Two dimensional dynamical systems which admit Lie and Noether symmetries

We prove two theorems which relate the Lie point symmetries and the Noether symmetries of a dynamical system moving in a Riemannian space with the special projective group and the homothetic group of the space respectively. The theorems are applied to classify the two dimensional Newtonian dynamical systems, which admit a Lie point/Noether symmetry. Two cases are considered, the non-conservative and the conservative forces. The use of the results is demonstrated for the Kepler - Ermakov system, which in general is non-conservative and for potentials similar to the H\`enon Heiles potential. Finally it is shown that in a FRW background with no matter present, the only scalar cosmological model which is integrable is the one for which 3-space is flat and the potential function of the scalar field is exponential. It is important to note that in all applications the generators of the symmetry vectors are found by reading the appropriate entry in the relevant tables.Comment: 25 pages, 17 table

The nonlinear Schroedinger equation for the delta-comb potential: quasi-classical chaos and bifurcations of periodic stationary solutions

The nonlinear Schroedinger equation is studied for a periodic sequence of delta-potentials (a delta-comb) or narrow Gaussian potentials. For the delta-comb the time-independent nonlinear Schroedinger equation can be solved analytically in terms of Jacobi elliptic functions and thus provides useful insight into the features of nonlinear stationary states of periodic potentials. Phenomena well-known from classical chaos are found, such as a bifurcation of periodic stationary states and a transition to spatial chaos. The relation of new features of nonlinear Bloch bands, such as looped and period doubled bands, are analyzed in detail. An analytic expression for the critical nonlinearity for the emergence of looped bands is derived. The results for the delta-comb are generalized to a more realistic potential consisting of a periodic sequence of narrow Gaussian peaks and the dynamical stability of periodic solutions in a Gaussian comb is discussed.Comment: Enhanced and revised version, to appear in J. Nonlin. Math. Phy

Squeezed States of the Generalized Minimum Uncertainty State for the Caldirola-Kanai Hamiltonian

We show that the ground state of the well-known pseudo-stationary states for the Caldirola-Kanai Hamiltonian is a generalized minimum uncertainty state, which has the minimum allowed uncertainty $\Delta q \Delta p = \hbar \sigma_0/2$, where $\sigma_0 (\geq 1)$ is a constant depending on the damping factor and natural frequency. The most general symmetric Gaussian states are obtained as the one-parameter squeezed states of the pseudo-stationary ground state. It is further shown that the coherent states of the pseudo-stationary ground state constitute another class of the generalized minimum uncertainty states.Comment: RevTex4, 9 pages, no fingure; to be published in Journal of Physics

sPLA2-V inhibits EPCR anticoagulant and antiapoptotic properties by accommodating lysophosphatidylcholine or PAF in the hydrophobic groove

The endothelial protein C receptor (EPCR) plays an important role in cardiovascular disease by binding protein C/activated protein C (APC). EPCR structure contains a hydrophobic groove filled with an unknown phospholipid needed to perform its function. It has not been established whether lipid exchange takes place in EPCR as a regulatory mechanism of its activity. Our objective was to identify this phospholipid and to explore the possibility of lipid exchange as a regulatory mechanism of EPCR activity driven by the endothelially expressed secretory group V phospholipase A2 (sPLA2-V). We identified phosphatidylcholine (PCh) as the major phospholipid bound to human soluble EPCR (sEPCR). PCh in EPCR could be exchanged for lysophosphatidylcholine (lysoPCh) and platelet activating factor (PAF). Remarkably, lysoPCh and PAF impaired the protein C binding ability of sEPCR. Inhibition of sPLA2-V, responsible for lysoPCh and PAF generation, improved APC binding to endothelial cells. EPCR-dependent protein C activation and APC antiapoptotic effect were thus significantly enhanced. In contrast, endothelial cell supplementation with sPLA2-V inhibited both APC generation and its antiapoptotic effects. We conclude that APC generation and function can be modulated by changes in phospholipid occupancy of its endothelial cell receptor

Understanding consumer demand for new transport technologies and services, and implications for the future of mobility

The transport sector is witnessing unprecedented levels of disruption. Privately owned cars that operate on internal combustion engines have been the dominant modes of passenger transport for much of the last century. However, recent advances in transport technologies and services, such as the development of autonomous vehicles, the emergence of shared mobility services, and the commercialization of alternative fuel vehicle technologies, promise to revolutionise how humans travel. The implications are profound: some have predicted the end of private car dependent Western societies, others have portended greater suburbanization than has ever been observed before. If transport systems are to fulfil current and future needs of different subpopulations, and satisfy short and long-term societal objectives, it is imperative that we comprehend the many factors that shape individual behaviour. This chapter introduces the technologies and services most likely to disrupt prevailing practices in the transport sector. We review past studies that have examined current and future demand for these new technologies and services, and their likely short and long-term impacts on extant mobility patterns. We conclude with a summary of what these new technologies and services might mean for the future of mobility.Comment: 15 pages, 0 figures, book chapte

