Do thermodynamically stable rigid solids exist?

Customarily, crystalline solids are defined to be {\em rigid} since they resist changes of shape determined by their boundaries. However, rigid solids cannot exist in the thermodynamic limit where boundaries become irrelevant. Particles in the solid may rearrange to adjust to shape changes eliminating stress without destroying crystalline order. Rigidity is therefore valid only in the {\em metastable} state that emerges because these particle rearrangements in response to a deformation, or strain, are associated with slow collective processes. Here, we show that a thermodynamic collective variable may be used to quantify particle rearrangements that occur as a solid is deformed at zero strain rate. Advanced Monte Carlo simulation techniques are then employed to obtain the equilibrium free energy as a function of this variable. Our results lead to a new view on rigidity: While at zero strain a rigid crystal coexists with one that responds to infinitesimal strain by rearranging particles and expelling stress, at finite strain the rigid crystal is metastable, associated with a free energy barrier that decreases with increasing strain. The rigid phase becomes thermodynamically stable by switching on an external field, which penalises particle rearrangements. This produces a line of first-order phase transitions in the field - strain plane that intersects the origin. Failure of a solid once strained beyond its elastic limit is associated with kinetic decay processes of the metastable rigid crystal deformed with a finite strain rate. These processes can be understood in quantitative detail using our computed phase diagram as reference.Comment: 11 pages, 7 figure

AN INTEGRATED FRAMEWORK FOR QUALITY EVALUATION OF FRUITS AND VEGETABLE STORE LOCATED IN THE SUPERMARKET UNDER UTOPIAN ENVIRONMENT

Customer satisfaction depends on the availability of different varieties of fruits and vegetables in a supermarket store as well as the quality of this supermarket store for fruits and vegetables. The store may contain different variety of fruits and vegetables in a utopian environment. Apart from this, there are several quality parameters of a fruits and vegetable store. The quality evaluation of fruits and vegetable stores located in a supermarket is a big challenge for managerial personnel. Here, a quality evaluation framework is proposed for the fruits and vegetable store. The committee of experts identifies and finalizes the quality evaluation parameters through a brainstorming session. Fuzzy AHP is used to calculate the weights of evaluation parameters. A fuzzy TOPSIS generally ranks for the alternative stores. An improved fuzzy TOPSIS, which is named fuzzy k-TOPSIS, is proposed here to evaluate the quality of fruits and vegetable stores located in a supermarket. The fuzzy k-TOPSIS will provide rank as well as classification of the alternatives. A numerical example is demonstrated for a better understanding of the proposed framework

Collapse and Revival Oscillation in Double Jaynes-Cummings Model

We develop a systematic method of solving two non-interacting Jaynes-Cummings models by using the dressed state formalism in Hilbert space $\mathcal{H}_{AB}^{(2\otimes2)}$. It is shown that such model, called Double Jaynes-Cummings model (D-JCM), can be exactly solved if we take the initial bare state as the linear superposition of two Bell states. The collapse and revival oscillation, which is the standard trait of typical Jaynes-Cummings model, can be recovered if we make measurement at each local sites. Some consequence of the entanglement-induced dressing is discussed.Comment: 4 figures, 12 page