Chaotic behaviour of hyperbolic dynamical systems in a Banach space

In this thesis, C2 maps and semi-flows on separable Banach spaces with invariant ergodic Borel probability measure are considered. By assuming the absence of zero Lyapunov exponents for the discrete case and at most one central direction for the continuous case respectively, there exist periodic orbits and horseshoes. Katok originally established these results for diffeomorphisms on compact manifolds in [12]. In 2011 and 2012, Lian and Young had extended these results for maps and semiflows on infinite dimensional Hilbert space in [17] and [18] respectively. In these three papers, they all have inner product structure of tangent space of each point in the domain. In order to overcome the impact of the absence of inner product, two tools were reconstructed under Banach space setting. A measurable Lyapunov chart was reestablished, the invariant manifolds theory was reconstructed to fit the setting of Banach spaces with changing norms along orbits. Using these tools, the existence of periodic orbits and horseshoes for maps and semiflows on Banach spaces was proved.</p

Chaotic behaviour of hyperbolic dynamical systems in a Banach space

Chaotic behaviour of hyperbolic dynamical systems in a Banach spac

Molecular Dynamics Simulation of Conformational Transition and Frictional Performance Modulation of Densely Packed Self-Assembled Monolayers Based on Electrostatic Stimulation

Self-assembled monolayers (SAMs) terminated with functional end groups such as polyethylene glycols (PEG) have attracted considerable attention because of their unique and flexible structure that exhibits conformational transition under electrostatic stimulation. Molecular dynamics simulations are used to investigate the conformational transition and associated modulation of frictional performance of densely packed PEG-terminated SAMs subjected to electrical field stimulation. Previously reported empirical potentials and atomic charges were used to model the intrachain bonds and electrostatic and interchain interactions. Simulation results indicate that significant conformational transition is generated because of the electrostatic forces. Under positive electrical fields, PEG groups are compressed and twisted into the helical form, “gauche” state, whereas under negative electrical fields, PEG groups are stretched into the straight form, “all-trans” state. Such conformational transition may lead to substantial alteration of frictional response upon SAMs. By shallow penetration and sliding using a repulsive indenter, the SAMs under positive electrical fields exhibit a level of frictional response that is comparatively lower than those under zero and negative potentials, which may be attributed to reduced interchain space for deformation, limited conformational transition, and less energy absorption. The simulation results demonstrate that with appropriate selection of functional end groups attached to SAM backbone chains it is possible to modulate frictional performance of densely packed SAMs via electrostatic stimuli

Identification and characterization of key residues in Zika virus envelope protein for virus assembly and entry

Zika virus (ZIKV), a family member in the Flavivirus genus, has re-emerged as a global public health concern. The envelope (E) proteins of flaviviruses play a dual role in viral assembly and entry. To identify the key residues of E in virus entry, we generated a ZIKV trans-complemented particle (ZIKVTCP) system, in which a subgenomic reporter replicon was packaged by trans-complementation with expression of CprME. We performed mutagenesis studies of the loop regions that protrude from the surface of the virion in the E ectodomains (DI, DII, DIII). Most mutated ZIKVTCPs exhibited deficient egress. Mutations in DII and in the hinge region of DI and DIII affected prM expression. With a bioorthogonal system, photocrosslinking experiments identified crosslinked intracellular E trimers and demonstrated that egress-deficient mutants in DIII impaired E trimerization. Of these mutants, an E-trimerization-dead mutation D389A that nears the E-E interface between two neighbouring spikes in the immature virion completely abolished viral egress. Several mutations abolished ZIKVTCPs’ entry, without severely affecting viral egress. Further virus binding experiments demonstrated a deficiency of the mutated ZIKVTCPs in virus attachment. Strikingly, synthesized peptide containing residues of two mutants (268-273aa in DII) could bind to host cells and significantly compete for viral attachment and interfere with viral infection, suggesting an important role of these resides in virus entry. Our findings uncovered the requirement for DIII mediated-E trimerization in viral egress, and discovered a key residue group in DII that participates in virus entry.</p

Relationship and comparison between the Monge–Ampère equation and the transport of intensity equation for phase retrieval

Phase retrieval from two or more irradiance (or intensity) distributions is a fundamental and important inverse problem in optics. One of the most widely used phase retrieval methods is based on the transport of intensity equation (TIE). Although simple in form, the TIE method suffers the problems of weak paraxial and weak defocus approximations, etc. The phase retrieval problem can be more generally formulated as a Monge–Ampère equation (MAE) in the framework of geometrical optics. Here, we first prove that the TIE can be derived from MAE when applying paraxial and weak defocus approximations. We then verify through numerical experiments that MAE could sufficiently reduce the phase recovery errors compared with TIE

Chitinous Bioplastic Enabled by Noncovalent Assembly

Natural polymeric-based bioplastics usually lack good mechanical or processing performance. It is still challenging to achieve simultaneous improvement for these two usual trade-off features. Here, we demonstrate a full noncovalent mediated self-assembly design for simultaneously improving the chitinous bioplastic processing and mechanical properties via plane hot-pressing. Tannic acid (TA) is chosen as the noncovalent mediator to (i) increase the noncovalent cross-link intensity for obtaining the tough noncovalent network and (ii) afford the dynamic noncovalent cross-links to enable the mobility of chitin molecular chains for benefiting chitinous bioplastic nanostructure rearrangement during the shaping procedure. The multiple noncovalent mediated network (chitin–TA and chitin–chitin cross-links) and the pressure-induced orientation nanofibers structure endow the chitinous bioplastics with robust mechanical properties. The relatively weak chitin–TA noncovalent interactions serve as water mediation switches to enhance the molecular mobility for endowing the chitin/TA bioplastic with hydroplastic processing properties, rendering them readily programmable into versatile 2D/3D shapes. Moreover, the fully natural resourced chitinous bioplastic exhibits superior weld, solvent resistance, and biodegradability, enabling the potential for diverse applications. The full physical cross-linking mechanism highlights an effective design concept for balancing the trade-off of the mechanical properties and processability for the polymeric materials

MLR factors associated with treatment outcome of women in Tigray and Zigong January 2007 December 2016 N = 2084 and N = 4047.

MLR factors associated with treatment outcome of women in Tigray and Zigong January 2007 December 2016 N = 2084 and N = 4047.</p

Trend of women treatment success in Tigray and Zigong January 2007–December 2016 N = 2084 and N = 4047.

Trend of women treatment success in Tigray and Zigong January 2007–December 2016 N = 2084 and N = 4047.</p

Funnel plot to assess for evidence of publication bias.

Oblique line represented the pseudo 95% confidence interval. Circles represented the included studies.</p