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Contact geometric descriptions of vector fields on dually flat spaces and their applications in electric circuit models and nonequilibrium statistical mechanics

Shin-itiro Goto
2016 Journal of Mathematical Physics  
In this paper contact geometric descriptions of vector fields on dually flat spaces are proposed on the basis of the theory of contact Hamiltonian vector fields.  ...  Based on these descriptions, two ways of lifting vector fields on Legendre submanifolds to contact manifolds are given.  ...  Shikano and Institute for Molecular Science for supporting my work, and thank T. Wada, M. Koga and Y Nakata for giving various comments on this work.  ... 
doi:10.1063/1.4964751 fatcat:oapzhcc63jgrbauuamv4g44suq

Singular compactifications and cosmology [article]

Laur Jarv, Thomas Mohaupt, Frank Saueressig
2003 arXiv   pre-print
The dynamics of the additional states, which become massless at the transition point and give rise to a scalar potential, helps to stabilize the moduli and triggers short periods of accelerated cosmological  ...  We summarize our recent results of studying five-dimensional Kasner cosmologies in a time-dependent Calabi-Yau compactification of M-theory undergoing a topological flop transition.  ...  In [5] we considered an explicit model for a CY compactification undergoing a flop with N = 1 and investigated the effect of the transition states on five-dimensional Kasner cosmologies, 2 ds 2 = −dτ  ... 
arXiv:hep-th/0311016v1 fatcat:s32bmozzcbcrxbepbasewe5s4y

Basic Procedures and Methodological Support of the "Object-Based Environment for Engineering Calculation in the MATLAB System" Course

Stanislav A. Lyushnin, Y.I. Dimitrienko, E.N. Grigorieva
2020 ITM Web of Conferences  
This paper looks at methodological aspects of the «Object-based environment for engineering calculation in the MATLAB system» course offered to the second year students of Bauman Moscow State Technical  ...  University for mastering tools in the MATLAB environment, learning MATLAB language and object-oriented technology of working with classes and applications, designed for engineering calculations of ammunition  ...  Object X is created by a constructor of one of the random variable classes with the corresponding parameters, for example, X = Norm_2([1; 2], [3, 2] , 0.5) is a normal distribution on the plane object  ... 
doi:10.1051/itmconf/20203504016 fatcat:us6leeq3krf3vmqbn546amsgnu

Degenerate Hessian structures on radiant manifolds

M. Á. García Ariza
2018 International Journal of Geometric Methods in Modern Physics (IJGMMP)  
A manifold M is said to be radiant if it is endowed with a symmetric, flat connection ∇̅ and a global vector field ρ whose covariant derivative is the identity mapping.  ...  A function on M is said to be extensive if its Lie derivative with respect to ρ is the function itself.  ...  Montesinos for the encouraging discussions and the advice that helped to shape this paper. The author is also grateful to B. Díaz for his comments and suggestions on the manuscript, and to I.  ... 
doi:10.1142/s0219887818500871 fatcat:lnhrbldru5fadbf6thf5qwelbu

Flop transitions in M-theory cosmology

Matthias Brändle, André Lukas
2003 Physical Review D, Particles and fields  
We study flop-transitions for M-theory on Calabi-Yau three-folds and their applications to cosmology in the context of the effective five-dimensional supergravity theory.  ...  We find the potential for this hypermultiplet which includes quadratic and quartic terms as well as additional dependence on the Kahler moduli.  ...  Acknowledgements We would like to thank Natxo Alonso-Alberca for collaboration at an early stage of this project. A. L. is supported by a PPARC Advanced Fellowship. M.  ... 
doi:10.1103/physrevd.68.024030 fatcat:h5bbyd2ykvavlibjm5tsbehhbu

A Lie-Backlund approach to equivalence and flatness of nonlinear systems

M. Fliess, J. Levine, P. Martin, P. Rouchon
1999 IEEE Transactions on Automatic Control  
They correspond to systems which are equivalent to a trivial one, with time preservation or not.  ...  Trivial systems are, in turn, equivalent to any linear controllable system with the same number of inputs, and consequently flat systems are linearizable by endogenous feedback.  ...  For any , , which may be identified with the state space , is finite-dimensional; is called a fiber.  ... 
doi:10.1109/9.763209 fatcat:c7rm7eq5gnhijocpuho6fi6vfa

Designing spin-textured flat bands in twisted graphene multilayers via helimagnet encapsulation [article]

Guangze Chen, Maryam Khosravian, Jose L. Lado, Aline Ramires
2021 arXiv   pre-print
The two-dimensional nature of these systems makes them suitable for encapsulation by materials that break specific symmetries.  ...  Our results put forward helimagnetic encapsulation as a powerful way of designing spin-textured flat band systems, providing a starting point to engineer a new family of correlated moire states.  ...  Törmä for useful discussions.  ... 
arXiv:2109.13130v2 fatcat:rg3hz7aqnrgvzk45r3llfm6puy

Differentially flat mobile manipulators mounted with an under-actuated vertical arm

