Exotic Quantum States for Charmed Baryons at Finite Temperature

The significantly screened heavy-quark potential in hot medium provides the possibility to study exotic quantum states of three-heavy-quark systems. By solving the Schr\"odinger equation for a three-charm-quark system at finite temperature, we found that, there exist Borromean states which might be realized in high energy nuclear collisions, and the binding energies of the system satisfy precisely the scaling law for Efimov states in the resonance limit

Approximate Set Union Via Approximate Randomization

We develop an randomized approximation algorithm for the size of set union problem \arrowvert A_1\cup A_2\cup...\cup A_m\arrowvert, which given a list of sets $A_1,...,A_m$ with approximate set size $m_i$ for $A_i$ with $m_i\in \left((1-\beta_L)|A_i|, (1+\beta_R)|A_i|\right)$, and biased random generators with Prob(x=\randomElm(A_i))\in \left[{1-\alpha_L\over |A_i|},{1+\alpha_R\over |A_i|}\right] for each input set $A_i$ and element $x\in A_i,$ where $i=1, 2, ..., m$. The approximation ratio for \arrowvert A_1\cup A_2\cup...\cup A_m\arrowvert is in the range $[(1-\epsilon)(1-\alpha_L)(1-\beta_L), (1+\epsilon)(1+\alpha_R)(1+\beta_R)]$ for any $\epsilon\in (0,1)$, where $\alpha_L, \alpha_R, \beta_L,\beta_R\in (0,1)$. The complexity of the algorithm is measured by both time complexity, and round complexity. The algorithm is allowed to make multiple membership queries and get random elements from the input sets in one round. Our algorithm makes adaptive accesses to input sets with multiple rounds. Our algorithm gives an approximation scheme with O(\setCount\cdot(\log \setCount)^{O(1)}) running time and $O(\log m)$ rounds, where $m$ is the number of sets. Our algorithm can handle input sets that can generate random elements with bias, and its approximation ratio depends on the bias. Our algorithm gives a flexible tradeoff with time complexity O\left(\setCount^{1+\xi}\right) and round complexity $O\left({1\over \xi}\right)$ for any $\xi\in(0,1)$

Landau meets Newton: time translation symmetry breaking in classical mechanics

Every classical Newtonian mechanical system can be equipped with a nonstandard Hamiltonian structure, in which the Hamiltonian is the square of the canonical Hamiltonian up to a constant shift, and the Poisson bracket is nonlinear. In such a formalism, time translation symmetry can be spontaneously broken, provided the potential function becomes negative. A nice analogy between time translation symmetry breaking and the Landau theory of second order phase transitions is established, together with several example cases illustrating time translation breaking ground states. In particular, the $\Lambda$CDM model of FRW cosmology is reformulated as the time translation symmetry breaking ground states.Comment: 10 pages, 1 figure. V2: minor correction

Searching for Ξcc+\Xi_{cc}^+ in Relativistic Heavy Ion Collisions

We study the doubly charmed baryon $\Xi_{cc}^+$ in high energy nuclear collisions. We solve the three-body Schroedinger equation with relativistic correction and calculate the $\Xi_{cc}^+$ yield and transverse momentum distribution via coalescence mechanism. For $\Xi_{cc}^+$ production in central Pb+Pb collisions at LHC energy, the yield is extremely enhanced, and the production cross section per binary collision is one order of magnitude larger than that in p+p collisions. This indicates that, it is most probable to discover $\Xi_{cc}^+$ in heavy ion collisions and its discovery can be considered as a probe of the quark-luon plasma formation.Comment: 5 pages and 4 figure

Design of high-performance Triboelectric Nanogenerators (TENGs) for energy harvesting applications

