Trapped modes along a periodic array of freely floating obstacles

We consider the coupled problem describing the motion of a linear array of three‐dimensional obstacles floating freely in a homogeneous fluid layer of finite depth. The interaction of time‐harmonic waves with the floating objects is analyzed under the usual assumptions of linear water‐wave theory. Quasi‐periodic boundary conditions and a simplified reduction scheme turn the system into a linear spectral problem for a self‐adjoint operator in Hilbert space. Based upon the operator formulation, we derive a sufficient condition for the nonemptiness of its discrete spectrum. Various examples of obstacles that generate trapped modes are given. Copyright © 2014 John Wiley & Sons, Ltd.     

Vibrations of a continuous web on elastic supports

We consider an infinite, homogenous linearly elastic beam resting on a system of linearly elastic supports, as an idealized model for a paper web in the middle of a cylinder-based dryer section. We obtain closed-form analytical expressions for the eigenfrequencies and the eigenmodes. The frequencies increase as the support rigidity is increased. Each frequency is bounded from above by the solution with absolutely rigid supports, and from below by the solution in the limit of vanishing support rigidity. Thus in a real system, the natural frequencies will be lower than predicted by commonly used models with rigid supports.     

Stability of functions in Boolean models of gene regulatory networks

Boolean networks are used to model large nonlinear systems such as gene regulatory networks. We will present results that can be used to understand how the choice of functions affects the network dynamics. The so called bias-map and its fixed points depict much of the function's dynamical role in the network. We define the concept of stabilizing functions and show that many Post and canalizing functions are also stabilizing functions. Boolean networks constructed using the same type of stabilizing functions are always stable regardless of the average in-degree of network functions. We derive the number of all stabilizing functions and find it to be much larger than the number of Post and canalizing functions. We also discuss the implementation of functions and apply the presented results to biological data that give an approximation of the distribution of regulatory functions in eucaryotic cells. We find that the obtained theoretical results on the number of active genes are biologically plausible. Finally, based on the presented results, we discuss why canalizing and Post regulatory functions seem to be common in cells.     

Optimal multiqubit operations for Josephson charge qubits

We introduce a method for finding the required control parameters for a quantum computer that yields the desired quantum algorithm without invoking elementary gates. We concentrate on the Josephson charge-qubit model, but the scenario is readily extended to other physical realizations. Our strategy is to numerically find any desired double- or triple-qubit gate. The motivation is the need to significantly accelerate quantum algorithms in order to fight decoherence.     

On Certain Extensions of a Rotation Invariant Markov Process

Let (X _t ,P ^x ) be a rotation invariant (RI) Feller process on R ^d {0}, d2. We study certain type of strong Markov extensions of (X _t ,P ^x ) to R ^d . It turns out that that the unique (RI) extension always exists and is of that type. We give a kind of quasi-ergodicy condition (E) under which the (RI) extension is the only extension of that type. A class of processes fulfilling (E) is also characterized.     

Avoiding eddy-current problems in ultra-low-field MRI with self-shielded polarizing coils

In ultra-low-field magnetic resonance imaging (ULF MRI), superconductive sensors are used to detect MRI signals typically in fields on the order of 10-100 μT. Despite the highly sensitive detectors, it is necessary to prepolarize the sample in a stronger magnetic field on the order of 10-100 mT, which has to be switched off rapidly in a few milliseconds before signal acquisition. In addition, external magnetic interference is commonly reduced by situating the ULF-MRI system inside a magnetically shielded room (MSR). With typical dipolar polarizing coil designs, the stray field induces strong eddy currents in the conductive layers of the MSR. These eddy currents cause significant secondary magnetic fields that may distort the spin dynamics of the sample, exceed the dynamic range of the sensors, and prevent simultaneous magnetoencephalography and MRI acquisitions. In this paper, we describe a method to design self-shielded polarizing coils for ULF MRI. The experimental results show that with a simple self-shielded polarizing coil, the magnetic fields caused by the eddy currents are largely reduced. With the presented shielding technique, ULF-MRI devices can utilize stronger and spatially broader polarizing fields than achievable with unshielded polarizing coils.     

Initial trace for a doubly nonlinear parabolic equation

This paper studies the Cauchy problem for a doubly nonlinear parabolic equation. The main result shows that if there is a nonnegative solution of the Cauchy problem, then the initial trace of the solution is uniquely given as a nonnegative Borel measure satisfying an exponential growth condition. This extends the known result for the heat equation to the nonlinear case.