Emergence of a tracer source from air concentration measurements, a new strategy for linear assimilation

The measurement of atmospheric concentrations by a monitoring network is a promising tool for the identification of the widespread sources of trace species. The paper addresses the case of the species scattered linearly by a known meteorology. The question is classical: what can be said about the source from a set of measurements? Is it possible to guess from the values observed by the measurements that the source is spread close to the detectors, or that the tracer comes from a remote region? And, if the source was a point source, would it be possible to understand it by just considering these values? A part of the answers is a matter of practical sense: the resolution with which an emission can be retrieved will always be limited and probably lower for a remote region, even if the detectors and dispersion model are error free. The paper proposes a linear strategy of inference: to any set of values taken by the observed concentrations is associated linearly an estimate of the source. Doubled values lead to a doubled estimate. The method, based on adjoint techniques, is intended to optimise the resolution by quantifying, with the concept of illumination, which regions are well, poorly or not seen at all. The illumination tied to ordinary adjoint functions becomes excessive close to the detectors thus leading to inversion artefacts. This may be corrected by attributing each point of the space time domain a geometric and statistical weight. The adjoint functions are transformed. The choice of this renormalising function is constrained by an unambiguous entropic criterion preventing any overestimation of the available information that would lead to artefacts. It amounts to evenly distribute the information between the points organised with their weights as a 'known domain'. The theory is illustrated by calculations performed with the experimental source ETEX1

Inverse transport for the verification of the Comprehensive Nuclear Test Ban Treaty

An international monitoring system is being built as a verification tool for the Comprehensive Test Ban Treaty. Forty stations will measure on a worldwide daily basis the concentration of radioactive noble gases. The paper introduces, by handling preliminary real data, a new approach of backtracking for the identification of sources of passive tracers after positive measurements. When several measurements are available the ambiguity about possible sources is reduced significantly. The approach is validated against ETEX data. A distinction is made between adjoint and inverse transport shown to be, indeed, different though equivalent ideas. As an interesting side result it is shown that, in the passive tracer dispersion equation, the diffusion stemming from a time symmetric turbulence is necessarily a self-adjoint operator, a result easily verified for the usual gradient closure, but more general

Emergence of a tracer source from air concentration measurements, a new strategy for linear assimilation

International audienceThe measurement of atmospheric concentrations by a monitoring network is a promising tool for the identification of the widespread sources of trace species. The paper addresses the case of the species scattered linearly by a known meteorology. The question is classical: what can be said about the source from a set of measurements? Is it possible to guess from the values observed by the measurements that the source is spread close to the detectors, or that the tracer comes from a remote region? And, if the source was a point source, would it be possible to understand it by just considering these values? A part of the answers is a matter of practical sense: the resolution with which an emission can be retrieved will always be limited and probably lower for a remote region, even if the detectors and dispersion model are error free. The paper proposes a linear strategy of inference: to any set of values taken by the observed concentrations is associated linearly an estimate of the source. Doubled values lead to a doubled estimate. The method, based on adjoint techniques, is intended to optimise the resolution by quantifying, with the concept of illumination, which regions are well, poorly or not seen at all. The illumination tied to ordinary adjoint functions becomes excessive close to the detectors thus leading to inversion artefacts. This may be corrected by attributing each point of the space time domain a geometric and statistical weight. The adjoint functions are transformed. The choice of this renormalising function is constrained by an unambiguous entropic criterion preventing any overestimation of the available information that would lead to artefacts. It amounts to evenly distribute the information between the points organised with their weights as a "known domain". The theory is illustrated by calculations performed with the experimental source ETEX1

Rebuilding sources of linear tracers after atmospheric concentration measurements

International audienceThe identification of widespread sources of passive tracers out of atmospheric concentration measurements has become an important challenge of modern meteorology. The paper proposes some mathematical tracks to address the reconstruction of the complex space-time geometry of the sources of linear tracers. The methods are based upon the use of retroplumes. The inverse problem is addressed in a deterministic non statistical frame. The information obtained by local measurements is spread by introducing the concept of illumination. The constraint that the source is non negative is also addressed. The experimental source ETEX1 is rebuilt in order to evaluate an impulse response of the algorithms

Rebuilding sources of linear tracers after atmospheric concentration concentration

International audienceThe identification of widespread sources of passive tracers out of atmospheric concentration measurements has become an important challenge of modern meteorology. The paper proposes some mathematical tracks to address this reconstruction of the complex space-time geometry of the sources. The methods are based upon the use of retroplumes. The inverse problem is addressed in a deterministic non statistical frame. The information obtained by local measurements is spread by introducing the concept of illumination. The constraint that the source to be rebuilt is non negative is also addressed. The experimental source ETEX1 is rebuilt in order to evaluate an impulse response of the algorithms

