What determines the wavelength of self-organized shoreline sand waves?

Shoreline undulations extending into the bathymetric contours with a length scale larger than that of the rhythmic surf zone bars are referred to as shoreline sand waves. Many observed undulations along sandy coasts display a wavelength in the order 1-7 km. Several models that are based on the hypothesis that sand waves emerge from a morphodynamic instability in case of very oblique wave incidence predict this range of wavelengths. Here we investigate the physical reasons for the wavelength selection and the main parametric trends of the wavelength in case of sand waves arising from such instability. It is shown that the existence of a minimum wavelength depends on an interplay between three factors affecting littoral drift: (A) the angle of wave fronts relative to local shoreline, which tends to cause maximum transport at the downdrift flank of the sand wave, (B) the refractive energy spreading which tends to cause maximum transport at the updrift flank and (C) wave focusing (de-focusing) by the capes (bays), which tends to cause maximum transport at the crest or slightly downdrift of it. Processes A and C cause decay of the sand waves while process B causes their growth. For low incidence angles, B is very weak so that a rectilinear shoreline is stable. For large angles and long sand waves, B is dominant and causes the growth of sand waves. For large angles and short sand waves C is dominant and the sand waves decay. Thus, wavelength selection depends on process C, which essentially depends on shoreline curvature. The growth rate of very long sand waves is weak because the alongshore gradients in sediment transport decrease with the wavelength. This is why there is an optimum or dominant wavelength. It is found that sand wave wavelength scales with λ0/β where λ0 is the water wave wavelength in deep water and β is the mean bed slope from shore to the wave base.

Periodic orbits of integrable birational maps on the plane: blending dynamics and algebraic geometry, the Lyness' case

Contingut del Pòster presentat al congrés New Trends in Dynamical Systems

Rational periodic sequences for the Lyness recurrence

Consider the celebrated Lyness recurrence $x_{n+2}=(a+x_{n+1})/x_{n}$ with $a\in\Q$. First we prove that there exist initial conditions and values of $a$ for which it generates periodic sequences of rational numbers with prime periods $1,2,3,5,6,7,8,9,10$ or $12$ and that these are the only periods that rational sequences $\{x_n\}_n$ can have. It is known that if we restrict our attention to positive rational values of $a$ and positive rational initial conditions the only possible periods are $1,5$ and $9$. Moreover 1-periodic and 5-periodic sequences are easily obtained. We prove that for infinitely many positive values of $a,$ positive 9-period rational sequences occur. This last result is our main contribution and answers an open question left in previous works of Bastien \& Rogalski and Zeeman. We also prove that the level sets of the invariant associated to the Lyness map is a two-parameter family of elliptic curves that is a universal family of the elliptic curves with a point of order $n, n\ge5,$ including $n$ infinity. This fact implies that the Lyness map is a universal normal form for most birrational maps on elliptic curves.

Integrability and non-integrability of periodic non-autonomous Lyness recurrences

This paper studies non-autonomous Lyness type recurrences of the form x_{n+2}=(a_n+x_n)/x_{n+1}, where a_n is a k-periodic sequence of positive numbers with prime period k. We show that for the cases k in {1,2,3,6} the behavior of the sequence x_n is simple(integrable) while for the remaining cases satisfying k not a multiple of 5 this behavior can be much more complicated(chaotic). The cases k multiple of 5 are studied separately.

Integrability and non-integrability of periodic non-autonomous Lyness recurrences (revised and enlarged version)

This paper studies non-autonomous Lyness type recurrences of the form xn+2 = (an+xn+1)=xn, where fang is a k-periodic sequence of positive numbers with primitive period k. We show that for the cases k 2 f1; 2; 3; 6g the behavior of the sequence fxng is simple (integrable) while for the remaining cases satisfying this behavior can be much more complicated (chaotic). We also show that the cases where k is a multiple of 5 present some di erent features.