Distinguishing Various Models of the 125 GeV Boson in Vector Boson Fusion

The hint of a new particle around 125 GeV at the LHC through the decay modes of diphoton and a number of others may point to quite a number of possibilities. While at the LHC the dominant production mechanism for the Higgs boson of the standard model and some other extensions is via the gluon fusion process, the alternative vector boson fusion is more sensitive to electroweak symmetry breaking through the gauge-Higgs couplings and therefore can be used to probe for models beyond the standard model. In this work, using the well known dijet-tagging technique to single out the vector boson fusion mechanism, we investigate its capability to discriminate a number of models that have been suggested to give an enhanced inclusive diphoton production rate, including the standard model Higgs boson, fermiophobic Higgs boson, Randall-Sundrum radion, inert-Higgs-doublet model, two-Higgs-doublet model, and the MSSM. The rates in vector-boson fusion can give more information of the underlying models to help distinguishing among the models.Comment: 31 pages, 3 figures; in this version some wordings are change

Shopping centre siting and modal choice in Belgium: a destination based analysis

Although modal split is only one of the elements considered in decision-making on new shopping malls, it remarkably often arises in arguments of both proponents and opponents. Today, this is also the case in the debate on the planned development of three major shopping malls in Belgium. Inspired by such debates, the present study focuses on the impact of the location of shopping centres on the travel mode choice of the customers. Our hypothesis is that destination-based variables such as embeddedness in the urban fabric, accessibility and mall size influence the travel mode choice of the visitors. Based on modal split data and location characteristics of seventeen existing shopping centres in Belgium, we develop a model for a more sustainable siting policy. The results show a major influence of the location of the shopping centre in relation to the urban form, and of the size of the mall. Shopping centres that are part of a dense urban fabric, measured through population density, are less car dependent. Smaller sites will attract more cyclists and pedestrians. Interestingly, our results deviate significantly from the figures that have been put forward in public debates on the shopping mall issue in Belgium

Higgs decay to dark matter in low energy SUSY: is it detectable at the LHC ?

Due to the limited statistics so far accumulated in the Higgs boson search at the LHC, the Higgs boson property has not yet been tightly constrained and it is still allowed for the Higgs boson to decay invisibly to dark matter with a sizable branching ratio. In this work, we examine the Higgs decay to neutralino dark matter in low energy SUSY by considering three different models: the minimal supersymmetric standard model (MSSM), the next-to-minimal supersymmetric standard models (NMSSM) and the nearly minimal supersymmetric standard model (nMSSM). Under current experimental constraints at 2-sigma level (including the muon g-2 and the dark matter relic density), we scan over the parameter space of each model. Then in the allowed parameter space we calculate the branching ratio of the SM-like Higgs decay to neutralino dark matter and examine its observability at the LHC by considering three production channels: the weak boson fusion VV->h, the associated production with a Z-boson pp->hZ+X or a pair of top quarks pp->htt_bar+X. We find that in the MSSM such a decay is far below the detectable level; while in both the NMSSM and nMSSM the decay branching ratio can be large enough to be observable at the LHC.Comment: Version in JHE

Inflationary Perturbations: the Cosmological Schwinger Effect

This pedagogical review aims at presenting the fundamental aspects of the theory of inflationary cosmological perturbations of quantum-mechanical origin. The analogy with the well-known Schwinger effect is discussed in detail and a systematic comparison of the two physical phenomena is carried out. In particular, it is demonstrated that the two underlying formalisms differ only up to an irrelevant canonical transformation. Hence, the basic physical mechanisms at play are similar in both cases and can be reduced to the quantization of a parametric oscillator leading to particle creation due to the interaction with a classical source: pair production in vacuum is therefore equivalent to the appearance of a growing mode for the cosmological fluctuations. The only difference lies in the nature of the source: an electric field in the case of the Schwinger effect and the gravitational field in the case of inflationary perturbations. Although, in the laboratory, it is notoriously difficult to produce an electric field such that pairs extracted from the vacuum can be detected, the gravitational field in the early universe can be strong enough to lead to observable effects that ultimately reveal themselves as temperature fluctuations in the Cosmic Microwave Background. Finally, the question of how quantum cosmological perturbations can be considered as classical is discussed at the end of the article.Comment: 49 pages, 6 figures, to appear in a LNP volume "Inflationary Cosmology