Thermal conduction in a quasi-stationary one-dimensional lattice system

2019 ◽  
Vol 33 (17) ◽  
pp. 1950178
Author(s):  
Mohammad Khorrami ◽  
Amir Aghamohammadi
Keyword(s):  
Heat Transfer ◽  
Ising Model ◽  
Diffusion Equation ◽  
Thermal Conduction ◽  
Nearest Neighbor ◽  
Entropy Change ◽  
Neighbor Interaction ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Special Case

A system of nearest-neighbor interaction on a one-dimensional lattice is investigated, which has a quasi-stationary (and position-dependent) temperature profile. The rates of heat transfer and entropy change, as well as the diffusion equation for the temperature are studied. A q-state Potts model, and its special case, a two-state Ising model, are considered as an example.

ATTRACTORS FOR STOCHASTIC LATTICE DYNAMICAL SYSTEMS

2006 ◽  
Vol 06 (01) ◽  
pp. 1-21 ◽  
Author(s):  
PETER W. BATES ◽  
HANNELORE LISEI ◽  
KENING LU
Keyword(s):  
Initial Data ◽  
Nearest Neighbor ◽  
Invariant Set ◽  
Neighbor Interaction ◽  
Forward Flow ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Nonlinear Reaction ◽  
Lattice Dynamical Systems ◽  
Bounded Sets

We consider a one-dimensional lattice with diffusive nearest neighbor interaction, a dissipative nonlinear reaction term and additive independent white noise at each node. We prove the existence of a compact global random attractor within the set of tempered random bounded sets. An interesting feature of this is that, even though the spatial domain is unbounded and the solution operator is not smoothing or compact, pulled back bounded sets of initial data converge under the forward flow to a random compact invariant set.

scholarly journals Ground states for infinite lattices with nearest neighbor interaction

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Peng Chen ◽  
Die Hu ◽  
Yuanyuan Zhang
Keyword(s):  
Periodic Solution ◽  
Dynamical Systems ◽  
Nearest Neighbor ◽  
Ground States ◽  
Neighbor Interaction ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Lattice Dynamical Systems ◽  
Infinite Lattices ◽  
Least Energy

Abstract Sun and Ma (J. Differ. Equ. 255:2534–2563, 2013) proved the existence of a nonzero T-periodic solution for a class of one-dimensional lattice dynamical systems, $$\begin{aligned} \ddot{q_{i}}=\varPhi _{i-1}'(q_{i-1}-q_{i})- \varPhi _{i}'(q_{i}-q_{i+1}),\quad i\in \mathbb{Z}, \end{aligned}$$ q i ¨ = Φ i − 1 ′ ( q i − 1 − q i ) − Φ i ′ ( q i − q i + 1 ) , i ∈ Z , where $q_{i}$ q i denotes the co-ordinate of the ith particle and $\varPhi _{i}$ Φ i denotes the potential of the interaction between the ith and the $(i+1)$ ( i + 1 ) th particle. We extend their results to the case of the least energy of nonzero T-periodic solution under general conditions. Of particular interest is a new and quite general approach. To the best of our knowledge, there is no result for the ground states for one-dimensional lattice dynamical systems.

Integrated Thermal Conduction and Hardenability Laboratory Activity

2013 ◽  
Author(s):  
Natasha L. Smith ◽  
Brandon S. Field
Keyword(s):  
Heat Transfer ◽  
Thermal Conduction ◽  
Machine Design ◽  
Engineering Curriculum ◽  
Laboratory Activity ◽  
One Dimensional ◽  
Practical Applications ◽  
Transformation Curve ◽  
Transient Thermal ◽  
Quench Test

This paper describes an integrated laboratory project between separate heat transfer and machine design courses. The project was structured around a Jominy end quench hardenability test. Most of the students participating were simultaneously enrolled in both classes. In the heat transfer class, students were required to model one-dimensional, transient thermal conduction for an end quench geometry of 4140 steel. In machine design, students applied their theoretical temperature profiles to a continuous cooling transformation curve (CCT) of 4140 steel to predict microstructure and matched the theoretical cooling rates with hardenability curves from literature to predict hardness. In laboratory, students then performed an end quench test in accordance with ASTM A255 on four steel rods. By combining activities across the two courses, students developed an appreciation for the interconnectivity of material within the engineering curriculum, and learned that practical applications typically require they employ knowledge from a variety of sources.

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