On periodic solutions of 2-periodic Lyness difference equations

We study the existence of periodic solutions of the non--autonomous periodic Lyness' recurrence u_{n+2}=(a_n+u_{n+1})/u_n, where {a_n} is a cycle with positive values a,b and with positive initial conditions. It is known that for a=b=1 all the sequences generated by this recurrence are 5-periodic. We prove that for each pair (a,b) different from (1,1) there are infinitely many initial conditions giving rise to periodic sequences, and that the family of recurrences have almost all the even periods. If a is not equal to b, then any odd period, except 1, appears.

Real-time, in vivo intracellular recordings of caterpillar-induced depolarization waves in sieve elements using aphid electrodes.

Plants propagate electrical signals in response to artificial wounding. However, little is known about the electrophysiological responses of the phloem to wounding, and whether natural damaging stimuli induce propagating electrical signals in this tissue. Here, we used living aphids and the direct current (DC) version of the electrical penetration graph (EPG) to detect changes in the membrane potential of Arabidopsis sieve elements (SEs) during caterpillar wounding. Feeding wounds in the lamina induced fast depolarization waves in the affected leaf, rising to maximum amplitude (c. 60 mV) within 2 s. Major damage to the midvein induced fast and slow depolarization waves in unwounded neighbor leaves, but only slow depolarization waves in non-neighbor leaves. The slow depolarization waves rose to maximum amplitude (c. 30 mV) within 14 s. Expression of a jasmonate-responsive gene was detected in leaves in which SEs displayed fast depolarization waves. No electrical signals were detected in SEs of unwounded neighbor leaves of plants with suppressed expression of GLR3.3 and GLR3.6. EPG applied as a novel approach to plant electrophysiology allows cell-specific, robust, real-time monitoring of early electrophysiological responses in plant cells to damage, and is potentially applicable to a broad range of plant-herbivore interactions.

Landslides cause tsunami waves: insights from Aysén Fjord, Chile

On 21 April 2007, an Mw 6.2 earthquake produced an unforeseen chain of events in the Aysén fjord (Chilean Patagonia, 45.5°S). The earthquake triggered hundreds of subaerial landslides along the fjord flanks. Some of the landslides eventually involved a subaqueous component that, in turn, generated a series of displacement waves tsunami- like waves produced by the fast entry of a ubaerial landmass into a water body within the fjord [Naranjo et al., 2009; Sepúlveda and Serey, 2009; Hermanns et al., 2013]. These waves, with run-ups several meters high along the shoreline, caused 10 fatalities. In addition, they severely damaged salmon farms, which constitute the main economic activity in the region, setting free millions of cultivated salmon with still unknown ecological consequences.

Childhood epilepsy with neuropsychological regression and continuous spike waves during sleep: epilepsy surgery in a young adult.

We describe the case of a man with a history of complex partial seizures and severe language, cognitive and behavioural regression during early childhood (3.5 years), who underwent epilepsy surgery at the age of 25 years. His early epilepsy had clinical and electroencephalogram features of the syndromes of epilepsy with continuous spike waves during sleep and acquired epileptic aphasia (Landau-Kleffner syndrome), which we considered initially to be of idiopathic origin. Seizures recurred at 19 years and presurgical investigations at 25 years showed a lateral frontal epileptic focus with spread to Broca's area and the frontal orbital regions. Histopathology revealed a focal cortical dysplasia, not visible on magnetic resonance imaging. The prolonged but reversible early regression and the residual neuropsychological disorders during adulthood were probably the result of an active left frontal epilepsy, which interfered with language and behaviour during development. Our findings raise the question of the role of focal cortical dysplasia as an aetiology in the syndromes of epilepsy with continuous spike waves during sleep and acquired epileptic aphasia.

