On the temporal development of oscillations in a one-dimensional chain of coupled harmonic oscillators

1969 ◽  
Vol 5 (11) ◽  
pp. 1226-1229
Author(s):  
A. S. Dolgov ◽  
N. A. Khizhnyak
Keyword(s):  
Harmonic Oscillators ◽  
Dimensional Chain ◽  
Temporal Development ◽  
One Dimensional ◽  
Coupled Harmonic Oscillators

The effect of the mass of the center spring in one‐dimensional coupled harmonic oscillators

1988 ◽  
Vol 56 (12) ◽  
pp. 1120-1123 ◽  
Author(s):  
David L. Wallach ◽  
William Beatty ◽  
Karl Beisler ◽  
Peter Chronowski ◽  
Matthew Holloway ◽  
...  
Keyword(s):  
Harmonic Oscillators ◽  
One Dimensional ◽  
Coupled Harmonic Oscillators

scholarly journals Heat flow in a harmonic chain due to an impulse disturbance

2020 ◽  
Vol 20 (1) ◽  
pp. 52-57
Author(s):  
A.I. Gudimenko ◽  
Keyword(s):  
Initial Conditions ◽  
Local Heat ◽  
Harmonic Oscillators ◽  
Heat Current ◽  
Maxwell Distribution ◽  
State Correlation ◽  
One Dimensional ◽  
Coupled Harmonic Oscillators ◽  
Harmonic Chain ◽  
Analytical Expressions

The heat motion in a one-dimensional semi-infinite chain of coupled harmonic oscillators is studied for the Maxwell distribution of initial velocities and zero initial displacements of the chain particles. It is believed that such initial conditions are achieved by an impulse heating of the sample. Exact analytical expressions for the state correlation functions, local temperature, and local heat current of the chain are obtained.

scholarly journals Measurement of the Temperature Using the Tomographic Representation of Thermal States for Quadratic Hamiltonians

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1445
Author(s):  
Julio A. López-Saldívar ◽  
Margarita A. Man’ko ◽  
Vladimir I. Man’ko
Keyword(s):  
Covariance Matrix ◽  
Wigner Function ◽  
Temperature Scale ◽  
Quantum Systems ◽  
Harmonic Oscillators ◽  
One Dimensional ◽  
Coupled Harmonic Oscillators ◽  
Quadratic Hamiltonians ◽  
Tomographic Representation ◽  
Thermal States

The Wigner and tomographic representations of thermal Gibbs states for one- and two-mode quantum systems described by a quadratic Hamiltonian are obtained. This is done by using the covariance matrix of the mentioned states. The area of the Wigner function and the width of the tomogram of quantum systems are proposed to define a temperature scale for this type of states. This proposal is then confirmed for the general one-dimensional case and for a system of two coupled harmonic oscillators. The use of these properties as measures for the temperature of quantum systems is mentioned.

A new one-dimensional CdIIcoordination polymer with a two-dimensional layered structure incorporating 2-[(1H-imidazol-1-yl)methyl]-1H-benzimidazole and benzene-1,2-dicarboxylate ligands

2016 ◽  
Vol 72 (6) ◽  
pp. 480-484 ◽  
Author(s):  
Qiu-Ying Huang ◽  
Xiao-Yi Lin ◽  
Xiang-Ru Meng
Keyword(s):  
Layered Structure ◽  
Room Temperature ◽  
Weak Interactions ◽  
Coordination Geometry ◽  
Dimensional Chain ◽  
Two Dimensional ◽  
One Dimensional ◽  
Heterocyclic Ligand ◽  
Rich Variety ◽  
Solvent Molecules

The N-heterocyclic ligand 2-[(1H-imidazol-1-yl)methyl]-1H-benzimidazole (imb) has a rich variety of coordination modes and can lead to polymers with intriguing structures and interesting properties. In the coordination polymercatena-poly[[cadmium(II)-bis[μ-benzene-1,2-dicarboxylato-κ4O1,O1′:O2,O2′]-cadmium(II)-bis{μ-2-[(1H-imidazol-1-yl)methyl]-1H-benzimidazole}-κ2N2:N3;κ2N3:N2] dimethylformamide disolvate], {[Cd(C8H4O4)(C11H10N4)]·C3H7NO}n, (I), each CdIIion exhibits an irregular octahedral CdO4N2coordination geometry and is coordinated by four O atoms from two symmetry-related benzene-1,2-dicarboxylate (1,2-bdic2−) ligands and two N atoms from two symmetry-related imb ligands. Two CdIIions are connected by two benzene-1,2-dicarboxylate ligands to generate a binuclear [Cd2(1,2-bdic)2] unit. The binuclear units are further connected into a one-dimensional chain by pairs of bridging imb ligands. These one-dimensional chains are further connected through N—H...O hydrogen bonds and π–π interactions, leading to a two-dimensional layered structure. The dimethylformamide solvent molecules are organized in dimeric pairsviaweak interactions. In addition, the title polymer exhibits good fluorescence properties in the solid state at room temperature.

scholarly journals The magneto-elastica : from self-buckling to self-assembly

2014 ◽  
Vol 470 (2162) ◽  
pp. 20130609 ◽  
Author(s):  
Dominic Vella ◽  
Emmanuel du Pontavice ◽  
Cameron L. Hall ◽  
Alain Goriely
Keyword(s):  
Self Assembly ◽  
Permanent Magnets ◽  
Energy Estimates ◽  
Dimensional Chain ◽  
Elastic Rod ◽  
Straight Chain ◽  
One Dimensional ◽  
Vibration Dynamics ◽  
Magnetic Strength ◽  
A Chain

Spherical neodymium–iron–boron magnets are permanent magnets that can be assembled into a variety of structures owing to their high magnetic strength. A one-dimensional chain of these magnets responds to mechanical loadings in a manner reminiscent of an elastic rod. We investigate the macroscopic mechanical properties of assemblies of ferromagnetic spheres by considering chains, rings and chiral cylinders of magnets. Based on energy estimates and simple experiments, we introduce an effective magnetic bending stiffness for a chain of magnets and show that, used in conjunction with classic results for elastic rods, it provides excellent estimates for the buckling and vibration dynamics of magnetic chains. We then use this estimate to understand the dynamic self-assembly of a cylinder from an initially straight chain of magnets.

Poly[[μ2-1,3-bis(pyridin-4-yl)propane](μ3-1,4-phenylenediacetato)cadmium]

2012 ◽  
Vol 68 (2) ◽  
pp. m34-m36 ◽  
Author(s):  
Dong Liu
Keyword(s):  
Title Complex ◽  
Point Of View ◽  
Solvothermal Reaction ◽  
Dimensional Chain ◽  
Two Dimensional ◽  
One Dimensional ◽  
Connected Network ◽  
Dimensional Network

Solvothermal reaction between Cd(NO3)2, 1,4-phenylenediacetate (1,4-PDA) and 1,3-bis(pyridin-4-yl)propane (bpp) afforded the title complex, [Cd(C10H8O4)(C13H14N2)]n. Adjacent carboxylate-bridged CdIIions are related by an inversion centre. The 1,4-PDA ligands adopt acisconformation and connect the CdIIions to form a one-dimensional chain extending along thecaxis. These chains are in turn linked into a two-dimensional network through bpp bridges. The bpp ligands adopt ananti–gaucheconformation. From a topological point of view, each bpp ligand and each pair of 1,4-PDA ligands can be considered as linkers, while the dinuclear CdIIunit can be regarded as a 6-connecting node. Thus, the structure can be simplified to a two-dimensional 6-connected network.

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