues about the quantum structure of spacetime and the gravitational dynamics, which are almost universally ignored in the conventional approaches to quantize gravity. The first clue is that null surfaces exhibit (observer-dependent) thermal properties and possess a heat density. This suggests that spacetime, like matter, has microscopic degrees of freedom and its long wavelength limit should be described in thermodynamic language and not in a geometric language. Second clue is related to the existence of the cosmological constant. Its understanding from first-principles will require the dynamical principles of the theory to be invariant under the shift [Formula: see text]. This puts strong constraints on the nature of gravitational dynamics and excludes metric tensor as a fundamental dynamical variable. In fact, these two clues are closely related to each other. When the dynamical principles are recast, respecting the symmetry [Formula: see text], they automatically acquire a thermodynamic interpretation related to the first clue. The first part of this review provides a pedagogical introduction to thermal properties of the horizons, including some novel derivations. The second part describes some aspects of cosmological constant problem and the last part provides a perspective on gravity which takes into account these principles.

scholarly journals Interfacial charge-transfer Mott state in iridate–nickelate superlattices

2019 ◽  
Vol 116 (40) ◽  
pp. 19863-19868 ◽  
Author(s):  
Xiaoran Liu ◽  
Michele Kotiuga ◽  
Heung-Sik Kim ◽  
Alpha T. N’Diaye ◽  
Yongseong Choi ◽  
...  
Keyword(s):  
Charge Transfer ◽  
First Principles ◽  
Degrees Of Freedom ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
First Principles Calculations ◽  
Experimental Characterization ◽  
Large Crystal ◽  
Interfacial Charge Transfer ◽  
Interfacial Charge

We investigate SrIrO3/LaNiO3 superlattices in which we observe a full electron transfer at the interface from Ir to Ni, triggering a massive structural and electronic reconstruction. Through experimental characterization and first-principles calculations, we determine that a large crystal field splitting from the distorted interfacial IrO6 octahedra surprisingly dominates over the spin–orbit coupling and together with the Hund’s coupling results in the high-spin (S = 1) configurations on both the Ir and Ni sites. This demonstrates the power of interfacial charge transfer in coupling lattice, charge, orbital, and spin degrees of freedom, opening fresh avenues of investigation of quantum states in oxide superlattices.

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