Approximate decoherence free subspaces for distributed sensing

We consider the sensing of scalar valued fields with specific spatial dependence using a network of sensors, e.g. multiple atoms located at different positions within a trap. We show how to harness the spatial correlations to sense only a specific signal, and be insensitive to others at different positions or with unequal spatial dependence by constructing a decoherence-free subspace for noise sources at fixed, known positions. This can be extended to noise sources lying on certain surfaces, where we encounter a connection to mirror charges and equipotential surfaces in classical electrostatics. For general situations, we introduce the notion of an approximate decoherence-free subspace, where noise for all sources within some volume is significantly suppressed, at the cost of reducing the signal strength in a controlled way. We show that one can use this approach to maintain Heisenberg-scaling over long times and for a large number of sensors, despite the presence of multiple noise sources in large volumes. We introduce an efficient formalism to construct internal states and sensor configurations, and apply it to several examples to demonstrate the usefulness and wide applicability of our approach.

COMPUTATION OF GRAVITY FIELD FUNCTIONALS WITH A LOCALIZED LEVEL ELLIPSOID

The description of the earth’s gravity field is usually expressed in terms of spherical harmonic coefficients, derived from global geopotential models. These coefficients may be used to evaluate such quantities as geoid undulations, gravity anomalies, gravity disturbances, deflection of the vertical, etc. To accomplish this, a global reference normal ellipsoid, such as WGS84 and GRS80, is required to provide the computing reference surface. These global ellipsoids, however, may not always provide the best fit of the local geoid and may provide results that are aliased. In this study, a regional or localized geocentric level ellipsoid is used alongside the EGM2008 to compute gravity field functionals in the state of Johor. Residual gravity field quantities are then computed using GNSS-levelled and raw gravity data, and the results are compared with both the WGS84 and the GRS80 equipotential surfaces. It is demonstrated that regional level ellipsoids may be used to compute gravity field functionals with a better fit, provided the zero-degree spherical harmonic is considered. The resulting residual quantities are smaller when compared with those obtained with global ellipsoids. It is expected that when the remove-compute-restore method is employed with such residuals, the numerical quadrature of the Stoke’s integral may be evaluated on reduced gravity anomalies that are smoother compared to when global equipotential surfaces are used

EQUIPOTENTIAL SURFACES FOR UNIFORMLY CHARGED SYMMETRIC POLYHEDRAL CONDUCTORS

<p>In this paper, it has been explained how the equipotential surface is influenced by the shape of the symmetric polyhedral conductor and how it finally becomes spherical as it would be if the polyhedral conductor is replaced by a point charge placed at the centre of that conductor. As we move away from the polyhedral conductor the consecutive equipotential surfaces curve more at the sharp bends. A patter n is observed when the diagonal distance from the vertex of the conductor to the first occurrence of its spherical equipotential surface for all symmetric polyhedral conductors is mathematically calculated which is half of the length of its side.</p>

EQUIPOTENTIAL SURFACES FOR UNIFORMLY CHARGED SYMMETRIC POLYHEDRAL CONDUCTORS

<p>In this paper, it has been explained how the equipotential surface is influenced by the shape of the symmetric polyhedral conductor and how it finally becomes spherical as it would be if the polyhedral conductor is replaced by a point charge placed at the centre of that conductor. As we move away from the polyhedral conductor the consecutive equipotential surfaces curve more at the sharp bends. A patter n is observed when the diagonal distance from the vertex of the conductor to the first occurrence of its spherical equipotential surface for all symmetric polyhedral conductors is mathematically calculated which is half of the length of its side.</p>

COMPUTER PREDICTION OF TECHNOLOGICAL REGIMES OF RAPID CONE-SHAPED ADSORPTION FILTERS WITH CHEMICAL REGENERATION OF HOMOGENEOUS POROUS LOADS

Mathematical models for predicting technological regimes of filtration (water purification from the present impurities), backwashing, chemical regeneration and direct washing of rapid cone-shaped adsorption filters, taking into account the influence of temperature effects on the internal mass transfer kinetics at constant rates of the appropriate regimes, are formulated. Algorithms for numerical-asymptotic approximations of solutions of the corresponding nonlinear singularly perturbed boundary value problems for a model cone-shaped domain bounded by two equipotential surfaces and a flow surface are obtained. The proposed models in the complex allow computer experiments to be conducted to investigate the change of impurity concentrations in the filtration flow and on the surface of the load adsorbent, temperature of the filtration flow, filtration coefficient and active porosity along the filter height due to adsorption and desorption processes, and on their basis, to predict a good use of adsorbents and increase the protective time of rapid cone-shaped adsorption filters with chemical regeneration of homogeneous porous loads.

Differential geometry and curvatures of equipotential surfaces in the realization of the World Height System

&lt;p&gt;The notion of an equipotential surface of the Earth&amp;#8217;s gravity potential is of key importance for vertical datum definition. The aim of this contribution is to focus on differential geometry properties of equipotential surfaces and their relation to parameters of Earth&amp;#8217;s gravity field models. The discussion mainly rests on the use of Weingarten&amp;#8217;s theorem that has an important role in the theory of surfaces and in parallel an essential tie to Brun&amp;#8217;s equation (for gravity gradient) well known in physical geodesy. Also Christoffel&amp;#8217;s theorem and its use will be mentioned. These considerations are of constructive nature and their content will be demonstrated for high degree and order gravity field models. The results will be interpreted globally and also in merging segments expressing regional and local features of the gravity field of the Earth. They may contribute to the knowledge important for the realization of the World Height System.&lt;/p&gt;

Computer Prediction of Adsorption Water Purification Process in Rapid Cone-Shaped Filters

In the paper a mathematical model for computer predicting the process of adsorption purification of water from impurities in rapid filters taking into account changes in the temperature of the filtration flow along the height of the filter while observing the constant filtration rate is formulated. Analgorithm for numerically-asymptotic approximation of solution of the corresponding nonlinear singularly perturbed boundary value problem for a model region of a conical shape, bounded two equipotential surfaces and a surface flow, is developed. The proposed model allows through computer experiments to investigate changes in the characteristics of porous loads (filtration coefficients, active porosity), to predict the optimal variants for using adsorbents, and increasing the duration of the filters operation due to the choice of their shape, taking into account the effect on the process of adsorption purification ofwater not only changes in the filtration rate flow along the height of the filter, but also the temperature.