arXiv subjects

G. Rowlands

Publications and source records attributed to G. Rowlands.

At least 19 recordsLinked to original sources

arXiv2017

Recycling controls membrane domains

We study the coarsening of strongly microphase separated membrane domains in the presence of recycling of material. We study the dynamics of the domain size distribution under both scale-free and size-dependent recycling. Closed form solutions to the steady state distributions and its associated central moments are obtained in both cases. Moreover, for the size-independent case, the~time evolution of the moments is analytically calculated, which provide us with exact results for their corresponding relaxation times. Since these moments and relaxation times are measurable quantities, the biophysically significant free parameters in our model may be determined by comparison with experimental data.

q-bio.SC↗

arXiv2016

Nonlinear waves in the terrestrial quasi-parallel foreshock

We study the applicability of the derivative nonlinear Schr\"{o}dinger (DNLS) equation, for the evolution of high frequency nonlinear waves, observed at the foreshock region of the terrestrial quasi-parallel bow shock. The use of a pseudo-potential is elucidated and, in particular, the importance of canonical representation in the correct interpretation of solutions in this formulation is discussed. Numerical solutions of the DNLS equation are then compared directly with the wave forms observed by Cluster spacecraft. Non harmonic slow variations are filtered out by applying the empirical mode decomposition. We find large amplitude nonlinear wave trains at frequencies above the proton cyclotron frequency, followed in time by nearly harmonic low amplitude fluctuations. The approximate phase speed of these nonlinear waves, indicated by the parameters of numerical solutions, is of the order of the local Alfv\'{e}n speed.

physics.plasm-ph↗

arXiv2014

Some exact solutions to the Lighthill Whitham Richards Payne traffic flow equations II: moderate congestion

We find a further class of exact solutions to the Lighthill Whitham Richards Payne (LWRP) traffic flow equations. As before, using two consecutive Lagrangian transformations, a linearization is achieved. Next, depending on the initial density, we either obtain exact formulae for the dependence of the car density and velocity on x, t, or else, failing that, the same result in a parametric representation. The calculation always involves two possible factorizations of a consistency condition. Both must be considered. In physical terms, the lineup usually separates into two offshoots at different velocities. Each velocity soon becomes uniform. This outcome in many ways resembles not only Rowlands, Infeld and Skorupski J. Phys. A: Math. Theor. 46 (2013) 365202 (part I) but also the two soliton solution to the Korteweg-de Vries equation. This paper can be read independently of part I. This explains unavoidable repetitions. Possible uses of both papers in checking numerical codes are indicated at the end. Since LWRP, numerous more elaborate models, including multiple lanes, traffic jams, tollgates etc. abound in the literature. However, we present an exact solution. These are few and far between, other then found by inverse scattering. The literature for various models, including ours, is given. The methods used here and in part I may be useful in solving other problems, such as shallow water flow.

physics.flu-dyn↗

arXiv2013

Similarity Analysis of Macroecology

We perform a full similarity analysis of an idealized ecosystem using Buckingham's $Π$ theorem to obtain dimensionless similarity parameters given that some (non- unique) method exists that can differentiate different functional groups of individuals within an ecosystem. We then obtain the relationship between the similarity parameters under the assumptions of (i) that the ecosystem is in a dynamically balanced steady state and (ii) that these functional groups are connected to each other by the flow of resource. The expression that we obtain relates the level of complexity that the ecosystem can support to intrinsic macroscopic variables such as density, diversity and characteristic length scales for foraging or dispersal, and extrinsic macroscopic variables such as habitat size and the rate of supply of resource. This expression relates these macroscopic variables to each other, generating commonly observed macroecological patterns; these broad trends simply reflect the similarity property of ecosystems. We thus find that details of the ecosystem function are not required to obtain these broad macroecological patterns this may explain why they are ubiquitous. Departures from our relationship may indicate that the ecosystem is in a state of rapid change, i.e., abundance or diversity explosion or collapse. Our result provides normalised variables that can be used to isolate the trend in one ecosystem variable from another, providing a new method for isolating macroecological patterns in data. A dimensionless control parameter for ecosystem complexity emerges from our analysis and this will be a control parameter in dynamical models for ecosystems based on energy flow and conservation and will order the emergent behaviour of these models.

physics.bio-ph↗

arXiv2013

Some exact solutions to the Lighthill Whitham Richards Payne traffic flow equations