Emergence of a linear tracer source from air concentration measurements

International audienceThe measurement of atmospheric concentrations by a monitoring network is potentially a useful tool investigated for the identification of the widespread sources of trace species. The paper addresses inversion strategies using base functions multiplicatively deduced from the concentrations adjoint to the measurements. This follows the concept of illumination: the various regions are well, poorly or not seen at all. With ordinary adjoint functions the illumination becomes excessive close to the detectors. This may be corrected by attributing each point of the space time domain a geometric weight. After stating the statistical implications, the choice of this renormalising function is shown to be constrained by an unambiguous formal criterion. The expectable values of the measurements are distinguished from the measurement errors. The entropic nature of the criterion is explained; it amounts to evenly distribute the information between the points organised with their weights as a "known domain" describing the influence of the measurements. Finally the criterion is shown to coincide with the definition of the pure states of quantum statistics, and this interpretation is investigated to describe the influence of the measurement uncertainties on the quality of a source estimate. The theory is illustrated by calculations performed with the experimental source ETEX1

Adjoint backtracking for the verification of the Comprehensive Test Ban Treaty

International audienceAn international monitoring system is being built as a verification tool for the Comprehensive Test Ban Treaty. Forty stations will measure on a worldwide daily basis the concentration of radioactive noble gases. The paper introduces, by handling preliminary real data, a new approach of backtracking for the identification of sources after positive measurements. When several measurements are available the ambiguity about possible sources is reduced significantly. As an interesting side result it is shown that diffusion in the passive tracer dispersion equation is necessarily a self-adjoint operator

Inverse transport for the verification of the Comprehensive Nuclear Test Ban Treaty

International audienceAn international monitoring system is being built as a verification tool for the Comprehensive Test Ban Treaty. Forty stations will measure on a worldwide daily basis the concentration of radioactive noble gases. The paper introduces, by handling preliminary real data, a new approach of backtracking for the identification of sources of passive tracers after positive measurements. When several measurements are available the ambiguity about possible sources is reduced significantly. The approach is validated against ETEX data. A distinction is made between adjoint and inverse transport shown to be, indeed, different though equivalent ideas. As an interesting side result it is shown that, in the passive tracer dispersion equation, the diffusion stemming from a time symmetric turbulence is necessarily a self-adjoint operator, a result easily verified for the usual gradient closure, but more general

Generalized quantum potentials in scale relativity

We first recall that the system of fluid mechanics equations (Euler and continuity) that describes a fluid in irrotational motion subjected to a generalized quantum potential (in which the constant is no longer reduced to the standard quantum constant hbar) is equivalent to a generalized Schrodinger equation. Then we show that, even in the case of the presence of vorticity, it is also possible to obtain, for a large class of systems, a Schrodinger-like equation of the vectorial field type from the continuity and Euler equations including a quantum potential. The same kind of transformation also applies to a classical charged fluid subjected to an electromagnetic field and to an additional potential having the form of a quantum potential. Such a fluid can therefore be described by an equation of the Ginzburg-Landau type, and is expected to show some superconducting-like properties. Moreover, a Schrodinger form can be obtained for the fluctuating rotational motion of a solid. In this case the mass is replaced by the tensor of inertia, and a generalized form of the quantum potential is derived. We finally reconsider the case of a standard diffusion process, and we show that, after a change of variable, the diffusion equation can also be given the form of a continuity and Euler system including an additional potential energy. Since this potential is exactly the opposite of a quantum potential, the quantum behavior may be considered, in this context, as an anti-diffusion.Comment: 33 pages, submitted for publicatio

Analysis of Locally Coupled 3D Manipulation Mappings Based on Mobile Device Motion

We examine a class of techniques for 3D object manipulation on mobile devices, in which the device's physical motion is applied to 3D objects displayed on the device itself. This "local coupling" between input and display creates specific challenges compared to manipulation techniques designed for monitor-based or immersive virtual environments. Our work focuses specifically on the mapping between device motion and object motion. We review existing manipulation techniques and introduce a formal description of the main mappings under a common notation. Based on this notation, we analyze these mappings and their properties in order to answer crucial usability questions. We first investigate how the 3D objects should move on the screen, since the screen also moves with the mobile device during manipulation. We then investigate the effects of a limited range of manipulation and present a number of solutions to overcome this constraint. This work provides a theoretical framework to better understand the properties of locally-coupled 3D manipulation mappings based on mobile device motion