On the foundations of cancer modelling: selected topics, speculations, & perspectives

This paper presents a critical review of selected topics related to the modelling of cancer onset, evolution and growth, with the aim of illustrating, to a wide applied mathematical readership, some of the novel mathematical problems in the field. This review attempts to capture, from the appropriate literature, the main issues involved in the modelling of phenomena related to cancer dynamics at all scales which characterise this highly complex system: from the molecular scale up to that of tissue. The last part of the paper discusses the challenge of developing a mathematical biological theory of tumour onset and evolution

Geometry and the anomalous Hall effet in ferromagnets

The geometric ideas underlying the Berry phase and the modern viewpoint of Karplus and Luttinger's theory of the anomalous Hall effect are discussed in an elementary way. We briefly review recent Hall and Nernst experiments which support the dominant role of the KL velocity term in ferromagnets.Comment: 6 pages, 4 figures, conference proceedings, tutorial revie

Ratcheting Heat Flux against a Thermal Bias

Merely rocking the temperature in one heat bath can direct a steady heat flux from cold to hot against a non-zero thermal bias in stylized nonlinear lattice junctions that are sandwiched between two heat baths. Likewise, for an average zero-temperature difference between the two contacts a net, ratchet-like heat flux emerges. Computer simulations show that this very heat flux can be controlled and reversed by suitably tailoring the frequency ($\lesssim$ 100 MHz) of the alternating temperature field.Comment: 5 pages, 6 figure

NΩN\Omega and ΔΩ\Delta\Omega dibaryons in SU(3) chiral quark model

The binding energy of the six quark system with strangeness s=-3 is investigated under the chiral SU(3) constituent quark model in the framework of $RGM$. The calculations of the single $N\Omega$ channel with spin S=2 and the single $\Delta\Omega$ channel with spin S=3 are performed. The results show that both systems could be dibaryons and the interaction induced by the chiral field plays a very important role on forming bound states in the systems considered. The phase shifts and scattering lengths in corresponding channels are also given.Comment: LaTex file with 5 figure

Phase fluctuations versus Gaussian fluctuations in optimally-doped YBa2_2Cu3_3O7_7

We analyze recent torque measurements of the magnetization $M_d$ vs. magnetic field $H$ in optimally doped YBa$_2$Cu$_3$O$_{7-y}$ (OPT YBCO) to argue against a recent proposal by Rey et al that the magnetization results above $T_c$ are consistent with Gaussian fluctuations. We find that, despite its strong interlayer coupling, OPT YBCO displays an anomalous non-monotonic dependence of $M_d$ on $H$ which represents direct evidence for the locking of the pair wavefunction phase $\theta_n$ at $T_c$ and the subsequent unlocking by a relatively weak $H$. These unusual features characterize the unusual nature of the transition to the Meissner state in cuprate superconductors. They are absent in low-$T_c$ superconductors to our knowledge. We also stress the importance of the vortex liquid state, as well as the profiles of the melting field $H_m(T)$ and the upper critical field curve $H_{c2}(T)$ in the $T$-$H$ plane. Contrary to the claims of Rey et al, we show that the curves of the magnetization and the Nernst signal illustrate the inaccessibility of the $H_{c2}$ line near $T_c$. The prediction of the $H_{c2}$ line by Rey et al is shown to be invalid in OPT YBCO.Comment: 6 pages, 6 figure

The zero-energy state in graphene in a high magnetic field

The fate of the charge-neutral Dirac point in graphene in a high magnetic field $H$ has been investigated at low temperatures ($T\sim$ 0.3 K). In samples with small $V_0$ (the gate voltage needed to access the Dirac point), the resistance $R_0$ at the Dirac point diverges steeply with $H$, signalling a crossover to an insulating state in intense field. The approach to the insulating state is highly unusual. Despite the steep divergence in $R_0$, the profile of $R_0$ vs. $T$ in fixed $H$ saturates to a $T$-independent value below 2 K, consistent with charge carrying gapless excitations.Comment: 4 pages, 4 figures. Four new sub-figures have been added. Text expanded to discuss data from more sample

Consequences of Cadmium exposure on growth and reproduction across three generations of earthworm

Heavy metal pollution disturbs the soil ecosystem by negatively affecting soil fauna and flora. In term of biomass and activity Annelids are a very important part of the soil invertebrate community. They are one of the first organisms affected by heavy metal contamination in soil and as such are good model organisms for assessing soil contamination. The aim of this research is to observe how Cd impacts on health and reproduction in three consecutive generations of E. fetida. [...]falseOnlin

Symmetry breaking and manipulation of nonlinear optical modes in an asymmetric double-channel waveguide

We study light-beam propagation in a nonlinear coupler with an asymmetric double-channel waveguide and derive various analytical forms of optical modes. The results show that the symmetry-preserving modes in a symmetric double-channel waveguide are deformed due to the asymmetry of the two-channel waveguide, yet such a coupler supports the symmetry-breaking modes. The dispersion relations reveal that the system with self-focusing nonlinear response supports the degenerate modes, while for self-defocusingmedium the degenerate modes do not exist. Furthermore, nonlinear manipulation is investigated by launching optical modes supported in double-channel waveguide into a nonlinear uniform medium.Comment: 10 page

Study of 0-π\pi phase transition in hybrid superconductor-InSb nanowire quantum dot devices

Hybrid superconductor-semiconducting nanowire devices provide an ideal platform to investigating novel intragap bound states, such as the Andreev bound states (ABSs), Yu-Shiba-Rusinov (YSR) states, and the Majorana bound states. The competition between Kondo correlations and superconductivity in Josephson quantum dot (QD) devices results in two different ground states and the occurrence of a 0-$\pi$ quantum phase transition. Here we report on transport measurements on hybrid superconductor-InSb nanowire QD devices with different device geometries. We demonstrate a realization of continuous gate-tunable ABSs with both 0-type levels and $\pi$-type levels. This allow us to manipulate the transition between 0 and $\pi$ junction and explore charge transport and spectrum in the vicinity of the quantum phase transition regime. Furthermore, we find a coexistence of 0-type ABS and $\pi$-type ABS in the same charge state. By measuring temperature and magnetic field evolution of the ABSs, the different natures of the two sets of ABSs are verified, being consistent with the scenario of phase transition between the singlet and doublet ground state. Our study provides insights into Andreev transport properties of hybrid superconductor-QD devices and sheds light on the crossover behavior of the subgap spectrum in the vicinity of 0-$\pi$ transition

Unusual Nernst effect suggestive of time-reversal violation in the striped cuprate La2−x_{2-x}Bax_xCuO4_4

The striped cuprate La$_{2-x}$Ba$_x$CuO$_4$ ($x=\frac18)$ undergoes several transitions below the charge-ordering temperature $T_{co}$ = 54 K. From Nernst experiments, we find that, below $T_{co}$, there exists a large, anomalous Nernst signal $e_{N,even}(H,T)$ that is symmetric in field $H$, and remains finite as $H\to 0$. The time-reversal violating signal suggests that, below $T_{co}$, vortices of one sign are spontaneously created to relieve interlayer phase frustration.Comment: 5 pages, 4 figure