Approximation of the Invariant Measure for the Stochastic Navier-Stokes (2009)
Kolmogorov's statistical theory of turbulence is based on the existence of the invariant measure of the Navier-Stokes flow. Recently the existence of the invariant measure was established in the...
The Existence and Uniqueness of Turbulent Solutions of the Stochastic Navier-Stokes Equation (2008)
The existence and uniqueness of solutions of the Navier-Stokes equation driven with additive noise in three dimensions is proven, in the presence of a strong uni-directional mean flow with some...
Modeling and Simulations of the Spawning Migration of Pelagic Fish (2008)
Barbaro, Alethea B. T., Einarsson, Baldvin, Birnir, Bjorn, Sigurðsson, Sven Ã., Valdimarsson, Héðinn, Pálsson, Ãlafur K., ...
We model the spawning migration of the Icelandic capelin stock using an interacting particle model with added environmental fields. Without artificial forcing terms or a homing instinct, we...
Meanderings of fluid streams on acrylic surfaces, driven by external noise (2008)
Birnir, Bjorn, Mertens, Keith, Putkaradze, Vakhtang, Vorobieff, Peter
A stream of fluid flowing down a partially wetting inclined plane usually meanders, unless the volume flow rate is maintained at a highly constant value. However, fluctuations in the flow rate are...
The Dynamics of Myxobacteria Life Cycle (2008)
Hendrata, Melisa, Birnir, Bjorn
We develop the off-lattice model to simulate the life cycle of Myxococcus xanthus. When the food is abundant, they grow as swarms that spread away from the colony. In this stage, their movement and...
Parallel Modeling of Fish Interactions (2008)
Youseff, Lamia, Barbaro, Alethea, Trethewey, Peterson F, Birnir, Bjorn, Gilbert, J R
This paper summarizes work on a parallel algorithm for an interacting particle model, derived from the model by Czirok, Vicsek, et. al. [13] [3] [14] [4] [5]. Our model is particularly geared toward...
Discrete and continuous models of the dynamics of pelagic fish: application to the capelin (2008)
Barbaro, Alethea, Taylor, Kirk, Trethewey, Peterson F, Youseff, Lamia, Birnir, Bjorn
In this paper, we study simulations of the schooling and swarming behavior of a mathematical model for the motion of pelagic fish. We use a derivative of a discrete model of interacting particles...
The existence of solutions describing the turbulent flow in rivers is proven. The existence of an associated invariant measure describing the statistical properties of this one dimensional turbulence...
Turbulence of a Unidirectional Flow (2008)
Recent advances in the theory of turbulent solutions of the Navier-Stokes equations are discussed and the existence of their associated invariant measures. The statistical theory given by the...
Turbulence of a Unidirectional Flow (2007)
Recent advances in the theory of turbulent solutions of the Navier-Stokes equations are discussed and the existence of their associated invariant measures. The statistical theory given by the...
Some existence results for the Navier-Stokes equation driven by heat conduction (2007)
The Navier-Stokes equation driven by heat conduction is studied. As a prototype we consider Rayleigh-B'enard convection, in the Boussinesq approximation. Under a large aspect ratio assumption,...
Alisher S. Abdullayev, Daljit Ahluwalia, Mark J. Ablowitz, Bjorn Birnir
This paper presents a direct analog of the Borg-Levinson theorem on the recovery of a potential from the sequence of eigenvalues and norming constants for differential equations of the form
this paper the following theorem will be proven.
A Model for Aperiodicity in Earthquakes (2007)
Erickson, Brittany, Birnir, Bjorn, Lavallée, Daniel
Conditions under which a single oscillator model coupled with Dieterich-Ruina's rate and state dependent friction exhibits chaotic dynamics is studied. Properties of spring-block models are...
Barbaro, Alethea, Birnir, Bjorn, Taylor, Kirk
In this paper, we study simulations of the schooling and swarming behavior of a mathematical model for the motion of pelagic fish. We use a derivative of a discrete model of interacting particles...
An ODE Model of the Motion of Pelagic Fish (2007)
A system of ordinary differential equations (ODEs) is derived from a discrete system of Vicsek, Czir\'ok et al. 1995, describing the motion of a school of fish. Classes of linear and stationary...
Derivation of the Viscous Moore-Greitzer Equation for Aeroengine Flow (2007)
Birnir, Bjorn, Hou, Songming, Wellander, Niklas
The viscous Moore-Greitzer equation modeling the airflow through the compression system in turbomachines, such as a jet engine, is derived using a scaled Navier-Stokes equation. The method utilizes a...
Shocks in the Evolution of an Eroding Channel (2006)
Welsh , Edward, Birnir, Bjorn, Bertozzi, Andrea L.
Analysis of an evolution model for a river channel shows how three types of shocks determine the profile of the channel. This model shows that in a young river channel, evolution is driven by white...
The Stochastic Theory of Fluvial Landsurfaces (2004)
Birnir, Bjorn, Feldman, Raisa, Hernandez, Jorge, Smith, Terence R
A stochastic theory of fluvial landsurfaces is developed for transport-limited erosion, using well-established models for the water and sediment fluxes. The mathematical models and analysis is...
A Hopf bifurcation with a strong incommensurate frequency response in quantum wells (2001)
Batista, Adriano A., Birnir, Bjorn, Tamborenea, Pablo I.
The behavior of delta-doped wide quantum well heterostructures in the presence of intense far-infrared radiation is studied using semiconductor Bloch equations. A quantum well is designed where one...
Basic Dynamical Systems Control of Aeroengine Flow (2000)
Birnir, Bjorn, Hauksson, Hoskuldur A.
The notions of basic controllability and basic control are defined using dynamical systems theory of partial differential equations. A quadratic optimal control of the linearized viscous...
The low-dimensional flow on the basic attractor of the viscous Moore-Greitzer equation (1999)
Bjorn Birnir, Hoskuldur Ari Hauksson
An explicit formula for traveling wave solutions of the viscous Moore-Greitzer equation is given. These traveling waves describe stall in jet engines. The formula yields a one parameter family of...