Phase separation in optical lattices in a spin-dependent external potential

We investigate the phase separation in one-dimensional Fermi gases on optical lattices. The density distributions and the magnetization are calculated by means of density-matrix renormalization method. The phase separation between spin-up and spin-down atoms is induced by the interplay of the spin-dependent harmonic confinement and the strong repulsive interaction between intercomponent fermions. We find the existence of a critical repulsive interaction strength above which the phase separation evolves. By increasing the trap imbalance, the composite phase of Mott-insulating core is changed into the one of ferromagnetic insulating core, which is incompressible and originates from the Pauli exclusion principle.Comment: 6 pages, 7 figure

On the Triality Theory for a Quartic Polynomial Optimization Problem

This paper presents a detailed proof of the triality theorem for a class of fourth-order polynomial optimization problems. The method is based on linear algebra but it solves an open problem on the double-min duality left in 2003. Results show that the triality theory holds strongly in a tri-duality form if the primal problem and its canonical dual have the same dimension; otherwise, both the canonical min-max duality and the double-max duality still hold strongly, but the double-min duality holds weakly in a symmetrical form. Four numerical examples are presented to illustrate that this theory can be used to identify not only the global minimum, but also the largest local minimum and local maximum.Comment: 16 pages, 1 figure; J. Industrial and Management Optimization, 2011. arXiv admin note: substantial text overlap with arXiv:1104.297

Public Versus Private Mobility for the Poor: Transit Improvements Versus Increased Car Ownership in the Sacramento Region, MTI Research Report 08-02

Whether to aid welfare recipients in overcoming transportation barriers with increased car ownership or better transit became an issue after the Personal Responsibility and Work Opportunity Reconciliation Act of 1996 was signed into law. Empirical studies pointed out that welfare recipients owning a car had a high probability of moving from welfare to work. In this study, the authors examined the impacts of car ownership promotion versus transit improvements on job accessibility, work trips, and traveler´s economic welfare by running a travel demand model adopted by the Sacramento Area Council of Governments (SACOG). In the car scenario, the zero-car households who were assigned a car had higher job accessibility and larger traveler benefits than in the Base Case scenario. The other households had lower traveler benefits, compared to the Base Case, due to slight increases in congestion. In the transit scenario, all households had gains in traveler benefits and the households without a car gained more than those with a car. The households without a car gained more in traveler benefits in the transit scenario than in the car scenario. The total gain in traveler benefits was higher in the transit scenario. In both scenarios, the changes in total travel time, congestion, and vehicle miles traveled (VMT) were small, but mode shares changed substantially

Interacting cells driving the evolution of multicellular life cycles

Author summary Multicellular organisms are ubiquitous. But how did the first multicellular organisms arise? It is typically argued that this occurred due to benefits coming from interactions between cells. One example of such interactions is the division of labour. For instance, colonial cyanobacteria delegate photosynthesis and nitrogen fixation to different cells within the colony. In this way, the colony gains a growth advantage over unicellular cyanobacteria. However, not all cell interactions favour multicellular life. Cheater cells residing in a colony without any contribution will outgrow other cells. Then, the growing burden of cheaters may eventually destroy the colony. Here, we ask what kinds of interactions promote the evolution of multicellularity? We investigated all interactions captured by pairwise games and for each of them, we look for the evolutionarily optimal life cycle: How big should the colony grow and how should it split into offspring cells or colonies? We found that multicellularity can evolve with interactions far beyond cooperation or division of labour scenarios. More surprisingly, most of the life cycles found fall into either of two categories: A parent colony splits into two multicellular parts, or it splits into multiple independent cells