The 4-beaches survey in Uganda: Nkombe Beach

This paper analyses the location, potentialities and set-backs of Nkombe Beach, the landing site chosen in Uganda for the 4-beaches survey

The Jinja Stakeholders' Workshop, February 21st -23rd, 2001

This book section is a review of a workshop, the one held at Jinja in Uganda, which aimed to assess the potential local stakeholders within the frame of the co-management of Lake Victoria's fisheries

Spatial solitons in a medium composed of self-focusing and self-defocusing layers

We introduce a model combining Kerr nonlinearity with a periodically changing sign ("nonlinearity management") and a Bragg grating (BG). The main result, obtained by means of systematic simulations, is presented in the form of a soliton's stability diagram on the parameter plane of the model; the diagram turns out to be a universal one, as it practically does not depend on the soliton's power. Moreover, simulations of the nonlinear Schroedinger (NLS) model subjected to the same "nonlinearity management" demonstrate that the same diagram determines the stability of the NLS solitons, unless they are very narrow. The stability region of very narrow NLS solitons is much smaller, and soliton splitting is readily observed in that case. The universal diagram shows that a minimum non-zero average value of the Kerr coefficient is necessary for the existence of stable solitons. Interactions between identical solitons with an initial phase difference between them are simulated too in the BG model, resulting in generation of stable moving solitons. A strong spontaneous symmetry breaking is observed in the case when in-phase solitons pass through each other due to attraction between them.Comment: a latex text file and 9 eps files with figures. Physics Letters A, in pres

Stability and interactions of solitons in two-component active systems

We demonstrate that solitary pulses in linearly coupled nonlinear Schrödinger equations with gain in one mode and losses in another one, which is a model of an asymmetric erbium-doped nonlinear optical coupler, exist and are stable, as was recently predicted analytically. Next, we consider interactions between the pulses. The in-phase pulses attract each other and merge into a single one. Numerical and analytical consideration of the repulsive interaction between π-out-of-phase pulses reveals the existence of their robust pseudobound state, when a final separation between them takes an almost constant minimum value, as a function of the initial separation, Tin, in a certain interval of Tin. In the case of the phase difference π/2, the interaction is also repulsive. © 1996 The American Physical Society

A Rapid X-ray Flare from Markarian 501

We present X-ray observations of the BL Lacertae (BL Lac) object Markarian 501 (Mrk 501), taken with the Rossi X-ray Timing Explorer in 1998 May as part of a multi-wavelength campaign. The X-ray light curve shows a very rapid flare in which the 2-10 keV flux increased by ~60% in <200 seconds. This rapid rise is followed by a drop-off in the 2-10 keV flux of ~40% in <600 seconds. The 10-15 keV variation in this flare is roughly a factor of two on similar time-scales. During the rise of the flare, the 3-15 keV spectral index hardened from 2.02 +/- 0.03 to 1.87 +/- 0.04, where it remained during the decay of the flare. This is the fastest variation ever seen in X-rays from Mrk 501 and among the fastest seen at any wavelength for this object. The shift in the energy at which the spectral power peaks (from 30 keV during the flare) is also among the most rapid shifts seen from this object. This flare occurs during an emission state (2-10 keV flux approximately 1.2e-10 erg cm^-2 s^-1) that is approximately 25% of the peak flux observed in 1997 April from this object but which is still high compared to its historical average X-ray flux. The variations in the hardness ratio are consistent with the low energy variations leading those at high energies during the development and decay of the flare. This pattern is rare among high frequency peaked BL Lac objects like Mrk 501, but has been seen recently in two other TeV emitting BL Lacs, Mrk 421 and PKS 2155-304. The hard lag is consistent with a flare dominated by the acceleration time-scale for a simple relativistic shock model of flaring.Comment: 11 pages, 3 figures, accepted for publication in Astrophys. J. Letter

On integers for which the sum of divisors is the square of the squarefree core

We study integers n > 1 satisfying the relation σ(n) = γ(n) ² , where σ(n) and γ(n) are the sum of divisors and the product of distinct primes dividing n, respectively. We show that the only solution n with at most four distinct prime factors is n = 1782. We show that there is no solution which is fourth power free. We also show that the number of solutions up to x > 1 is at most x ⅟⁴⁺ᵉ for any ε > 0 and all x > xε. Further, call n primitive if no proper unitary divisor d of n satisfies σ(d) | γ(d) ² . We show that the number of primitive solutions to the equation up to x is less than xᵉ for x > xₑ

Breathing and randomly walking pulses in a semilinear Ginzburg-Landau system

A system consisting of the cubic complex Ginzburg-Landau equation which is linearly coupled to an additional linear dissipative equation, is considered. The model was introduced earlier in the context of dual-core nonlinear optical fibers with one active and one passive cores. We argue that it may also possibly describe traveling-wave convection in a channel with an inner vertical partition. By means of systematic simulations, we find new types of stable localized excitations, which exist in the system in addition to the earlier found stationary pulses. The new localized excitations include pulses existing on top of a small-amplitude background (that may be regular or chaotic) {\em above} the threshold of instability of the zero solution, and breathers into which stationary pulses are transformed through a Hopf bifurcation below the zero-solution instability threshold. A sharp border between the stable stationary pulses and breathers, precluding their coexistence, is identified. Stable bound states of two breathers with a phase shift $\pi /2$ between their internal vibrations are found too. Above the threshold, the pulses are standing if the small-amplitude background oscillations are regular; if the background is chaotic, the pulses are randomly walking. With the increase of the system's size, more randomly walking pulses are spontaneously generated. The random walk of different pulses in a multi-pulse state is synchronized (but not completely) due to their mutual repulsion. At a large overcriticality, the multi-pulse state goes over into a spatiotemporal chaos.Comment: 16page,12figure

Stable autosolitons in dispersive media with saturable gain and absorption

We introduce the simplest one-dimensional model of a dispersive optical medium with saturable dissipative nonlinearity and filtering (dispersive loss) which gives rise to stable solitary pulses (autosolitons). In the particular case when the dispersive loss is absent, the same model may also be interpreted as describing a stationary field in a planar optical waveguide with uniformly distributed saturable gain and absorption. In a certain region of the model's parameter space, two coexisting solitary-pulse solutions are found numerically, one of which may be stable. Solving the corresponding linearized eigenvalue problem, we identify stability borders for the solitary pulses in their parametric plane. Beyond one of the borders, the symmetric pulse is destroyed by asymmetric perturbations, and at the other border it undergoes a Hopf bifurcation, which may turn it into a breather.Comment: A latex text file and four ps files with figures. Physics Letters A, in pres