A model of Poincaré and Rigorous Proof of the Second Element of Thermodynamics from Mechanics

1994 ◽  
pp. 295-297
Author(s):  
L. D. Pustyl’nikov
Keyword(s):  
Rigorous Proof

Constraint-following servo control for an underactuated mobile robot under hard constraints

2021 ◽  
pp. 095965182110248
Author(s):  
Duo Fu ◽  
Jin Huang ◽  
Wen-Bin Shangguan ◽  
Hui Yin
Keyword(s):  
Mobile Robot ◽  
Control Problem ◽  
Servo Control ◽  
Robot Motion ◽  
Soft Constraints ◽  
Rigorous Proof ◽  
Control Approach ◽  
Hard Constraints

This article formulates the control problem of underactuated mobile robot as servo constraint-following, and develops a novel constraint-following servo control approach for underactuated mobile robot under both servo soft and hard constraints. Servo soft constraints are expressed as equalities, which may be holonomic or non-holonomic. Servo hard constraints are expressed as inequalities. It is required that the underactuated mobile robot motion eventually converges to servo soft constraints, and satisfies servo hard constraints at all times. Diffeomorphism is employed to incorporate hard constraints into soft constraints, yielding new soft constraints to relax hard constraints. By this, we design a constraint-following servo control based on the new servo soft constraints, which drives the system to strictly follow the original servo soft and hard constraints. The effectiveness of the proposed approach is proved by rigorous proof and simulations.

Chaotic Vibration of a Two-dimensional Non-strictly Hyperbolic Equation

2018 ◽  
Vol 61 (4) ◽  
pp. 768-786 ◽  
Author(s):  
Liangliang Li ◽  
Jing Tian ◽  
Goong Chen
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Hyperbolic Equation ◽  
Method Of Characteristics ◽  
Nonlinear Boundary ◽  
Chaotic Oscillation ◽  
Nonlinear Boundary Conditions ◽  
Rigorous Proof ◽  
Two Dimensional ◽  
Chaotic Vibration

AbstractThe study of chaotic vibration for multidimensional PDEs due to nonlinear boundary conditions is challenging. In this paper, we mainly investigate the chaotic oscillation of a two-dimensional non-strictly hyperbolic equation due to an energy-injecting boundary condition and a distributed self-regulating boundary condition. By using the method of characteristics, we give a rigorous proof of the onset of the chaotic vibration phenomenon of the zD non-strictly hyperbolic equation. We have also found a regime of the parameters when the chaotic vibration phenomenon occurs. Numerical simulations are also provided.

A rigorous proof of the Alkemade theorem

Calphad ◽  
2004 ◽  
Vol 28 (2) ◽  
pp. 209-211 ◽  
Author(s):  
Dmitri V. Malakhov
Keyword(s):  
Rigorous Proof

MAGNETIZATION OF THE PURE STATES IN THE p-SPIN INTERACTION MODEL

2004 ◽  
Vol 18 (04n05) ◽  
pp. 773-784
Author(s):  
M. TALAGRAND
Keyword(s):  
Low Temperature ◽  
Finite Number ◽  
Interaction Model ◽  
Spin Interaction ◽  
Rigorous Proof ◽  
Pure States ◽  
Number Of Cells

We study the magnetization of the pure states in (a suitable version of) the p-spin interaction model at low temperature. We give a rigorous proof of the phenomenon, discovered in 1 that (very roughly speaking), at a given level of accuracy, the set of sites decomposes in a finite number of cells on which the magnetization of any different pure states are uncorrelated.

The semi-analytic theory of standing waves

1987 ◽  
Vol 411 (1840) ◽  
pp. 123-137 ◽  
Keyword(s):  
Numerical Calculation ◽  
Power Series ◽  
Deep Water ◽  
Standing Waves ◽  
Affirmative Answer ◽  
Rigorous Proof ◽  
Series Solutions ◽  
Wave Problem ◽  
Power Series Solutions ◽  
Formal Power

The algorithm proposed by Schwartz & Whitney ( J. Fluid Mech . 107, 147–171 (1981)) for the numerical calculation of formal power series solutions of the classical standing-wave problem is vindicated by a rigorous proof that resonances do not occur in the calculations. A detailed account of a successful algorithm is given. The analytical question of the convergence of the power series whose coefficients have been calculated remains open. An affirmative answer would be a first demonstration of the existence of standing waves on deep water.

scholarly journals FREE ENERGY IN THE GENERALIZED SHERRINGTON–KIRKPATRICK MEAN FIELD MODEL

2005 ◽  
Vol 17 (07) ◽  
pp. 793-857 ◽  
Author(s):  
DMITRY PANCHENKO
Keyword(s):  
Free Energy ◽  
Real Line ◽  
Prior Distribution ◽  
Field Model ◽  
Mean Field ◽  
Rigorous Proof ◽  
Bounded Subset ◽  
Mean Field Model ◽  
The Real ◽  
Parisi Formula

In [11], Talagrand gave a rigorous proof of the Parisi formula in the classical Sherrington–Kirkpatrick (SK) model. In this paper, we build upon the methodology developed in [11] and extend Talagrand's result to the class of SK type models in which the spins have arbitrary prior distribution on a bounded subset of the real line.

Sign in / Sign up

Export Citation Format

Share Document