We find a class of exact solutions to the Lighthill Whitham Richards Payne (LWRP) traffic flow equations. Using two consecutive lagrangian transformations, a linearization is achieved. Next, depending on the initial density, we either apply (again two) Lambert functions and obtain exact formulas for the dependence of the car density and velocity on x and t, or else, failing that, the same result in a parametric representation. The calculation always involves two possible factorizations of a consistency condition. Both must be considered. In physical terms, the lineup usually separates into two offshoots at different velocities. Each velocity soon becomes uniform. This outcome in many ways resembles the two soliton solution to the Korteweg-de Vries equation. We check general conservation requirements. Although traffic flow research has developed tremendously since LWRP, this calculation, being exact, may open the door to solving similar problems, such as gas dynamics or water flow in rivers. With this possibility in mind, we outline the procedure in some detail at the end.

physics.flu-dyn↗

arXiv2009

One-dimensional particle simulation of the filamentation instability: electrostatic field driven by the magnetic pressure gradient force

Two counter-propagating cool and equally dense electron beams are modelled with particle-in-cell (PIC) simulations. The electron beam filamentation instability is examined in one spatial dimension, which is an approximation for a quasi-planar filament boundary. It is confirmed, that the force on the electrons imposed by the electrostatic field, which develops during the nonlinear stage of the instability, oscillates around a mean value that equals the magnetic pressure gradient force. The forces acting on the electrons due to the electrostatic and the magnetic field have a similar strength. The electrostatic field reduces the confining force close to the stable equilibrium of each filament and increases it farther away, limiting the peak density. The confining time-averaged total potential permits an overlap of current filaments with an opposite flow direction.

physics.plasm-ph↗

arXiv2009

Analytically Solvable Model of Nonlinear Oscillations in a Cold but Viscous and Resistive Plasma

A method for solving model nonlinear equations describing plasma oscillations in the presence of viscosity and resistivity is given. By first going to the Lagrangian variables and then transforming the space variable conveniently, the solution in parametric form is obtained. It involves simple elementary functions. Our solution includes all known exact solutions for an ideal cold plasma and a large class of new ones for a more realistic plasma. A new nonlinear effect is found of splitting of the largest density maximum, with a saddle point between the peaks so obtained. The method may sometimes be useful where Inverse Scattering fails.

physics.plasm-ph↗

arXiv2009

Macroscopic control parameter for avalanche models for bursty transport

Similarity analysis is used to identify the control parameter $R_A$ for the subset of avalanching systems that can exhibit Self- Organized Criticality (SOC). This parameter expresses the ratio of driving to dissipation. The transition to SOC, when the number of excited degrees of freedom is maximal, is found to occur when $R_A \to 0$. This is in the opposite sense to (Kolmogorov) turbulence, thus identifying a deep distinction between turbulence and SOC and suggesting an observable property that could distinguish them. A corollary of this similarity analysis is that SOC phenomenology, that is, power law scaling of avalanches, can persist for finite $R_A$, with the same $R_A \to 0$ exponent, if the system supports a sufficiently large range of lengthscales; necessary for SOC to be a candidate for physical ($R_A$ finite) systems.

math-ph↗

arXiv2008

Control parameters in turbulence, Self Organized Criticality and ecosystems

From the starting point of the well known Reynolds number of fluid turbulence we propose a control parameter $R$ for a wider class of systems including avalanche models that show Self Organized Criticality (SOC) and ecosystems. $R$ is related to the driving and dissipation rates and from similarity analysis we obtain a relationship $R\sim N^{β_N}$ where $N$ is the number of degrees of freedom. The value of the exponent $β_N$ is determined by detailed phenomenology but its sign follows from our similarity analysis. For SOC, $R=h/ε$ and we show that $β_N<0$ hence we show independent of the details that the transition to SOC is when $R \to 0$, in contrast to fluid turbulence, formalizing the relationship between turbulence (since $β_N >0$, $R \to \infty$) and SOC ($R=h/ε\to 0$). A corollary is that SOC phenomenology, that is, power law scaling of avalanches, can persist for finite $R$ with unchanged exponent if the system supports a sufficiently large range of lengthscales; necessary for SOC to be a candidate for physical systems. We propose a conceptual model ecosystem where $R$ is an observable parameter which depends on the rate of throughput of biomass or energy; we show this has $β_N>0$, so that increasing $R$ increases the abundance of species, pointing to a critical value for species 'explosion'.