Ji-Chul Ryu, Sunil K Agrawal
2010 2010 IEEE International Conference on Robotics and Automation  
In addition, the trajectory planning and feedback controller design for point-to-point motions in state space is considerably simplified despite the under-actuation of the arm and nonholonomic constraints  ...  This paper discusses how mobile manipulators with an under-actuated vertical arm can be designed to be differentially flat.  ...  ., considering v as an additional state, one gets a welldefined relative degree of 3 for each of F 1 and F 2 .  ... 
doi:10.1109/robot.2010.5509208 dblp:conf/icra/RyuA10 fatcat:26p7zbj3lvdkhlklfbecobjq4a

Flatness Based Control of a HVAC System

Arvo Kaldmäe, Ülle Kotta
2017 Information Technology and Control  
Since the flat outputs are also the variables, which one usually wants to control, it is relatively easy to construct a flatness-based feedforward control for the HVAC model.  ...  We define the appropriate trajectories for the flat outputs and then the controller is computed from the parametrization of system inputs in terms of flat outputs and their derivatives.  ...  Actuator input values for the extended system  ... 
doi:10.5755/j01.itc.46.4.17697 fatcat:zybs6z2qozdntcdh2uojp4sjdu

Engineering Three-Dimensional Moiré Flat Bands

Lede Xian, Ammon Fischer, Martin Claassen, Jin Zhang, Angel Rubio, Dante Marvin Kennes
2021 Nano letters 21(18)  
We exemplify the general concept by considering graphitic systems, boron nitride, and WSe 2 , but the approach is applicable to any two-dimensional van der Waals material.  ...  Twisting two adjacent layers of van der Waals materials with respect to each other can lead to flat two-dimensional electronic bands which enables a wealth of physical phenomena.  ...  Figure 2 . 2 Figure 2. Three-dimensional flat bands for different materials, graphene, WSe 2 and boron nitride. Atomic structures of 3D twisted graphene (a), WSe 2 (b), boron nitride (c).  ... 
doi:10.18154/rwth-2021-10595 fatcat:y427fsgl2reprkwvpbaxbnzjxi

Differential-Geometric Decomposition of Flat Nonlinear Discrete-Time Systems [article]

Bernd Kolar, Markus Schöberl, Johannes Diwold
2021 arXiv   pre-print
If the system is flat, then the algorithm yields a flat output which only depends on the state variables.  ...  Hence, every flat discrete-time system has a flat output which does not depend on the inputs and their forward-shifts. Again, no comparable result for flat continuous-time systems is available.  ...  Since the constructed flat output only depends on the state variables, we obtain the additional result that every flat discretetime system has a flat output which is independent of the inputs and their  ... 
arXiv:1907.00596v2 fatcat:qoqtpy332fbnvmmpi632j75iqa

An Improved Vector Control of an Induction Motor Based on Flatness

Liping Fan, Liang Zhang
2011 Procedia Engineering  
This paper presents a differential flatness-based controller for induction motor vector control system.  ...  The flatness-based approach uses the characterization of system dynamics to generate a suitable output and it can control continuous nonlinear systems with good performances in term of tracking trajectory  ...  Acknowledgements The authors thank the Education Department of Liao Ning Province of China which provided financial support for this study, under contract LS2010127.  ... 
doi:10.1016/j.proeng.2011.08.116 fatcat:ff5awffnorfk5jj2dhb76sw24y

Checking Robust Practical Stability for Flatness Based Tracking Controllers Using Interval Methods

Felix Antritter, Marco Kletting
2011 IFAC Proceedings Volumes  
The robustness analysis of tracking controllers based on differential flatness is a field of research with many open problems.  ...  In earlier publications the authors have shown that interval methods can be used to determine maximal admissible uncertainties in the plant such that the controlled system can be guaranteed to remain within  ...  In this contribution the following relations for nonlinear single input systems are used, where explicitely the dependence of the relations on the parameters are stated: For a flat systeṁ x = f (p, x,  ... 
doi:10.3182/20110828-6-it-1002.03239 fatcat:rcvoobnjsbe67fxxddubqa7pcm

Sufficient statistic and reduced-dimensionality equivalent symbol-space model for frequency-flat MIMO channel with spatially nonuniform delay

J. Sykora
2005 IEE Proceedings - Communications  
However for the purpose of channel capacity investigation, code design, etc., it is useful to work with a discrete time model (see e.g. [1], [2], [3] for some applications).  ...  Introduction Motivation This paper focuses on the investigation of equivalent symbol space model of MIMO (Multiple Input Multiple Output) spatial diversity communication system with frequency flat fading  ...  The system equivalent signal space model now corresponds with the one which is traditionally used for flat fading MIMO channel with an extension for multidimensional channel symbols per antenna.  ... 
doi:10.1049/ip-com:20045018 fatcat:aaal5yvyb5dxzfkhamwkqg4vae

Hierarchical control via approximate simulation and feedback linearization

Jie Fu, Shridhar Shah, Herbert G. Tanner
2013 2013 American Control Conference  
system obtained via feedback, to recast the problem of trajectory planning and control for the nonlinear system into a reduced dimensional space.  ...  Two different hierarchical control architectures are proposed for this framework and the method is demonstrated with a quadrotor system.  ...  For practical realization, one needs to measure the complete state vector for feedback. The flat outputs and their derivatives are computed using ξ = T (x).  ... 
doi:10.1109/acc.2013.6580099 fatcat:drx5enrozvc5zelujgc6spu4j4
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