Superfast non-linear diffusion: capillary transport in particulate porous media

The migration of liquids in porous media, such as sand, has been commonly considered at high saturation levels with liquid pathways at pore dimensions. In this letter we reveal a low saturation regime observed in our experiments with droplets of extremely low volatility liquids deposited on sand. In this regime the liquid is mostly found within the grain surface roughness and in the capillary bridges formed at the contacts between the grains. The bridges act as variable-volume reservoirs and the flow is driven by the capillary pressure arising at the wetting front according to the roughness length scales. We propose that this migration (spreading) is the result of interplay between the bridge volume adjustment to this pressure distribution and viscous losses of a creeping flow within the roughness. The net macroscopic result is a special case of non-linear diffusion described by a superfast diffusion equation (SFDE) for saturation with distinctive mathematical character. We obtain solutions to a moving boundary problem defined by SFDE that robustly convey a time power law of spreading as seen in our experiments.

Movement time for motion-impaired users assisted by force-feedback: effects of movement amplitude, target width and gravity well width

This paper presents a study investigating how the performance of motion-impaired computer users in point and click tasks varies with target distance (A), target width (W), and force-feedback gravity well width (GWW). Six motion-impaired users performed point and click tasks across a range of values for A, W, and GWW. Times were observed to increase with A, and to decrease with W. Times also improved with GWW, and, with the addition of a gravity well, a greater improvement was observed for smaller targets than for bigger ones. It was found that Fitts Law gave a good description of behaviour for each value of GWW, and that gravity wells reduced the effect of task difficulty on performance. A model based on Fitts Law is proposed, which incorporates the effect of GWW on movement time. The model accounts for 88.8% of the variance in the observed data.

Neural network enhanced generalised minimum variance self-tuning controller for nonlinear discrete-time systems

A neural network enhanced self-tuning controller is presented, which combines the attributes of neural network mapping with a generalised minimum variance self-tuning control (STC) strategy. In this way the controller can deal with nonlinear plants, which exhibit features such as uncertainties, nonminimum phase behaviour, coupling effects and may have unmodelled dynamics, and whose nonlinearities are assumed to be globally bounded. The unknown nonlinear plants to be controlled are approximated by an equivalent model composed of a simple linear submodel plus a nonlinear submodel. A generalised recursive least squares algorithm is used to identify the linear submodel and a layered neural network is used to detect the unknown nonlinear submodel in which the weights are updated based on the error between the plant output and the output from the linear submodel. The procedure for controller design is based on the equivalent model therefore the nonlinear submodel is naturally accommodated within the control law. Two simulation studies are provided to demonstrate the effectiveness of the control algorithm.

Lag-time effects on a naturally ventilated large thermometer screen

Systematic natural ventilation effects on measured temperatures within a standard large wooden thermometer screen are investigated under summer conditions, using well-calibrated platinum resistance thermometers. Under low ventilation (2mwind speed u2 < 1.1 m s−1), the screen slightly underestimates daytime air temperature but overestimates air temperature nocturnally by 0.2◦C. The screen’s lag time L lengthens with decreasing wind speed, following an inverse power law relationship between L and u2. For u2 > 2 m s−1, L ∼ 2.5 min, increasing, when calm, to at least 15 min. Spectral response properties of the screen to air temperature fluctuations vary with wind speed because of the lag changes. Ventilation effects are particularly apparent at the higher (>25◦C) temperatures, both through the lag effect and from solar heating. For sites where wind speed decreases with increasing daytime temperature, thermometer screen temperatures may consequently show larger uncertainties at the higher temperatures. Under strong direct beam solar radiation (>850W m−2) the radiation effect is likely to be <0.4◦C. Copyright c 2011 RoyalMeteorological Society

Redefining the outer boundaries of EU Law: the Zambrano, McCarthy and Dereci trilogy

In its three recent rulings in the cases of Zambrano, McCarthy, and Dereci, the Court appears to have been determined to redefine the external boundaries of EU law, in cases involving the family reunification rights of Union citizens.These three judgments can be read as an indication that for Article 20 TFEU to apply, there is no longer a requirement of a cross-border element on the facts of the case, and that it is sufficient if the contested national measure has the effect of ‘depriving citizens of the Union of the genuine enjoyment of the substance’ of their rights (the ‘Zambrano principle’).The cases can, at the same time, also be read as a confirmation that the free movement provisions do – still – require a cross-border element and, in particular, the exercise of inter-State movement, in order to apply. Though the result in these cases has not been entirely unexpected, especially in the aftermath of the Rottmann ruling, it is rather problematic in that, although it is obvious that the Court wishes to redraw the line dividing the national and EU spheres of competence, it does not make it entirely clear where this line now lies and leaves many essential questions unanswered, which will obviously require some time to be resolved. EU lawyers are consequently, once more, left with having to decipher as best as they can the real intentions of the Court in this new line of case-law, which has been further complicated by the fact that what the Court seems to have given with one hand in Zambrano (and before that in Rottmann), has taken it back to a large extent through its rulings in McCarthy and Dereci, which appear to confine the former two cases to their own exceptional facts.6 Moreover, the ‘reverse discrimination Pandora’s box’, the opening of which appears to have been the real target of these references, remains untouched: instead of providing a direct solution to this problem, the Court has chosen to – once again – broaden the scope of the Treaty provisions in order to include within it as many situations as possible and, thus, prevent the emergence of this type of differential treatment on a case-by-case basis.As will be explained, nonetheless, this is by no means an appropriate solution to the reverse discrimination conundrum.

