The Kolmogorov-Sinai Entropy for Dilute Gases in Equilibrium

We use the kinetic theory of gases to compute the Kolmogorov-Sinai entropy per particle for a dilute gas in equilibrium. For an equilibrium system, the KS entropy, h_KS is the sum of all of the positive Lyapunov exponents characterizing the chaotic behavior of the gas. We compute h_KS/N, where N is the number of particles in the gas. This quantity has a density expansion of the form h_KS/N = a\nu[-\ln{\tilde{n}} + b + O(\tilde{n})], where \nu is the single-particle collision frequency and \tilde{n} is the reduced number density of the gas. The theoretical values for the coefficients a and b are compared with the results of computer simulations, with excellent agreement for a, and less than satisfactory agreement for b. Possible reasons for this difference in b are discussed.Comment: 15 pages, 2 figures, submitted to Phys. Rev.

Temperature Dependence of the QCD Coupling

We present a one-loop calculation of a gauge invariant QCD beta function. Using both momentum and temperature renormalization group equations we investigate the running coupling in the magnetic sector as a function of temperature and momentum scale. At fixed momentum scale we find that, in contrast to $\lambda\phi^4$ or QED, high-temperature QCD is strongly coupled, even after renormalization group improvement. However, if the momentum scale is changed simultaneously with temperature in a specified manner, the coupling decreases. We also point out in what regime dimensional reduction occurs. Both the cases $N_f$ smaller and larger than $\frac{11}{2} N_c$ are discussed.Comment: 10 pages, LaTeX (5 postscript figures available), ITFA-93-11,THU-93/0

The Belgian deposit guarantee scheme in a European perspective

During the recent financial crisis, the deposit guarantee scheme in Belgium – as in other European countries – played a role in preventing bank runs and restoring confidence : to that end, the intervention ceilings were raised substantially and the scope of the scheme was extended to include certain life insurance policies. Finally, the expansion of the system’s coverage had to be financed by a sharp increase in the contributions from financial institutions. First of all, that measure had a positive impact on the budget ; secondly, increased contributions may also boost the credibility of the deposit guarantee system. A recent European initiative proposes further ambitious reforms. Besides a better consumer protection, the European deposit guarantee schemes would be largely harmonised, thus also promoting European financial integration. Risk-weighted financing of the schemes should counteract moral hazard, benefiting financial stability. However, this proposal has yet to be approved by the European Parliament and the Council. Its impact ought to be assessed in the light of the broader package of measures aimed at making the financial system more resilient, such as the new prudential supervision structure, the Basel III proposal for stricter capital and liquidity requirements, and the possible new levies on the financial sector.deposit assurance, financial institutions, financial crisis, moral hazard

Transversality of the logarithmic divergences in the Classical Finite Temperature SU(N) Self-Energy

We show that the logarithmic divergences that appear in the classical approximation of the finite temperature SU(N) self-energy are transverse. We use the Ward identities in linear gauges and the fact that the superficial degree of divergence d of a classical diagram only depends on the number of loops l via d=2-l. We comment on the relevance of this result to the construction of a low-energy effective theory beyond HTLs.Comment: 5 pages, 1 figure, REVTE

The impact of low interest rates on household financial behaviour

For the greater part of 2010, short-term and long-term interest rates in Belgium were at exceptionally low levels. Nominal interest rates reached historic lows ; in real terms, only the low point of 1974 remained unequalled. The yield curve was in turn relatively steep. In the first place, the question of whether these low interest rates have an impact on the overall financial transactions of households is examined. During the recent period, interest rates in real terms have only had a limited influence on the overall volume of savings of Belgian households. It seems that the increased savings behaviour of households and the associated accumulation of net financial assets during the period 2009-2010 can largely be attributed to economic uncertainty due to the financial crisis. But it can certainly be assumed that interest rates play some part in the selection of savings and investment vehicles by households. This is the case when they have to choose between short-term and long-term vehicles : long-term investments benefit from a clear preference in periods of high long-term interest rates or when the interest rate cycle has moved into a downward phase. During the few periods with a flat or inverted yield curve, private individuals reduce their short-term deposits since they then possibly expect a fall in long-term yields. It is primarily in the choices between short-term savings vehicles that interest rates have the greatest influence, as witnessed by the persistent switching between term and regulated savings deposits, where the recent fall in short-term interest rates worked strongly in favour of the latter vehicle. The build-up of claims on technical reserves of life insurance companies and pension funds is being stimulated by the current level of interest rates, since certain existing contracts offer a guaranteed return that is higher than the current market rates. Lastly, interest rates have some influence on the commitments entered into by households, and in the first place mortgage loans. It is primarily the number of mortgages that strongly grows in the case of low interest rates. Alongside this, low interest rates may prompt price rises on the housing market with a resulting higher level of recourse to mortgage lending. But lending does not entirely follow the trend in housing prices, partly due to a more restrictive lending policy on the part of the banks.saving, interest rates, credit, portfolio choice