The growing concerns around the long-term viability of the fossil fuel-based energy and its associated environmental cost are necessitating new research paradigms for energy generation and harvesting. An attractive and effective way to respond to the current energy crisis is through the harvesting of ambient mechanical energy from our environment. The conventional mechanical energy harvesting technologies are highly dependent on either the use of rare earth magnetic materials, high precision microfabrication techniques or composed of brittle materials, which are required to be driven at very high resonant frequencies, not frequently encountered beyond an industrial setting. Recently, triboelectric nanogenerators (TENG), based on the triboelectrification and electrostatic induction effects, have been demonstrated as a novel harvesting technique to collect and transform ambient mechanical energy into electric power. Unlike the other mechanical energy harvesters, the low-cost TENGs fabricated using commodity polymers and facile fabrication techniques, operate at low frequencies (1-10 Hz) with a high energy conversion efficiency. One of the key areas in TENG research is the enhancement of their electrical output to make them suitable for either making a self-powered system viable or powering small portable electronics directly. Except for the judicious use of tribo-materials or the tribo-layer architecture optimisation, the rest of the methods for enhancing the TENG output are reliant on expensive equipment and complicated processing, that undermine the advantages of TENGs and may not provide the required stability and reliability. This PhD study aims to establish novel strategies to enhance output performance of TENG by developing new tribo-materials and phenomena such as coupling of tribo-piezoelectric effects to showcase potential applications of the TENG devices. The research work conducted and the achievements are summarized as follows. Firstly, a novel output performance improvement strategy of utilising stress-induced polarization effect of the piezoelectric materials was proposed. An interfacial layer of piezoelectric zinc oxide (ZnO) nanosheets was deposited to generate additional piezoelectric charge induced by the vertical contact-separate generation cycle. This extra piezoelectric charge is injected into the upper polydimethylsiloxane (PDMS) tribo-negative layer for the enhancement of the surface charge density from ~110 μC.m-2 to ~225.7 μC.m-2. The introduction of the ZnO and Zn-Al:Layered Double Hydroxides (LDH), as charge injection layer and anionic clay, enhanced the instantaneous power output from ~11 W.m-2 to 47 W.m-2. Subsequently, based on a similar principle, a novel composite of lead-free perovskite, zinc stannate (ZnSnO3), and a fluoropolymer, poly(vinylidene fluoride), PVDF, was proposed for the stress-polarisation tribo-negative behaviour with a simplified structure. The PVDF-ZnSnO3 composite membranes were realised through a facile phase-inversion technique leading to higher piezoelectric constant (76.3 pm.V-1) and β-phase (72%) for the composites. When applied to the TENG devices, the PVDF-ZnSnO3 membranes allowed spontaneous polarisation effects which led to significant enhancement of the electrical outputs, with maximum peak-to-peak voltage and effective transferred current density of ~600 V and ~206 µC.m-2, respectively. The surface charge enhancement and distribution of the composite membrane were also probed and demonstrated through the electrostatic force (EFM) and piezoelectric force microscopy (PFM). To overcome the difficulty in processing of the currently known most tribo-negative material, polytetrafluoroethylene (PTFE), an emulsion electrospinning technique incorporating polyethene oxide (PEO) was introduced. It was observed that the subsequent thermal removal of PEO led to a significant degradation in the surface charge density of the obtained PTFE nanofibrous membranes, which was overcome using a facile negative ion-injection process. The measured electrical outputs, with a maximum peak-to-peak voltage output of ~900 V and charge density of ∼149 μC.m−2, demonstrated the excellent effect of the enhanced contact area to the improvement of the outputs. The work eliminates the demonstrated need for surface micro structuring using reactive ion etching of PTFE surfaces by introducing a relatively simple, costeffective, and environmentally friendly technique for fabricating fibrous fluoropolymers tribonegative layer for the energy harvesting applications. Finally, a unique mouldable material, aniline formaldehyde resin (AFR) was synthesised and characterised. The synthesised AFR, as a resinous polymer with significant amine (-NH2) groups acquires the most surface positive charge, is applied as a tribo-positive material. The heatpressed AFR thin-film based TENG was subsequently tested to demonstrate its outstanding performance serving as a tribo-positive layer compared to the Polyamide 6 (PA6) and polyethene oxide (PEO), as one of the most common used tribo-positive materials. In addition, a Kelvin Probe Force Microscopy (KPFM) was subsequently employed to study the surface potential of the produced AFR layer and the surface potential change of the contact layers during the energy generation cycles. All of the produced high-performance TENGs (power output ranging from 9 - 47 W.m-2) have the potential to be utilised further in enabling self-powered systems and can serve as a new alternative energy harvesting source of great significance