Generation of very flat optical frequency combs from continuous-wave lasers using cascaded intensity and phase modulators driven by tailored radio frequency waveforms

We demonstrate a scheme, based on a cascade of lithium niobate intensity and phase modulators driven by specially tailored radio frequency waveforms to generate an optical frequency comb with very high spectral flatness. In this work we demonstrate a 10 GHz comb with ~40 lines with spectral power variation below 1-dB and ~60 lines in total. The number of lines that can be generated is limited by the power handling capability of the phase modulator, and this can be scaled without compromising the spectral flatness. Furthermore, the spectral phase of the generated combs in our scheme is almost purely quadratic which, as we will demonstrate, allows for very high quality pulse compression using only single mode fiber.Comment: 12 pages, 3 figures, replaced the older version with the published versio

The Runaway Greenhouse: A History of Water on Venus

Radiative-convective equilibrium models of planetary atmospheres are discussed for the case when the infrared opacity is due to a vapor in equilibrium with its liquid or solid phase. For a grey gas, or for a gas which absorbs at all infrared wavelengths, equilibrium is impossible when the solar constant exceeds a critical value. Equilibrium therefore requires that the condensed phase evaporates into the atmosphere. Moist adiabatic and pseudoadiabatic atmospheres in which the condensing vapor is a major atmospheric constituent are considered. This situation would apply if the solar constant were supercritical with respect to an abundant substance such as water. It is shown that the condensing gas would be a major constituent at all levels in such an atmosphere. Photodissociation of water in the primordial Venus atmosphere is discussed in this context

Fast Mesh Refinement in Pseudospectral Optimal Control

Mesh refinement in pseudospectral (PS) optimal control is embarrassingly easy --- simply increase the order $N$ of the Lagrange interpolating polynomial and the mathematics of convergence automates the distribution of the grid points. Unfortunately, as $N$ increases, the condition number of the resulting linear algebra increases as $N^2$; hence, spectral efficiency and accuracy are lost in practice. In this paper, we advance Birkhoff interpolation concepts over an arbitrary grid to generate well-conditioned PS optimal control discretizations. We show that the condition number increases only as $\sqrt{N}$ in general, but is independent of $N$ for the special case of one of the boundary points being fixed. Hence, spectral accuracy and efficiency are maintained as $N$ increases. The effectiveness of the resulting fast mesh refinement strategy is demonstrated by using \underline{polynomials of over a thousandth order} to solve a low-thrust, long-duration orbit transfer problem.Comment: 27 pages, 12 figures, JGCD April 201

Exact Analytic Solutions for the Rotation of an Axially Symmetric Rigid Body Subjected to a Constant Torque

New exact analytic solutions are introduced for the rotational motion of a rigid body having two equal principal moments of inertia and subjected to an external torque which is constant in magnitude. In particular, the solutions are obtained for the following cases: (1) Torque parallel to the symmetry axis and arbitrary initial angular velocity; (2) Torque perpendicular to the symmetry axis and such that the torque is rotating at a constant rate about the symmetry axis, and arbitrary initial angular velocity; (3) Torque and initial angular velocity perpendicular to the symmetry axis, with the torque being fixed with the body. In addition to the solutions for these three forced cases, an original solution is introduced for the case of torque-free motion, which is simpler than the classical solution as regards its derivation and uses the rotation matrix in order to describe the body orientation. This paper builds upon the recently discovered exact solution for the motion of a rigid body with a spherical ellipsoid of inertia. In particular, by following Hestenes' theory, the rotational motion of an axially symmetric rigid body is seen at any instant in time as the combination of the motion of a "virtual" spherical body with respect to the inertial frame and the motion of the axially symmetric body with respect to this "virtual" body. The kinematic solutions are presented in terms of the rotation matrix. The newly found exact analytic solutions are valid for any motion time length and rotation amplitude. The present paper adds further elements to the small set of special cases for which an exact solution of the rotational motion of a rigid body exists.Comment: "Errata Corridge Postprint" version of the journal paper. The following typos present in the Journal version are HERE corrected: 1) Definition of \beta, before Eq. 18; 2) sign in the statement of Theorem 3; 3) Sign in Eq. 53; 4)Item r_0 in Eq. 58; 5) Item R_{SN}(0) in Eq. 6

