Preben Alstrøm

Perturbation theory of parametrically driven capillary waves at low viscosity

We present a critical review of the Hamiltonian and the Lagrangian theories of pattern formation in driven capillary waves at low viscosity and high aspect ratio. We construct a Hamiltonian perturbation theory in the spirit of Milners (1991) formulation, and derive the amplitude equations and their coefficients relevant at the onset of surface waves. Our presentation is detailed, and we carefully point out the differences between our results for the nonlinear coefficients and the results obtained by others. From our standing wave analysis we find that the square pattern is subcritical. Among the supercritical standing wave patterns, we find that the eightfold quasi-crystalline pattern, observed by Christiansen et al . (1992) and by Bosch (1995), is more stable than both rolls and hexagons. We outline the high-aspect-ratio experimental results obtained so far, and discuss them in the light of the theory.

Dissipation and ordering in capillary waves at high aspect ratios

We present an experimental study of high-aspect-ratio Faraday waves. We have measured the dispersion relation and the damping rate, together with the critical amplitude for the primary instability for a wide range of frequencies. We find that our results are well explained by the linear theory, if damping from the moving contact line is considered in addition to the bulk damping. Just above the primary instability a seemingly disordered stationary state is observed. We argue that this state is a superposition of normal modes. Approximately 5% above the primary instability this state breaks down in favour of a quasi-crystalline state. This result is discussed, partly in the light of the recent third-order nonlinear theory.

Gene expression profiling of two distinct neuronal populations in the rodent spinal cord

Background In the field of neuroscience microarray gene expression profiles on anatomically defined brain structures are being used increasingly to study both normal brain functions as well as pathological states. Fluorescent tracing techniques in brain tissue that identifies distinct neuronal populations can in combination with global gene expression profiling potentially increase the resolution and specificity of such studies to shed new light on neuronal functions at the cellular level. Methodology/Principal Findings We examine the microarray gene expression profiles of two distinct neuronal populations in the spinal cord of the neonatal rat, the principal motor neurons and specific interneurons involved in motor control. The gene expression profiles of the respective cell populations were obtained from amplified mRNA originating from 50–250 fluorescently identified and laser microdissected cells. In the data analysis we combine a new microarray normalization procedure with a conglomerate measure of significant differential gene expression. Using our methodology we find 32 genes to be more expressed in the interneurons compared to the motor neurons that all except one have not previously been associated with this neuronal population. As a validation of our method we find 17 genes to be more expressed in the motor neurons than in the interneurons and of these only one had not previously been described in this population. Conclusions/Significance We provide an optimized experimental protocol that allows isolation of gene transcripts from fluorescent retrogradely labeled cell populations in fresh tissue, which can be used to generate amplified aRNA for microarray hybridization from as few as 50 laser microdissected cells. Using this optimized experimental protocol in combination with our microarray analysis methodology we find 49 differentially expressed genes between the motor neurons and the interneurons that reflect the functional differences between these two cell populations in generating and transmitting the motor output in the rodent spinal cord.

Self-diffusion and relative diffusion in defect turbulence

Abstract We consider the motion of particles and scalar flow in the defect-turbulent regime of the complex Ginzburg-Landau field. We find that the particle motion is diffusion-like at large time scales, whereas the motion is dominated by trapping of particles by defects of the field at short time scales. Consequently the diffusion constant is constrained. For relative motion of two paricles we find that at a relative distance s the distribution of d s 2 d t is exponential rather than Gaussian as would be the case for Brownian motion.

Phase transition in an elementary probabilistic cellular automaton

Cellular automata exhibit a large variety of dynamical behaviors, from fixed-point convergence and periodic motion to spatio-temporal chaos. By introducing probabilistic interactions, and regarding the asymptotic density Φ of non-quiescent cell states as an order parameter, phase transitions may be identified from a quiescent phase with Φ = 0 to a chaotic phase with non-zero Φ. We consider an elementary one-dimensional probabilistic cellular automaton (PCA) with deterministic limits given by the quiescent rule 0, the rule 72 that evolves into a non-trivial fixed point, and the chaotic rules 18 and 90. Despite the simplicity of the rules, the PCA shows a surprising number of transition phenomena. We identify ‘second-order’ phase transitions from Φ = 0 to Φ > 0 with static and dynamic exponents that differ from those of directed percolation. Moreover, we find that the non-trivial fixed-point rule 72 is a singular point in PCA space.

Expectation and conditioning

We present a dynamical model that embodies both classical and instrumental conditioning paradigms in the same framework. The model is based on the formation of expectations of stimuli and of rewards. The expectations of stimuli are formed in a recurrent process called expectation learning in which one activity pattern evokes another. The expectation of rewards or punishments (motivation) is modelled using reinforcement learning.

Collective dynamics of coupled modulated oscillators with random pinning

Abstract We present a study of a large pool of coupled oscillators in the presence of a modulated external field. Random distributed pinning phases introduce a disordering element. We find that phase locking of the oscillator community to the harmonics of the frequency of the applied field always is associated with a complete loss of coherence between the oscillators. The phase-lock regions form islands in parameter space, the size of which decreases for increasing coupling strength to vanish completely at a critical value. By stability considerations the shape of the phase-locked islands is reduced to a two points boundary problem of a first order non-autonomous differential equation and an approximation is found for high frequencies. The structure of the coherent states is discussed and a first order approximation is found in the limit of strong coherence.

Relative diffusion in a chaotic system: Capillary waves in the Faraday experiment

Abstract We present experimental results for the motion of particles moving on capillary ripples. The ripples are formed on the surface of a fluid undergoing vertical oscillations. We find an anomalous relative diffusion: particles initially close separate in time, moving more rapidly apart as their distance increases. This result is surprising, as self-diffusion measurements indicate that single particles essentially move like random walkers.

Reliability of neural encoding

The reliability with which a neuron is able to create the same firing pattern when presented with the same stimulus is of critical importance to the understanding of neuronal information processing. We show that reliability is closely related to the process of phaselocking. Experimental results for the reliability of neuronal firing in the spinal cord of rat are presented and compared to results from an integrate and fire model.

Emergence of memory

We propose a new self-organizing mechanism behind the emergence of memory in which temporal sequences of stimuli are transformed into spatial activity patterns. In particular, the memory emerges despite the absence of temporal correlations in the stimuli. This suggests that neural systems may prepare a spatial structure for processing information before the information itself is available. A simple model illustrating the mechanism is presented based on three principles: 1) Competition between neural units, 2) Hebbian plasticity, and 3) recurrent connections.