Leaf plasticity in successive selection cycles of 'Saracura' maize in response to periodic soil flooding

The objective of this work was to assess the effect of successive selection cycles on leaf plasticity of 'Saracura' maize BRS-4154 under periodical flooding in field conditions. Soil flooding started at the six-leaf stage with the application of a 20-cm depth water layer three times a week. At flowering, samples of leaves were collected and fixed. Paradermic and transverse sections were observed under photonic microscope. Several changes were observed throughout the selection cycles, such as modifications in the number and size of the stomata, higher amount of vascular bundles and the resulting decrease of the distance between them, smaller diameter of the metaxylem, decrease of cuticle and epidermis thickness, decrease of number and size of bulliform cells, increase of phloem thickness, smaller sclerenchyma area. Therefore, the successive selection cycles of 'Saracura' maize resulted in changes in the leaf anatomy, which might be favorable to the plant's tolerance to the intermittent flooding of the soil.

Simulation of surface waves in porous media

We present a novel numerical algorithm for the simulation of seismic wave propagation in porous media, which is particularly suitable for the accurate modelling of surface wave-type phenomena. The differential equations of motion are based on Biot's theory of poro-elasticity and solved with a pseudospectral approach using Fourier and Chebyshev methods to compute the spatial derivatives along the horizontal and vertical directions, respectively. The time solver is a splitting algorithm that accounts for the stiffness of the differential equations. Due to the Chebyshev operator the grid spacing in the vertical direction is non-uniform and characterized by a denser spatial sampling in the vicinity of interfaces, which allows for a numerically stable and accurate evaluation of higher order surface wave modes. We stretch the grid in the vertical direction to increase the minimum grid spacing and reduce the computational cost. The free-surface boundary conditions are implemented with a characteristics approach, where the characteristic variables are evaluated at zero viscosity. The same procedure is used to model seismic wave propagation at the interface between a fluid and porous medium. In this case, each medium is represented by a different grid and the two grids are combined through a domain-decomposition method. This wavefield decomposition method accounts for the discontinuity of variables and is crucial for an accurate interface treatment. We simulate seismic wave propagation with open-pore and sealed-pore boundary conditions and verify the validity and accuracy of the algorithm by comparing the numerical simulations to analytical solutions based on zero viscosity obtained with the Cagniard-de Hoop method. Finally, we illustrate the suitability of our algorithm for more complex models of porous media involving viscous pore fluids and strongly heterogeneous distributions of the elastic and hydraulic material properties.

J2 effect and elliptic inclined periodic orbits in the collision three-body problem

The existence of a new class of inclined periodic orbits of the collision restricted three-body problem is shown. The symmetric periodic solutions found are perturbations of elliptic kepler orbits and they exist only for special values of the inclination and are related to the motion of a satellite around an oblate planet

Interaction of Spiral Waves in the Complex Ginzburg-Landau Equation

Solutions of the general cubic complex Ginzburg-Landau equation comprising multiple spiral waves are considered, and laws of motion for the centers are derived. The direction of the motion changes from along the line of centers to perpendicular to the line of centers as the separation increases, with the strength of the interaction algebraic at small separations and exponentially small at large separations. The corresponding asymptotic wave number and frequency are also determined, which evolve slowly as the spirals move

Goya's artwork imaging with Terahertz waves

In this paper we use a Terahertz (THz) time-domain system to image and analyze the structure of an artwork attributed to the Spanish artist Goya painted in 1771. The THz images show features that cannot be seen with optical inspection and complement data obtained with X-ray imaging that provide evidence of its authenticity, which is validated by other independent studies. For instance, a feature with a strong resemblance with one of Goya"s known signatures is seen in the THz images. In particular, this paper demonstrates the potential of THz imaging as a complementary technique along with X-ray for the verification and authentication of artwork pieces through the detection of features that remain hidden to optical inspection.

Report on the Status of Findings and Recommendations from the City of Cambridge’s Periodic Examination Report dated September 5, 2014 for the period June 1, 2015 through November 30, 2015

Report on the Status of Findings and Recommendations from the City of Cambridge’s Periodic Examination Report dated September 5, 2014 for the period June 1, 2015 through November 30, 2015