physics.bio-ph↗

arXiv2007

Weakly nonlinear waves in magnetized plasma with a slightly non-Maxwellian electron distribution. Part 2. Stability of cnoidal waves

We determine the growth rate of linear instabilities resulting from long-wavelength transverse perturbations applied to periodic nonlinear wave solutions to the Schamel-Korteweg-de Vries-Zakharov-Kuznetsov (SKdVZK) equation which governs weakly nonlinear waves in a strongly magnetized cold-ion plasma whose electron distribution is given by two Maxwellians at slightly different temperatures. To obtain the growth rate it is necessary to evaluate non-trivial integrals whose number is kept to minimum by using recursion relations. It is shown that a key instance of one such relation cannot be used for classes of solution whose minimum value is zero, and an additional integral must be evaluated explicitly instead. The SKdVZK equation contains two nonlinear terms whose ratio $b$ increases as the electron distribution becomes increasingly flat-topped. As $b$ and hence the deviation from electron isothermality increases, it is found that for cnoidal wave solutions that travel faster than long-wavelength linear waves, there is a more pronounced variation of the growth rate with the angle $\theta$ at which the perturbation is applied. Solutions whose minimum value is zero and travel slower than long-wavelength linear waves are found, at first order, to be stable to perpendicular perturbations and have a relatively narrow range of $\theta$ for which the first-order growth rate is not zero.

physics.plasm-ph↗

arXiv2006

Nonlinear magnetoacoustic waves in a cold plasma

The equations describing planar magnetoacoustic waves of permanent form in a cold plasma are rewritten so as to highlight the presence of a naturally small parameter equal to the ratio of the electron and ion masses. If the magnetic field is not nearly perpendicular to the direction of wave propagation, this allows us to use a multiple-scale expansion to demonstrate the existence and nature of nonlinear wave solutions. Such solutions are found to have a rapid oscillation of constant amplitude superimposed on the underlying large-scale variation. The approximate equations for the large-scale variation are obtained by making an adiabatic approximation and in one limit, new explicit solitary pulse solutions are found. In the case of a perpendicular magnetic field, conditions for the existence of solitary pulses are derived. Our results are consistent with earlier studies which were restricted to waves having a velocity close to that of long-wavelength linear magnetoacoustic waves.

physics.plasm-ph↗

arXiv2005

Stability analysis of three-dimensional breather solitons in a Bose-Einstein Condensate

We investigate the stability properties of breather soliton trains in a three-dimensional Bose-Einstein Condensate with Feshbach Resonance Management of the scattering length. This is done so as to generate both attractive and repulsive interaction. The condensate is con ned only by a one dimensional optical lattice and we consider both strong, moderate, and weak con nement. By strong con nement we mean a situation in which a quasi two dimensional soliton is created. Moderate con nement admits a fully three dimensional soliton. Weak con nement allows individual solitons to interact. Stability properties are investigated by several theoretical methods such as a variational analysis, treatment of motion in e ective potential wells, and collapse dynamics. Armed with all the information forthcoming from these methods, we then undertake a numerical calculation. Our theoretical predictions are fully con rmed, perhaps to a higher degree than expected. We compare regions of stability in parameter space obtained from a fully 3D analysis with those from a quasi two-dimensional treatment, when the dynamics in one direction are frozen. We nd that in the 3D case the stability region splits into two parts. However, as we tighten the con nement, one of the islands of stability moves toward higher frequencies and the lower frequency region becomes more and more like that for quasi 2D. We demonstrate these solutions in direct numerical simulations and, importantly, suggest a way of creating robust 3D solitons in experiments in a Bose Einstein Condensate in a one-dimensional lattice.

cond-mat.other↗

arXiv2005

Scaling collapse and structure functions: Identifying self-affinity in finite length time series

Empirical determination of the scaling properties and exponents of time series presents a formidable challenge in testing, and developing, a theoretical understanding of turbulence and other out-of-equilibrium phenomena. We discuss the special case of self affine time series in the context of a stochastic process. We highlight two complementary approaches to the differenced variable of the data: i) attempting a scaling collapse of the Probability Density Functions which should then be well described by the solution of the corresponding Fokker-Planck equation and ii) using structure functions to determine the scaling properties of the higher order moments. Using the example of a L\'{e}vy flight, we demonstrate a method for conditioning the time series that recovers the underlying self affine scaling in a finite length time series.

physics.flu-dyn↗

arXiv2005

Scaling and Commonality in Anomalous Fluctuation Statistics in Models for Turbulence and Ferromagnetism