Wave modelling - the state of the art

This paper is the product of the wave modelling community and it tries to make a picture of the present situation in this branch of science, exploring the previous and the most recent results and looking ahead towards the solution of the problems we presently face. Both theory and applications are considered. The many faces of the subject imply separate discussions. This is reflected into the single sections, seven of them, each dealing with a specific topic, the whole providing a broad and solid overview of the present state of the art. After an introduction framing the problem and the approach we followed, we deal in sequence with the following subjects: (Section) 2, generation by wind; 3, nonlinear interactions in deep water; 4, white-capping dissipation; 5, nonlinear interactions in shallow water; 6, dissipation at the sea bottom; 7, wave propagation; 8, numerics. The two final sections, 9 and 10, summarize the present situation from a general point of view and try to look at the future developments

Domination in Functigraphs

Let $G_1$ and $G_2$ be disjoint copies of a graph $G$, and let $f: V(G_1) \rightarrow V(G_2)$ be a function. Then a \emph{functigraph} $C(G, f)=(V, E)$ has the vertex set $V=V(G_1) \cup V(G_2)$ and the edge set $E=E(G_1) \cup E(G_2) \cup \{uv \mid u \in V(G_1), v \in V(G_2), v=f(u)\}$. A functigraph is a generalization of a \emph{permutation graph} (also known as a \emph{generalized prism}) in the sense of Chartrand and Harary. In this paper, we study domination in functigraphs. Let $\gamma(G)$ denote the domination number of $G$. It is readily seen that $\gamma(G) \le \gamma(C(G,f)) \le 2 \gamma(G)$. We investigate for graphs generally, and for cycles in great detail, the functions which achieve the upper and lower bounds, as well as the realization of the intermediate values.Comment: 18 pages, 8 figure

Effective temperature for finite systems

Under the Ansatz that the occupation times of a system with finitely many states are given by the Gibbs distribution, an effective temperature is uniquely determined (up to a choice of scale), and may be computed de novo, without any reference to a Hamiltonian for empirically accessible systems. As an example, the calculation of the effective temperature for a classical Bose gas is outlined and applied to the analysis of computer network traffic.Comment: 9 pages, 10 figure

A Search for Scalar Chameleons with ADMX

Scalar fields with a "chameleon" property, in which the effective particle mass is a function of its local environment, are common to many theories beyond the standard model and could be responsible for dark energy. If these fields couple weakly to the photon, they could be detectable through the "afterglow" effect of photon-chameleon-photon transitions. The ADMX experiment was used in the first chameleon search with a microwave cavity to set a new limit on scalar chameleon-photon coupling excluding values between 2*10^9 and 5*10^14 for effective chameleon masses between 1.9510 and 1.9525 micro-eV.Comment: 4 pages, 3 figure

Spacecraft design project: High latitude communications satellite

The spacecraft design project was part of AE-4871, Advanced Spacecraft Design. The project was intended to provide experience in the design of all major components of a satellite. Each member of the class was given primary responsibility for a subsystem or design support function. Support was requested from the Naval Research Laboratory to augment the Naval Postgraduate School faculty. Analysis and design of each subsystem was done to the extent possible within the constraints of an eleven week quarter and the design facilities (hardware and software) available. The project team chose to evaluate the design of a high latitude communications satellite as representative of the design issues and tradeoffs necessary for a wide range of satellites. The High-Latitude Communications Satellite (HILACS) will provide a continuous UHF communications link between stations located north of the region covered by geosynchronous communications satellites, i.e., the area above approximately 60 N latitude. HILACS will also provide a communications link to stations below 60 N via a relay Net Control Station (NCS), which is located with access to both the HILACS and geosynchronous communications satellites. The communications payload will operate only for that portion of the orbit necessary to provide specified coverage

Thermoacoustic refrigeration

A new refrigerator which uses resonant high amplitude sound in inert gases to pump heat is described and demonstrated. The phasing of the thermoacoustic cycle is provided by thermal conduction. This 'natural' phasing allows the entire refrigerator to operate with only one moving part (the loudspeaker diaphragm). The thermoacoustic refrigerator has no sliding seals, requires no lubrication, uses only low-tolerance machine parts, and contains no expensive components. Because the compressor moving mass is typically small and the oscillation frequency is high, the small amount of vibration is very easily isolated. This low vibration and lack of sliding seals makes thermoacoustic refrigeration an excellent candidate for food refrigeration and commercial/residential air conditioning applications. The design, fabrication, and performance of the first practical, autonomous thermoacoustic refrigerator, which will be flown on the Space Shuttle (STS-42), are described, and designs for terrestrial applications are presented