The curvature-induced gauge potential and the geometric momentum for a particle on a hypersphere

For a particle that is constrained to freely move on a hypersurface, the curvature of the surface can induce a gauge potential; and for a particle on the hypersphere, the gauge potential derived from the \textit{generalized angular momentum algebra }on it has been known long before (J. Math. Phys. \textbf{34}(1993)2827). We demonstrate that the momentum for the particle on the hyperspherecan be the geometric one which obey commutation relations $\left[ p_{i},p_{j}\right] =-i\hbar J_{ij}/r^{2}$, in which $\hbar$ is the Planck's constant, and $p_{i}$ ($i=1,2,3,...N$) symbolizes the $i-$th component of the geometric momentum, and $J_{ij}$ specifies the $ij-$th component of the angular momentum containing the spin-curvature coupling, and $r$ denotes the radius of the $N-1$ dimensional hypersphere.Comment: 6 pages, no figur

Mathematical Modelling of a Brain Tumour Initiation and Early Development: A Coupled Model of Glioblastoma Growth, Pre-Existing Vessel Co-Option, Angiogenesis and Blood Perfusion

We propose a coupled mathematical modelling system to investigate glioblastoma growth in response to dynamic changes in chemical and haemodynamic microenvironments caused by pre-existing vessel co-option, remodelling, collapse and angiogenesis. A typical tree-like architecture network with different orders for vessel diameter is designed to model pre-existing vasculature in host tissue. The chemical substances including oxygen, vascular endothelial growth factor, extra-cellular matrix and matrix degradation enzymes are alculated based on the haemodynamic environment which is obtained by coupled modelling of intravascular blood flow with interstitial fluid flow. The haemodynamic changes, including vessel diameter and permeability, are introduced to reflect a series of pathological characteristics of abnormal tumour vessels including vessel dilation, leakage, angiogenesis, regression and collapse. Migrating cells are included as a new phenotype to describe the migration behaviour of malignant tumour cells. The simulation focuses on the avascular phase of tumour development and stops at an early phase of angiogenesis. The model is able to demonstrate the main features of glioblastoma growth in this phase such as the formation of pseudopalisades, cell migration along the host vessels, the pre-existing vasculature co-option, angiogenesis and remodelling. The model also enables us to examine the influence of initial conditions and local environment on the early phase of glioblastoma growth.The authors like to thank Mr. Justin Halls for his kind help on manuscript preparation. This research is supported by the National Basic Research Program of China (973 Program) (No. 2013CB733800), the National Nature Science Foundation of China (No. 11302050, No. 11272091), the Nature Science Foundation of Jiangsu Province (No. BK20130593)

A nonlinear equation system approach to the dynamic stochastic user equilibrium simultaneous route and departure time choice problem

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A knowledge-based ideation approach for bio-inspired design

Bio-inspired design (BID) involves generating innovative ideas for engineering design by drawing inspiration from natural biological phenomena and systems, using a form of design-by-analogy. Despite its many successes, BID approaches encounter research challenges including unstructured data and existing models that hinder comprehension and processing, limited focus on finding biological knowledge compared to defined problems, and insufficient guidance of the ideation process with algorithms. This paper proposes a knowledge-based approach to address the challenges. The approach involves transforming unstructured data into structured knowledge, including information about natural sources, their benefits, and applications. The structured knowledge is then used to construct a semantic network, enabling designers to retrieve information for BID in two ways. Furthermore, a three-step ideation method is developed to encourage divergent thinking and explore additional potential solutions by drawing inspiration and utilizing knowledge. The knowledge-based BID approach is implemented as a tool and design cases are conducted to illustrate the process of applying this tool for BID

Elliptic flow of ϕ\phi meson and strange quark collectivity at RHIC

Based on A Multi-Phase Transport (AMPT) model, we have studied the elliptic flow $v_{2}$ of $\phi$ mesons from reconstructed $K^{+}K^{-}$ decay channel at the top Relativistic Heavy Ion Collider energy at Brookhaven National Laboratory. The dependences of $v_{2}$ on transverse momentum $p_T$ and collision centrality are presented and the rescattering effect of $\phi$ mesons in the hadronic phase is also investigated. The results show that experimental measurement of $v_{2}$ for $\phi$ mesons can retain the early collision information before $\phi$ decays and that the $\phi$ $v_2$ value obeys the constituent quark number scaling which has been observed for other mesons and baryons. Our study indicates that the $\phi$ $v_2$ mostly reflects partonic level collectivity developed during the early stage of the nucleus-nucleus collision and the strange and light up/down quarks have developed similar angular anistropy properties at the hadronization.Comment: 5 pages and 5 figures; accepted by Physical Review

Echoes of charged black-bounce spacetimes

In present work, the evolution of scalar field and electromagnetic field under the background of the charged black-bounce spacetimes are investigated, and we obtain an obvious echoes signal which appropriately reports the properties of the charged black-bounce spacetimes and disclose the physical reasons behind such phenomena. Furthermore, by studying the quasinormal ringdown, we analyze the three states of the charged black-bounce spacetimes in detail, our results show that the echoes signal only appears when $(\rvert {Q}\rvert \le m)$ and $(\rvert {l}\rvert > m+ \sqrt{m ^{2}-Q^{2} })$ in this spacetime, while when the parameters demand $(\rvert {Q}\rvert>m)$, the echoes signal will be transformed into a quasinormal ringdown of the two-way traversable wormhole, and the charged black-bounce is a regular black hole with normal horizons by requiring $(\rvert {Q}\rvert \le m)$ and $(\rvert {l}\rvert < m- \sqrt{m ^{2}-Q^{2} })$