798 research outputs found
Hysteretic Transition Between States of a Filled Hexagonal Magnetic Dipole Cluster
By minimizing the magnetostatic potential energy and by finding zeros in the sum of the squares of the torques, we find the equilibrium states of six dipoles of identical strength at the vertices of a regular hexagon and a variable-strength dipole at the center. The seven dipoles spin freely about fixed axes that are perpendicular to the plane of the hexagon, with their dipole moments directed parallel to the plane. When the central dipole is weak compared with the perimeter dipoles, a ‘‘circular’’ state applies in which the perimeter dipole moments circle around the central dipole, which points toward a perimeter dipole. When the central dipole is strong, a more symmetric ‘‘dipolar’’ state applies in which the perimeter dipole moments align approximately with the field of the central dipole. Over an intermediate range of dipole strengths bounded by two critical values, both states are locally stable and the state of the system depends upon its history. Iron filings are used to observe both states in experiments on small spherical neodymium magnets. A ‘‘misaligned’’ state that is barely unstable theoretically is also observed experimentally; this state resembles the circular state except that the central dipole moment points toward a point of contact between two perimeter magnets
Hysteretic Transition Between States of a Filled Hexagonal Magnetic Dipole Cluster
By minimizing the magnetostatic potential energy and by finding zeros in the sum of the squares of the torques, we find the equilibrium states of six dipoles of identical strength at the vertices of a regular hexagon and a variable-strength dipole at the center. The seven dipoles spin freely about fixed axes that are perpendicular to the plane of the hexagon, with their dipole moments directed parallel to the plane. When the central dipole is weak compared with the perimeter dipoles, a ‘‘circular’’ state applies in which the perimeter dipole moments circle around the central dipole, which points toward a perimeter dipole. When the central dipole is strong, a more symmetric ‘‘dipolar’’ state applies in which the perimeter dipole moments align approximately with the field of the central dipole. Over an intermediate range of dipole strengths bounded by two critical values, both states are locally stable and the state of the system depends upon its history. Iron filings are used to observe both states in experiments on small spherical neodymium magnets. A ‘‘misaligned’’ state that is barely unstable theoretically is also observed experimentally; this state resembles the circular state except that the central dipole moment points toward a point of contact between two perimeter magnets
How Should We Study District Judge Decision-Making?
Part I of this Essay describes in detail the institutional setting in which district judges function and how their role differs substantially from that of appellate judges. Part II critiques the existing empirical literature’s predominant method for studying district courts—analysis of district court opinions, usually published opinions—and discuss the limitations and biases inherent in this approach. Part III then proposes a new approach to studying decision-making by district judges
Narrow Line Cooling and Momentum-Space Crystals
Narrow line laser cooling is advancing the frontier for experiments ranging
from studies of fundamental atomic physics to high precision optical frequency
standards. In this paper, we present an extensive description of the systems
and techniques necessary to realize 689 nm 1S0 - 3P1 narrow line cooling of
atomic 88Sr. Narrow line cooling and trapping dynamics are also studied in
detail. By controlling the relative size of the power broadened transition
linewidth and the single-photon recoil frequency shift, we show that it is
possible to continuously bridge the gap between semiclassical and quantum
mechanical cooling. Novel semiclassical cooling process, some of which are
intimately linked to gravity, are also explored. Moreover, for laser
frequencies tuned above the atomic resonance, we demonstrate momentum-space
crystals containing up to 26 well defined lattice points. Gravitationally
assisted cooling is also achieved with blue-detuned light. Theoretically, we
find the blue detuned dynamics are universal to Doppler limited systems. This
paper offers the most comprehensive study of narrow line laser cooling to date.Comment: 14 pages, 19 figure
Systematic study of the Sr clock transition in an optical lattice
With ultracold Sr confined in a magic wavelength optical lattice, we
present the most precise study (2.8 Hz statistical uncertainty) to-date of the
- optical clock transition with a detailed analysis of
systematic shifts (20 Hz uncertainty) in the absolute frequency measurement of
429 228 004 229 867 Hz. The high resolution permits an investigation of the
optical lattice motional sideband structure. The local oscillator for this
optical atomic clock is a stable diode laser with its Hz-level linewidth
characterized across the optical spectrum using a femtosecond frequency comb.Comment: 4 pages, 4 figures, 1 tabl
Variational data assimilation for the initial-value dynamo problem
The secular variation of the geomagnetic field as observed at the Earth's surface results from the complex magnetohydrodynamics taking place in the fluid core of the Earth. One way to analyze this system is to use the data in concert with an underlying dynamical model of the system through the technique of variational data assimilation, in much the same way as is employed in meteorology and oceanography. The aim is to discover an optimal initial condition that leads to a trajectory of the system in agreement with observations. Taking the Earth's core to be an electrically conducting fluid sphere in which convection takes place, we develop the continuous adjoint forms of the magnetohydrodynamic equations that govern the dynamical system together with the corresponding numerical algorithms appropriate for a fully spectral method. These adjoint equations enable a computationally fast iterative improvement of the initial condition that determines the system evolution. The initial condition depends on the three dimensional form of quantities such as the magnetic field in the entire sphere. For the magnetic field, conservation of the divergence-free condition for the adjoint magnetic field requires the introduction of an adjoint pressure term satisfying a zero boundary condition. We thus find that solving the forward and adjoint dynamo system requires different numerical algorithms. In this paper, an efficient algorithm for numerically solving this problem is developed and tested for two illustrative problems in a whole sphere: one is a kinematic problem with prescribed velocity field, and the second is associated with the Hall-effect dynamo, exhibiting considerable nonlinearity. The algorithm exhibits reliable numerical accuracy and stability. Using both the analytical and the numerical techniques of this paper, the adjoint dynamo system can be solved directly with the same order of computational complexity as that required to solve the forward problem. These numerical techniques form a foundation for ultimate application to observations of the geomagnetic field over the time scale of centuries
Metabolic signature of squamous cell carcinoma of the head and neck: Consequences of TP53 mutation and therapeutic perspectives
Experimental demonstration of superresolution of partially coherent light sources using parity sorting
Analyses based on quantum metrology have shown that the ability to localize
the positions of two incoherent point sources can be significantly enhanced
through the use of mode sorting. Here we theoretically and experimentally
investigate the effect of partial coherence on the sub-diffraction limit
localization of two sources based on parity sorting. With the prior information
of a negative and real-valued degree of coherence, higher Fisher information is
obtained than that for the incoherent case. Our results pave the way to
clarifying the role of coherence in quantum limited metrology
Rho-associated kinase signalling and the cancer microenvironment: novel biological implications and therapeutic opportunities
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