Recently, Portelli et al (2003) have semi-numerically obtained a functional form of the probability distribution of fluctuations in the total energy flow in a model for fluid turbulence. This follows earlier work suggesting that fluctuations in the total magnetization in the 2D X-Y model for a ferromagnet also follow this distribution. Here, starting from the scaling ansatz that is the basis of the turbulence model we analytically derive the functional form of this distribution and find its single control parameter that depends upon the scaling exponents and system size of the model. Our analysis allows us to identify this explicitly with that of the X-Y model, and suggest a possible generalization.

cond-mat.stat-mech↗

arXiv2004

Scaling and a Fokker-Planck model for fluctuations in geomagnetic indices and comparison with solar wind epsilon as seen by WIND and ACE

The evolution of magnetospheric indices on temporal scales shorter than that of substorms is characterized by bursty, intermittent events that may arise from turbulence intrinsic to the magnetosphere or may reflect solar wind-magnetosphere coupling. This leads to a generic problem of distinguishing between the features of the system and those of the driver. We quantify scaling properties of short term (up to few hours) fluctuations in the geomagnetic indices AL and AU during solar minimum and maximum along with the parameter epsilon that is a measure of the solar wind driver. We find that self-similar statistics provide a good approximation for the observed scaling properties of fluctuations in the geomagnetic indices, regardless of the solar activity level, and in the epsilon parameter at solar maximum. This self-similarity persists for fluctuations on time scales at least up to about 1-2 hours. The scaling exponent of AU index fluctuations show dependence on the solar cycle and the trend follows that found in the scaling of fluctuations in epsilon. The values of their corresponding scaling exponents, however, are always distinct. Fluctuations in the AL index are insensitive to the solar cycle as well as being distinct from those in the epsilon parameter. This approximate self-similar scaling leads to a Fokker-Planck model which, we show, captures the probability density function of fluctuations and provides a stochastic dynamical equation (Langevin equation) for time series of the geomagnetic indices.

physics.space-ph↗

arXiv2003

Scaling in long term data sets of geomagnetic indices and solar wind epsilon as seen by WIND spacecraft

We study scaling in fluctuations of the geomagnetic indices (AE, AU, and AL) that provide a measure of magnetospheric activity and of the epsilon parameter which is a measure of the solar wind driver. Generalized structure function (GSF) analysis shows that fluctuations exhibit self-similar scaling up to about 1 hour for the AU index and about 2 hours for AL, AE and epsilon when the most extreme fluctuations over 10 standard deviations are excluded. The scaling exponents of the GSF are found to be similar for the three AE indices, and to differ significantly from that of epsilon. This is corroborated by direct comparison of their rescaled probability density functions.

physics.space-ph↗

arXiv2003

Statistical characterisation of full-disk EUV/XUV solar irradiance and correlation with solar activity

We investigate the distribution of fluctuations in solar irradiance when integrated over the full disk, obtained using extreme ultraviolet/soft X-ray observations from the SOHO CELIAS/SEM instrument. This time series sums over both the contributions of single distinguishable flares, and of many other processes. By detrending we select events with timescales of less than a few hours such as waves, slow flows, and CMEs. The statistics generated by this range of phenomena can be characterised by power-law-tailed distributions. We show that (i) during the high-activity period 2000 Jan-June the tail exponent a(T)=1.5 +/- 0.1; (ii) during the low-activity period 1996 Jan-June a(T)=3.0 +/- 0.2; and (iii) in general a(T) decreases with increasing activity.

astro-ph↗

arXiv2003

Phase mixing of a three dimensional magnetohydrodynamic pulse

Phase mixing of a three dimensional magnetohydrodynamic (MHD) pulse is studied in the compressive, three-dimensional (without an ignorable coordinate) regime. It is shown that the efficiency of decay of an Alfvenic part of a compressible MHD pulse is related linearly to the degree of non-planeness of the pulse in the homogeneous transverse direction. In the developed stage of phase mixing (for large times), coupling to its compressive part does not alter the power-law decay of an Alfvenic part of a compressible MHD pulse. The same applies to the dependence upon the resistivity of the Alfvenic part of the pulse. All this implies that the dynamics of Alfven waves can still be qualitatively understood in terms of the previous 2.5D models. Thus, the phase mixing remains a relevant paradigm for the coronal heating applications in the realistic 3D geometry and compressive plasma.

astro-ph↗