Yang-Yang method for the thermodynamics of one-dimensional multi-component interacting fermions

Using Yang and Yang's particle-hole description, we present a thorough derivation of the thermodynamic Bethe ansatz equations for a general $SU(\kappa)$ fermionic system in one-dimension for both the repulsive and attractive regimes under the presence of an external magnetic field. These equations are derived from Sutherland's Bethe ansatz equations by using the spin-string hypothesis. The Bethe ansatz root patterns for the attractive case are discussed in detail. The relationship between the various phases of the magnetic phase diagrams and the external magnetic fields is given for the attractive case. We also give a quantitative description of the ground state energies for both strongly repulsive and strongly attractive regimes.Comment: 22 pages, 2 figures, slight improvements, some extra reference

Unified description of pairing, trionic and quarteting states for one-dimensional SU(4) attractive fermions

Paired states, trions and quarteting states in one-dimensional SU(4) attractive fermions are investigated via exact Bethe ansatz calculations. In particular, quantum phase transitions are identified and calculated from the quarteting phase into normal Fermi liquid, trionic states and spin-2 paired states which belong to the universality class of linear field-dependent magnetization in the vicinity of critical points. Moreover, unified exact results for the ground state energy, chemical potentials and complete phase diagrams for isospin $S=1/2, 1, 3/2$ attractive fermions with external fields are presented. Also identified are the magnetization plateaux of $m^z=M_s/3$ and $m^z=2M_s/3$, where $M_s$ is the magnetization saturation value. The universality of finite-size corrections and collective dispersion relations provides a further test ground for low energy effective field theory.Comment: 13 pages, 4 figure

Quantum phase diagram of an exactly solved mixed spin ladder

We investigate the quantum phase diagram of the exactly solved mixed spin-(1/2,1) ladder via the thermodynamic Bethe ansatz (TBA). In the absence of a magnetic field the model exhibits three quantum phases associated with su(2), su(4) and su(6) symmetries. In the presence of a strong magnetic field, there is a third and full saturation magnetization plateaux within the strong antiferromagnetic rung coupling regime. Gapless and gapped phases appear in turn as the magnetic field increases. For weak rung coupling, the fractional magnetization plateau vanishs and exhibits new quantum phase transitions. However, in the ferromagnetic coupling regime, the system does not have a third saturation magnetization plat eau. The critical behaviour in the vicinity of the critical points is also derived systematically using the TBA.Comment: 20 pages, 2 figure

High velocity impact resistance of fibre metal laminates

The high velocity impact resistance of fibre metal laminates (FMLs) based on combinations of three different aluminium alloys (6161-O, 6061-T6, 7075-T6) and a glass fibre reinforced epoxy resin have been investigated both experimentally and numerically. A series of perforation tests on multilayer configurations, ranging from a simple 2/1 lay-up to a seven ply 4/3 laminate. High velocity impact was conducted using a projectile gas-gun launcher, operating in the velocity range between 119 m/s and 252 m/s.[1] The impact response of fibre metal laminates samples was characterised by determining the energy required to perforate the panels. A stereoscopic Digital Image Correlation (DIC) method was adopted to measure full-field deformations and strain for FMLs which providing the full field strain history and 3D measurements up to sample perforation. The perforation resistance of the panels was predicted using the finite element analysis package Abaqus/Explicit. A vectorized user-defined material subroutine (VUMAT) was employed to define Hashin’s 3D rate-dependant damage criteria for the composite layers. The subroutine was implemented into the commercial finite element software ABAQUS/Explicit to simulate the deformation and failure of FMLs. Agreement between the predictions of the finite element models and the experimental data was good across the range of configurations. Ballistic limit of those FMLs was obtained from both the experimental tests and numerical approaches

Outsourcing CO2 within China

Recent studies have shown that the high standard of living enjoyed by people in the richest countries often comes at the expense of CO2 emissions produced with technologies of low efficiency in less affluent, developing countries. Less apparent is that this relationship between developed and developing can exist within a single country’s borders, with rich regions consuming and exporting high-value goods and services that depend upon production of low-cost and emission-intensive goods and services from poorer regions in the same country. As the world’s largest emitter of CO2, China is a prominent and important example, struggling to balance rapid economic growth and environmental sustainability across provinces that are in very different stages of development. In this study, we track CO2 emissions embodied in products traded among Chinese provinces and internationally. We find that 57% of China’s emissions are related to goods that are consumed outside of the province where they are produced. For instance, up to 80% of the emissions related to goods consumed in the highly developed coastal provinces are imported from less developed provinces in central and western China where many low–value-added but high–carbon-intensive goods are produced. Without policy attention to this sort of interprovincial carbon leakage, the less developed provinces will struggle to meet their emissions intensity targets, whereas the more developed provinces might achieve their own targets by further outsourcing. Consumption-based accounting of emissions can thus inform effective and equitable climate policy within China

Universal Tomonaga-Luttinger liquid phases in one-dimensional strongly attractive SU(N) fermionic cold atoms

A simple set of algebraic equations is derived for the exact low-temperature thermodynamics of one-dimensional multi-component strongly attractive fermionic atoms with enlarged SU(N) spin symmetry and Zeeman splitting. Universal multi-component Tomonaga-Luttinger liquid (TLL) phases are thus determined. For linear Zeeman splitting, the physics of the gapless phase at low temperatures belongs to the universality class of a two-component asymmetric TLL corresponding to spin-neutral N-atom composites and spin-(N-1)/2 single atoms. The equation of states is also obtained to open up the study of multi-component TLL phases in 1D systems of N-component Fermi gases with population imbalance.Comment: 12 pages, 3 figure

Two problems related to prescribed curvature measures

Existence of convex body with prescribed generalized curvature measures is discussed, this result is obtained by making use of Guan-Li-Li's innovative techniques. In surprise, that methods has also brought us to promote Ivochkina's $C^2$ estimates for prescribed curvature equation in \cite{I1, I}.Comment: 12 pages, Corrected typo

Impacts of Water Loop Management on Simultaneous Heating and Cooling in Coupled Control Air Handling Units

The impacts of the water loop management on the heating and cooling energy consumption are investigated by using model simulation. The simulation results show that the total thermal energy consumption can be increased by 24% for a typical AHU in San Antonio, Texas when the differential pressure is increased from 7 psi to 21 psi for both chilled water and hot water loops. It appears that significant amounts of energy consumption can be reduced by improving the differential pressure of water loops. This paper presents the system model, methods, and the results

Exactly solvable models and ultracold Fermi gases

Exactly solvable models of ultracold Fermi gases are reviewed via their thermodynamic Bethe Ansatz solution. Analytical and numerical results are obtained for the thermodynamics and ground state properties of two- and three-component one-dimensional attractive fermions with population imbalance. New results for the universal finite temperature corrections are given for the two-component model. For the three-component model, numerical solution of the dressed energy equations confirm that the analytical expressions for the critical fields and the resulting phase diagrams at zero temperature are highly accurate in the strong coupling regime. The results provide a precise description of the quantum phases and universal thermodynamics which are applicable to experiments with cold fermionic atoms confined to one-dimensional tubes.Comment: based on an invited talk at Statphys24, Cairns (Australia) 2010. 16 pages, 6 figure