L1L^1 semigroup generation for Fokker-Planck operators associated with general L\'evy driven SDEs

We prove a new generation result in $L^1$ for a large class of non-local operators with non-degenerate local terms. This class contains the operators appearing in Fokker-Planck or Kolmogorov forward equations associated with L\'evy driven SDEs, i.e. the adjoint operators of the infinitesimal generators of these SDEs. As a byproduct, we also obtain a new elliptic regularity result of independent interest. The main novelty in this paper is that we can consider very general L\'evy operators, including state-space depending coefficients with linear growth and general L\'evy measures which can be singular and have fat tails

Theoretical studies of photoinduced dynamics and topological states in materials with strong electron-lattice couplings

First, we study the nonequilibrium dynamics of photoinduced phase transitions in charge ordered (CO) systems with a strong electron-lattice interaction and analyze the interplay between electrons, periodic lattice distortions, and a phonon thermal reservoir. Simulations based on a tight-binding Hamiltonian and Boltzmann equations reveal partially decoupled oscillations of the electronic order parameter and the periodic lattice distortion during CO melting, which becomes more energy efficient with lower photon energy. The cooling rate of the electron system correlates with the CO gap dynamics, responsible for an order of magnitude decrease of the cooling rate upon the gap reopening. The work also find that the time-dependent frequency of coherent oscillation reflects the dynamics of the energy landscape, such as transition between single-well and double-well, which sensitively depends on the photon energy and the pump fluence. The results demonstrate the intricate nonequilibrium dynamics in CO materials. Second, a model for two-dimensional electronic, photonic, and mechanical metamaterial systems is presented, which has flat one-dimensional zero-mode energy bands and stable localized states of a topological origin confined within twin boundaries, antiphase boundaries, and at open edges. Topological origins of these flat bands are analyzed for an electronic system as a specific example, using a two-dimensional extension of the Su-Schrieffer-Heeger Hamiltonian with alternating shift of the chains. It is demonstrated that the slow group velocities of the localized flat band states are sensitively controlled by the distance between the boundaries and the propagation can be guided through designed paths of these boundaries. We also discuss how to realize this model in metamaterials. Third, the study of topological mechanical metamaterials system made of 1D or 2D arrays of spinners, as an experimental realization of electron models in the second part. Compared with experimental data for 1D case and makes prediction for 2D case of ribbon with open edges. And also show how they slow group velocity of localized edge modes depend on the width of the ribbon

STEREOTYPE FILTER: A DIGITAL INTERFACE TO FOSTER CULTURAL AWARENESS

With the development of economic globalization, more and more people are immersed in a cross-cultural community. United States hosts the largest number of international students in the world. The cultural diversity of American college campuses makes them full of opportunity to learn about and from each other. However, huge portion of international students experience American colleges as culturally challenging. The cultural identities of international students are often stereotyped or misunderstood, causing barriers between students. Online questionnaires and analyzing related literatures suggests that the problem of stereotyping is a broad issue that is worth studying. Interaction design is a possible solution to help connect students on campus. However, as a communication medium, its application to solve the stereotype problem is still very limited. Therefore, the objective of this thesis is to explore how interaction design can foster cultural awareness and address stereotyping on college campuses. The “Stereotype Filter” was designed by developing a digital interface. Testing the prototypes of the design showed that the design effectively promotes cultural understanding among people of various backgrounds. It suggests that interaction design is a possible intervention to the cultural barriers that international students experience

Antioxidant activities of polyphenols extracted from Perilla frutescens varieties

Various cultivars of Perilla frutescens (L.) (var. crispa and var. frutescens) Britt. were harvested in China and Japan. They were easily differentiated on the basis of their foliage color, that varied from red to green. Water extracts of dried plants were investigated for their antioxidant activity (AA) and their polyphenolic compounds compared. Among them, cinnamic acid derivatives (coumaroyl tartaric acid, caffeic acid and rosmarinic acid), flavonoids (apigenin 7-O-caffeoylglucoside, scutellarein 7-Odiglucuronide, luteolin 7-O-diglucuronide, apigenin 7-O-diglucuronide, luteolin 7-Oglucuronide, and scutellarein 7-O-glucuronide) and anthocyanins (mainly cis-shisonin, shisonin, malonylshisonin and cyanidin 3-O-(E)-caffeoylglucoside-5-O-malonylglucoside) were quantified. AA assays are based on the inhibition of the free radical 2,2-diphenyl-1- picrylhydrazyl (DPPH). The DPPH radical scavenging activity was calculated as Trolox® [(±)-6-hydroxy-2,5,7,8-tetramethylchromane-2-carboxylic acid] equivalent antioxidant capacity (TEAC). The mean amount of total phenolics of the water extracts (4-29 ?mol/100 mL) and the TEAC value calculated (23-167 ?mol TE/100 mL) confirmed the high antioxidant activity of these leaf water extracts. These results were highly correlated within some o-dihydroxylated polyphenolic compounds and AA. (Résumé d'auteur

Hidden vortices in a Bose-Einstein condensate in a rotating double-well potential

We study vortex formation in a Bose-Einstein condensate in a rotating double-well potential. Besides the ordinary quantized vortices and elusive ghost vortices, "hidden" vortices are found distributing along the central barrier. These hidden vortices are invisible like ghost vortex but carry angular momentum. Moreover, their core size is not given by the healing length, but is strongly influenced by the external potential. We find that the Feynman's rule can be well satisfied only after including the hidden vortices. There is no critical rotating frequency for the formation of hidden vortex while there is one for the formation of ordinary visible vortices. Hidden vortices can be revealed in the free expansion of the Bose-Einstein condensates. In addition, the hidden vortices in a Bose-Einstein condensate can appear in other external potentials, such as a rotating anisotropic toroidal trap.Comment: 6pages,5figure

Stationary states and quantum quench dynamics of Bose-Einstein condensates in a double-well potential

We consider the properties of stationary states and the dynamics of Bose-Einstein condensates (BECs) in a double-well (DW) potential with pair tunneling by using a full quantum-mechanical treatment. Furthermore, we study the quantum quench dynamics of the DW system subjected to a sudden change of the Peierls phase. It is shown that strong pair tunneling evidently influences the energy spectrum structure of the stationary states. For relatively weak repulsive interatomic interactions, the dynamics of the DW system with a maximal initial population difference evolves from Josephson oscillations to quantum self-trapping as one increases the pair tunneling strength, while for large repulsion the strong pair tunneling inhibits the quantum self-trapping. In the case of attractive interatomic interactions, strong pair tunneling tends to destroy the Josephson oscillations and quantum self-trapping, and the system eventually enters a symmetric regime of zero population difference. Finally, the effect of the Peierls phase on the quantum quench dynamics of the system is analyzed and discussed. These new features are remarkably different from the usual dynamical behaviors of a BEC in a DW potential.Comment: 9 pages,7 figures,accepted for publication in Journal of Physics