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Mogens H Jensen

Publications and source records attributed to Mogens H Jensen.

11 recordsLinked to original sources
PubMed2006

Analytical approach to continuous and intermittent bottleneck flows.

We propose a many-particle-inspired theory for granular outflows from a hopper and for the escape dynamics through a bottleneck based on a continuity equation in polar coordinates. If the inflow is below the maximum outflow, we find an asymptotic stationary solution. If the inflow is above this value, we observe queue formation, which can be described by a shock wave equation. We also address the experimental observation of intermittent outflows, taking into account the lack of space in the merging zone by a minimum function and coordination problems by a stochastic variable. This results in avalanches of different sizes even if friction, force networks, inelastic collapse, or delay-induced stop-and-go waves are not assumed. Our intermittent flows result from a random alternation between particle propagation and gap propagation. Erratic flows in congested merging zones of vehicle traffic may be explained in a similar way.

Journal Article↗
PubMed2006

Minimal model of spiky oscillations in NF-kappaB signaling.

The NF-kappaB signaling system is involved in a variety of cellular processes including immune response, inflammation, and apoptosis. Recent experiments have found oscillations in the nuclear-cytoplasmic translocation of the NF-kappaB transcription factor [Hoffmann, A., et al. (2002) Science 298, ; Nelson, D. E., et al. (2004) Science 306, .] How the cell uses the oscillations to differentiate input conditions and send specific signals to downstream genes is an open problem. We shed light on this issue by examining the small core network driving the oscillations, which we show is designed to produce periodic spikes in nuclear NF-kappaB concentration. The presence of oscillations is extremely robust to variation of parameters, depending mainly on the saturation of the active degradation rate of IkappaB, an inhibitor of NF-kappaB. The oscillations can be used to regulate downstream genes in a variety of ways. In particular, we show that genes to whose operator sites NF-kappaB binds and dissociates fast can respond very sensitively to changes in the input signal, with effective Hill coefficients of >20.

Cytoplasm↗
PubMed2005

Diffusion, fragmentation, and coagulation processes: analytical and numerical results.

We formulate dynamical rate equations for physical processes driven by a combination of diffusive growth, size fragmentation, and fragment coagulation. Initially, we consider processes where coagulation is absent. In this case we solve the rate equation exactly leading to size distributions of Bessel type which fall off as exp(-x(3/2)) for large x values. Moreover, we provide explicit formulas for the expansion coefficients in terms of Airy functions. Introducing the coagulation term, the full nonlinear model is mapped exactly onto a Riccati equation that enables us to derive various asymptotic solutions for the distribution function. In particular, we find a standard exponential decay exp(-x) for large x and observe a crossover from the Bessel function for intermediate values of x . These findings are checked by numerical simulations, and we find perfect agreement between the theoretical predictions and numerical results.

Journal Article↗
PubMed2004

Dual multifractal spectra.

The multifractal formalism characterizes the scaling properties of a physical density rho as a function of the distance L. To each singularity alpha of the field is attributed a fractal dimension for its support f(alpha). An alternative representation has been proposed by considering the distribution of distances associated to a fixed mass. Computing these spectra for a multifractal Cantor set, it is shown that these two approaches are dual to each other, and that both spectra as well as the moment scaling exponents are simply related. We apply the same inversion formalism to exponents obtained for turbulent statistics in the Gledzer-Ohkitani-Yamada shell model and observe that the same duality relation holds here.

Journal Article↗
PubMed2003

Competition between diffusion and fragmentation: an important evolutionary process of nature.

We investigate systems of nature where the common physical processes diffusion and fragmentation compete. We derive a rate equation for the size distribution of fragments. The equation leads to a third order differential equation which we solve exactly in terms of Bessel functions. The stationary state is a universal Bessel distribution described by one parameter, which fits perfectly experimental data from two very different systems of nature, namely, the distribution of ice-crystal sizes from the Greenland ice sheet and the length distribution of alpha helices in proteins.

