In Silico Experimental Modeling of Cancer Treatment

In silico experimental modeling of cancer involves combining findings from biological literature with computer-based models of biological systems in order to conduct investigations of hypotheses entirely in the computer laboratory. In this paper, we discuss the use of in silico modeling as a precursor to traditional clinical and laboratory research, allowing researchers to refine their experimental programs with an aim to reducing costs and increasing research efficiency. We explain the methodology of in silico experimental trials before providing an example of in silico modeling from the biomathematical literature with a view to promoting more widespread use and understanding of this research strategy

A Modified Version of Taylor's Hypothesis for Solar Probe Plus Observations

The Solar Probe Plus (SPP) spacecraft will explore the near-Sun environment, reaching heliocentric distances less than $10 R_{\odot}$. Near Earth, spacecraft measurements of fluctuating velocities and magnetic fields taken in the time domain are translated into information about the spatial structure of the solar wind via Taylor's "frozen turbulence" hypothesis. Near the perihelion of SPP, however, the solar-wind speed is comparable to the Alfv\'en speed, and Taylor's hypothesis in its usual form does not apply. In this paper, we show that, under certain assumptions, a modified version of Taylor's hypothesis can be recovered in the near-Sun region. We consider only the transverse, non-compressive component of the fluctuations at length scales exceeding the proton gyroradius, and we describe these fluctuations using an approximate theoretical framework developed by Heinemann and Olbert. We show that fluctuations propagating away from the Sun in the plasma frame obey a relation analogous to Taylor's hypothesis when $V_{\rm sc,\perp} \gg z^-$ and $z^+ \gg z^-$, where $V_{\rm sc,\perp}$ is the component of the spacecraft velocity perpendicular to the mean magnetic field and $\bm{z}^+$ ($\bm{z}^-$) is the Elsasser variable corresponding to transverse, non-compressive fluctuations propagating away from (towards) the Sun in the plasma frame. Observations and simulations suggest that, in the near-Sun solar wind, the above inequalities are satisfied and $\bm{z}^+$ fluctuations account for most of the fluctuation energy. The modified form of Taylor's hypothesis that we derive may thus make it possible to characterize the spatial structure of the energetically dominant component of the turbulence encountered by SPP.Comment: 5 pages, 1 figure, accepted in ApJ Lette

On the Conservation of Cross Helicity and Wave Action in Solar-Wind Models with Non-WKB Alfven Wave Reflection

The interaction between Alfven-wave turbulence and the background solar wind affects the cross helicity in two ways. Non-WKB reflection converts outward-propagating Alfven waves into inward-propagating Alfven waves and vice versa, and the turbulence transfers momentum to the background flow. When both effects are accounted for, the total cross helicity is conserved. In the special case that the background density and flow speed are independent of time, the equations of cross-helicity conservation and total-energy conservation can be combined to recover a well-known equation derived by Heinemann and Olbert that has been interpreted as a non-WKB generalization of wave-action conservation. This latter equation (in contrast to cross-helicity and energy conservation) does not hold when the background varies in time.Comment: 9 pages, 1 figure, in press at Ap

Generating Entangled Microwave Radiation Over Two Transmission Lines

Using a superconducting circuit, the Josephson mixer, we demonstrate the first experimental realization of spatially separated two-mode squeezed states of microwave light. Driven by a pump tone, a first Josephson mixer generates, out of quantum vacuum, a pair of entangled fields at different frequencies on separate transmission lines. A second mixer, driven by a $\pi$-phase shifted copy of the first pump tone, recombines and disentangles the two fields. The resulting output noise level is measured to be lower than for vacuum state at the input of the second mixer, an unambiguous proof of entanglement. Moreover, the output noise level provides a direct, quantitative measure of entanglement, leading here to the demonstration of 6 Mebit.s$^{-1}$ (Mega entangled bits per second) generated by the first mixer.Comment: 5 pages, 4 figures. Supplementary Information can be found here as an ancillary fil

Application of the control volume method to a mathematical model of cell migration

In recent years, mathematical models of cell migration have become increasingly complex. These models have evolved from simple diffusion models to computationally troublesome reaction-diffusion-advection models. As such, the use of ``black box'' numerical solvers has become less appropriate. We discuss the application of the control volume technique for resolving a complicated nonlinear cell migration model. The nonlinearity is treated using an inexact Newton solver and flux limiting ensures that the cell migration fronts are captured adequately. Specifically, we analyse the model due to Perumpanani et al. (1999), comparing the numerical results of the proposed computational model developed in this research to previous results published by other researchers. We show that the finite volume computational model captures the physics of the processes with good accuracy using coarse meshes

Three-dimensional arrangement of β-tricalcium phosphate granules evaluated by microcomputed tomography and fractal analysis.

The macrophysical properties of granular biomaterials used to fill bone defects have rarely been considered. Granules of a given biomaterial occupy three-dimensional (3-D) space when packed together and create a macroporosity suitable for the invasion of vascular and bone cells. Granules of β-tricalcium phosphate were prepared using polyurethane foam technology and increasing the amount of material powder in the slurry (10, 11, 15, 18, 21 and 25g). After sintering, granules of 1000-2000μm were prepared by sieving. They were analyzed morphologically by scanning electron microscopy and placed in polyethylene test tubes to produce 3-D scaffolds. Microcomputed tomography (microCT) was used to image the scaffolds and to determine porosity and fractal dimension in three dimensions. Two-dimensional sections of the microCT models were binarized and used to compute classical morphometric parameters describing porosity (interconnectivity index, strut analysis and star volumes) and fractal dimensions. In addition, two newly important fractal parameters (lacunarity and succolarity) were measured. Compression analysis of the stacks of granules was done. Porosity decreased as the amount of material in the slurry increased but non-linear relationships were observed between microarchitectural parameters describing the pores and porosity. Lacunarity increased in the series of granules but succolarity (reflecting the penetration of a fluid) was maximal in the 15-18g groups and decreased noticeably in the 25g group. The 3-D arrangement of biomaterial granules studied by these new fractal techniques allows the optimal formulation to be derived based on the lowest amount of material, suitable mechanical resistance during crushing and the creation of large interconnected pores