On the time-dependent analysis of Gamow decay

Gamow's explanation of the exponential decay law uses complex 'eigenvalues' and exponentially growing 'eigenfunctions'. This raises the question, how Gamow's description fits into the quantum mechanical description of nature, which is based on real eigenvalues and square integrable wavefunctions. Observing that the time evolution of any wavefunction is given by its expansion in generalized eigenfunctions, we shall answer this question in the most straightforward manner, which at the same time is accessible to graduate students and specialists. Moreover, the presentation can well be used in physics lectures to students.

Law of large numbers for super-brownian motions with a single point source

We investigate the super-Brownian motion with a single point source in dimensions 2 and 3 as constructed by Fleischmann and Mueller in 2004. Using analytic facts we derive the long time behavior of the mean in dimension 2 and 3 thereby complementing previous work of Fleischmann, Mueller and Vogt. Using spectral theory and martingale arguments we prove a version of the strong law of large numbers for the two dimensional superprocess with a single point source and finite variance.

Time and retribution

Retributivists believe that punishment can be deserved, and that deserved punishment is intrinsically good. They also believe that certain crimes deserve certain quantities of punishment. On the plausible assumption that the overall amount of any given punishment is a function of its severity and duration, we might think that retributivists (qua retributivists) would be indifferent as to whether a punishment were long and light or short and sharp, provided the offender gets the overall amount of punishment he deserves. In this paper I argue against this, showing that retributivists should actually prefer shorter and more severe punishments to longer, gentler options. I show this by focusing on, and developing a series of interpretations of, the retributivist claim that not punishing the guilty is bad, focussing on the relationship between that badness and time. I then show that each interpretation leads to a preference for shorter over longer punishment.

Critical slip and time dependence in sea ice friction

Recent research into sea ice friction has focussed on ways to provide a model which maintains much of the clarity and simplicity of Amonton's law, yet also accounts for memory effects. One promising avenue of research has been to adapt the rate- and state- dependent models which are prevalent in rock friction. In such models it is assumed that there is some fixed critical slip displacement, which is effectively a measure of the displacement over which memory effects might be considered important. Here we show experimentally that a fixed critical slip displacement is not a valid assumption in ice friction, whereas a constant critical slip time appears to hold across a range of parameters and scales. As a simple rule of thumb, memory effects persist to a significant level for 10 s. We then discuss the implications of this finding for modelling sea ice friction and for our understanding of friction in general.

Haworth's Law

The maximum 'Depth to Mate' (DTM(k)) data for k-man chess, k = 3-7, is now available: log(maxDTM(k)) demonstrates quasi-linear behaviour. This note predicts maxDTM for 8- to 10-man chess and the two-sigma distributions around these figures. 'Haworth's Law' is the conjecture that maxDTM will continue to demonstrate this behaviour for some time to come. The supporting datafile is a pgn of maxDTM positions, each having a DTM-minimaxing line of play from it to 'mate'.

Humanitarian law, human rights law and the bifurcation of armed conflict

This article offers a fresh examination of the distinction drawn in international humanitarian law (IHL) between international and non-international armed conflicts. In particular, it considers this issue from the under-explored perspective of the influence of international human rights law (IHRL). It is demonstrated how, over time, the effect of IHRL on this distinction in IHL has changed dramatically. Whereas traditionally IHRL encouraged the partial elimination of the distinction between types of armed conflict, more recently it has been invoked in debates in a manner that would preserve what remains of the distinction. By exploring this important issue, it is hoped that the present article will contribute to the ongoing debates regarding the future development of the law of non-international armed conflict.

Mapping power law distributions in digital health social networks: methods, interpretations, and practical implications

BACKGROUND: Social networks are common in digital health. A new stream of research is beginning to investigate the mechanisms of digital health social networks (DHSNs), how they are structured, how they function, and how their growth can be nurtured and managed. DHSNs increase in value when additional content is added, and the structure of networks may resemble the characteristics of power laws. Power laws are contrary to traditional Gaussian averages in that they demonstrate correlated phenomena. OBJECTIVES: The objective of this study is to investigate whether the distribution frequency in four DHSNs can be characterized as following a power law. A second objective is to describe the method used to determine the comparison. METHODS: Data from four DHSNs—Alcohol Help Center (AHC), Depression Center (DC), Panic Center (PC), and Stop Smoking Center (SSC)—were compared to power law distributions. To assist future researchers and managers, the 5-step methodology used to analyze and compare datasets is described. RESULTS: All four DHSNs were found to have right-skewed distributions, indicating the data were not normally distributed. When power trend lines were added to each frequency distribution, R(2) values indicated that, to a very high degree, the variance in post frequencies can be explained by actor rank (AHC .962, DC .975, PC .969, SSC .95). Spearman correlations provided further indication of the strength and statistical significance of the relationship (AHC .987. DC .967, PC .983, SSC .993, P<.001). CONCLUSIONS: This is the first study to investigate power distributions across multiple DHSNs, each addressing a unique condition. Results indicate that despite vast differences in theme, content, and length of existence, DHSNs follow properties of power laws. The structure of DHSNs is important as it gives insight to researchers and managers into the nature and mechanisms of network functionality. The 5-step process undertaken to compare actor contribution patterns can be replicated in networks that are managed by other organizations, and we conjecture that patterns observed in this study could be found in other DHSNs. Future research should analyze network growth over time and examine the characteristics and survival rates of superusers.

The Lieber Code and the regulation of civil war in international law

In this paper, we consider one particularly interesting feature of the Lieber Code, which is the fact that it was drawn up by the U.S. Government to regulate the conduct of its armed forces in a civil war. In so doing, we hope to explore the extent to which there may be links between the Lieber Code and the contemporary regulation of non-international armed conflicts. In particular, we explore some similarities and contrasts between the views on the regulation of civil war that existed at the time of the drafting of the Lieber Code and the position that exists today.