Largest Lyapunov Exponent for Many Particle Systems at Low Densities

The largest Lyapunov exponent $\lambda^+$ for a dilute gas with short range interactions in equilibrium is studied by a mapping to a clock model, in which every particle carries a watch, with a discrete time that is advanced at collisions. This model has a propagating front solution with a speed that determines $\lambda^+$, for which we find a density dependence as predicted by Krylov, but with a larger prefactor. Simulations for the clock model and for hard sphere and hard disk systems confirm these results and are in excellent mutual agreement. They show a slow convergence of $\lambda^+$ with increasing particle number, in good agreement with a prediction by Brunet and Derrida.Comment: 4 pages, RevTeX, 2 Figures (encapsulated postscript). Submitted to Phys. Rev. Let

A slow coronal mass ejection with rising X-ray source

An eruptive event, which occurred on 16th April 2002, is discussed. Using images from the Transition Region and Coronal Explorer ( TRACE) at 195 angstrom, we observe a lifting flux rope which gives rise to a slow coronal mass ejection ( CME). There are supporting velocity observations from the Coronal Diagnostic Spectrometer ( CDS) on the Solar and Heliospheric Observatory ( SOHO), which illustrate the helical nature of the structure. Additionally a rising coronal hard X- ray source, which is observed with the Reuven Ramaty High Energy Solar Spectroscopic Imager ( RHESSI), is shown to follow the flux rope with a speed of similar to 60 km s(-1). It is also sampled by the CDS slit, although it has no signature in the Fe XIX band. Following the passage of this source, there is evidence from the CDS for down- flowing ( cooling) material along newly reconnected loops through Doppler velocity observations, combined with magnetic field modeling. Later, a slow CME is observed with the Large Angle and Spectroscopic Coronagraph ( LASCO). We combine a height- time profile of the flux rope at lower altitudes with the slow CME. The rising flux rope speeds up by a factor of 1.7 at the start of the impulsive energy release and goes through further acceleration before reaching 1.5 solar radii. These observations support classical CME scenarios in which the eruption of a filament precedes flaring activity. Cusped flare loops are observed following the erupting flux rope and their altitude increases with time. In addition we find RHESSI sources both below and above the probable location of the reconnection region

An exploratory analysis of the corporate identity of selected national government departments in South Africa

A communication task team appointed by the Government of South Africa in 1996suggested that there should be one corporate identity for the government. A problemresulting from this suggestion was what this unitary corporate identity should reflectand which elements it should include.This article is based on a study into the viability of creating one corporate identity forall the South African government departments.Background is given for a government decision to create one corporate identity. Theview that corporate identity consists of the integration between visual identity andbehavioural identity and its possible application on the government departments ofSouth Africa is discussed.The main finding of this study is that the current corporate identity of four selectedgovernment departments consists of corporate service and behaviour, dynamism andvisual identit

Inapproximability of the Standard Pebble Game and Hard to Pebble Graphs

Pebble games are single-player games on DAGs involving placing and moving pebbles on nodes of the graph according to a certain set of rules. The goal is to pebble a set of target nodes using a minimum number of pebbles. In this paper, we present a possibly simpler proof of the result in [CLNV15] and strengthen the result to show that it is PSPACE-hard to determine the minimum number of pebbles to an additive $n^{1/3-\epsilon}$ term for all $\epsilon > 0$, which improves upon the currently known additive constant hardness of approximation [CLNV15] in the standard pebble game. We also introduce a family of explicit, constant indegree graphs with $n$ nodes where there exists a graph in the family such that using constant $k$ pebbles requires $\Omega(n^k)$ moves to pebble in both the standard and black-white pebble games. This independently answers an open question summarized in [Nor15] of whether a family of DAGs exists that meets the upper bound of $O(n^k)$ moves using constant $k$ pebbles with a different construction than that presented in [AdRNV17].Comment: Preliminary version in WADS 201

Comment on ``Lyapunov Exponent of a Many Body System and Its Transport Coefficients''

In a recent Letter, Barnett, Tajima, Nishihara, Ueshima and Furukawa obtained a theoretical expression for the maximum Lyapunov exponent $\lambda_1$ of a dilute gas. They conclude that $\lambda_1$ is proportional to the cube root of the self-diffusion coefficient $D$, independent of the range of the interaction potential. They validate their conjecture with numerical data for a dense one-component plasma, a system with long-range forces. We claim that their result is highly non-generic. We show in the following that it does not apply to a gas of hard spheres, neither in the dilute nor in the dense phase.Comment: 1 page, Revtex - 1 PS Figs - Submitted to Physical Review Letter