Crystallization↗
PubMed2003

Scaling exponent of the maximum growth probability in diffusion-limited aggregation.

An early (and influential) scaling relation in the multifractal theory of diffusion limited aggregation (DLA) is the Turkevich-Scher conjecture that relates the exponent alpha(min) that characterizes the "hottest" region of the harmonic measure and the fractal dimension D of the cluster, i.e., D=1+alpha(min). Due to lack of accurate direct measurements of both D and alpha(min), this conjecture could never be put to a serious test. Using the method of iterated conformal maps, D was recently determined as D=1.713+/-0.003. In this paper, we determine alpha(min) accurately with the result alpha(min)=0.665+/-0.004. We thus conclude that the Turkevich-Scher conjecture is incorrect for DLA.

Journal Article↗
PubMed2003

Compact phases of polymers with hydrogen bonding.

We propose an off-lattice model for a self-avoiding homopolymer chain with two different competing attractive interactions, mimicking the hydrophobic effect and the hydrogen-bond formation, respectively. By means of Monte Carlo simulations, we are able to trace out the complete phase diagram for different values of the relative strengths of the two competing interactions. For strong enough hydrogen bonding, the ground state is a helical conformation, whereas with decreasing hydrogen-bonding strength, helices get eventually destabilized at low temperature in favor of more compact conformations resembling beta sheets appearing in the native structures of proteins. For weaker hydrogen bonding helices are not thermodynamically relevant anymore.

Journal Article↗
PubMed2002

Tip splittings and phase transitions in the dielectric breakdown model: mapping to the diffusion-limited aggregation model.

We show that the fractal growth described by the dielectric breakdown model exhibits a phase transition in the multifractal spectrum of the growth measure. The transition takes place because the tip splitting of branches forms a fixed angle. This angle is eta dependent but it can be rescaled onto an "effectively" universal angle of the diffusion-limited aggregation branching process. We derive an analytic rescaling relation which is in agreement with numerical simulations. The dimension of the clusters decreases linearly with the angle and the growth becomes non-ractal at an angle close to 74 degrees (which corresponds to eta = 4.0+/-0.3).

Journal Article↗
PubMed2002

Multifractal structure of the harmonic measure of diffusion-limited aggregates.

The method of iterated conformal maps allows one to study the harmonic measure of diffusion-limited aggregates with unprecedented accuracy. We employ this method to explore the multifractal properties of the measure, including the scaling of the measure in the deepest fjords that were hitherto screened away from any numerical probing. We resolve probabilities as small as 10(-35), and present an accurate determination of the generalized dimensions and the spectrum of singularities. We show that the generalized dimensions D(q) are infinite for q<q*, where q* is of the order of -0.2. In the language of f(alpha) this means that alpha(max) is finite. The f(alpha) curve loses analyticity (the phenomenon of "phase transition") at alpha(max) and a finite value of f(alpha(max)). We consider the geometric structure of the regions that support the lowest parts of the harmonic measure, and thus offer an explanation for the phase transition, rationalizing the value of q* and f(alpha(max)). We thus offer a satisfactory physical picture of the scaling properties of this multifractal measure.

Journal Article↗
PubMed2002

Critical "dimension" in shell model turbulence.

We investigate the Gledzer-Ohkitani-Yamada (GOY) shell model within the scenario of a critical dimension in fully developed turbulence. By changing the conserved quantities, one can continuously vary an "effective dimension" between d=2 and d=3. We identify a critical point between these two situations where the flux of energy changes sign and the helicity flux diverges. Close to the critical point the energy spectrum exhibits a turbulent scaling regime followed by a plateau of thermal equilibrium. The corrections due to intermittency persist close to the critical point. We identify scaling laws and perform a rescaling argument to derive a relation between the critical exponents. We further discuss the distribution function of the energy flux.

Journal Article↗