# Alexandre GondranEcole Nationale de l'Aviation Civile | ENAC · MAIAA

Alexandre Gondran

PhD

## About

68

Publications

13,325

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445

Citations

## Publications

Publications (68)

We present a new interpretation of quantum mechanics, called the double-scale theory, which expends on the de Broglie-Bohm (dBB) theory. It is based, for any quantum system, on the simultaneous existence of two wave functions in the laboratory reference frame : an external wavefunction and an internal one. The external wave function corresponds to...

We present a semiclassical gravity in the framework of the double scale theory, a new interpretation of quantum mechanics which expands on the de Broglie-Bohm (dBB) theory. In this interpretation, any quantum system is associated with two wave functions, one external and one internal. The external wave function drives the center-of-mass, as in the...

The Gate Allocation Problem (GAP) is one of the numerous operational problems that all busy airports have to handle and to optimize every day. In this article, we focus on two important objectives for the GAP: the robustness and the taxiing times. We first analyze a basic model which optimizes the robustness of the solution to the GAP and propose a...

One shows that the Feynman’s Path Integral designed for quantum mechanics has an analogous in classical mechanics, the so-called (min, +) Path Integral. This former is build on (min, +)-algebra and (min, +)-analysis which permit to handle in a linear way non-linear problems occurring in mathematical physics. The Hamilton-Jacobi equations and their...

One of the key challenges towards more automation in Air Traffic Control is the resolution of en-route conflicts. In this article we present a generic framework for the conflict resolution problem that clearly separates the trajectory and conflict models from the resolution. It is able to handle any kind of maneuver and detection models, though we...

We propose an interpretative framework for quantum mechanics corresponding to the specifications of Louis de Broglie's double-solution theory. The principle is to decompose the evolution of a quantum system into two wave functions: an external wave function corresponding to the evolution of its center of mass and an internal wave function correspon...

The Minimum Sum Coloring Problem is a variant of the Graph Vertex Coloring Problem, for which each color has a weight. This paper presents a new way to find a lower bound of this problem, based on a relaxation into an integer partition problem with additional constraints. We improve the lower bound for 18 graphs of standard benchmark DIMACS, and pr...

In this paper, a new approach is presented to qualify or not, a solution found by a heuristic for a potential optimal solution. Our approach is based on the following observation: for a minimization problem, the number of admissible solutions decreases with the value of the objective function. Concerning the Graph Coloring Problem (GCP), we confirm...

In this paper, we present a new approach which qualifies or not a solution found by a heuristic as a potential optimal solution. Our approach is based on the following observation: for a minimization problem, the number of admissible solutions decreases with the value of the objective function. For the Graph Coloring Problem (GCP), we confirm this...

Graph vertices coloring with a given number of colors is a famous and
much-studied NP-complete problem. The best methods to solve this problem are
hybrid algorithms such as memetic algorithms [Galinier99, Lu10, Wu12] or
quantum annealing [Titiloye11a, Titiloye11b, Titiloye12]. Those hybrid
algorithms use a powerful local search inside a population-...

One develops a new mathematical tool, the complex (min, +)-analysis which permits to define a new variational calculus analogous to the classical one (Euler-Lagrange and Hamilton Jacobi equations), but which is well-suited for functions defined from C^n to C. We apply this complex variational calculus to Born-Infeld theory of electromagnetism and s...

One develops a new mathematical tool, the complex (min, +)-analysis which permits to define a new variational calculus analogous to the classical one (Euler-Lagrange and Hamilton Jacobi equations), but which is well-suited for functions defined from ℂ n to ℂ. We apply this complex variational calculus to Born-Infeld theory of electromagnetism and s...

Optimization problems are often compared to mountain climbing. In particular, the classical Hill Climber is a so used local search. In this paper we propose to explore further the analogy with climbing a mountain, not alone as it is generally the case but in rope team. Indeed, for difficult problems a single climber (heuristic) can easily be trappe...

Playing the game of heads or tails in zero gravity demonstrates that there exists a contextual "measurement" in classical mechanics. When the coin is flipped, its orientation is a continuous variable. However, the "measurement" that occurs when the coin is caught by clapping two hands together gives a discrete value (heads or tails) that depends on...

Recently, for spinless non-relativistic particles, Norsen (Found Phys 40:1858–1884, 2010) and Norsen et al. (Synthese 192:3125–3151, 2015) show that in the de Broglie–Bohm interpretation it is possible to replace the wave function in the configuration space by single-particle wave functions in physical space. In this paper, we show that this replac...

In this paper we propose an extended particle model whose evolution is
deterministic. In dimension 2, the extended particle is represented by four
points that define a small elastic string that vibrates, alternating between a
creation process and an annihilation process. First we show how the spin and
the Heisenberg uncertainty relations emerge fro...

Recently, for spinless non-relativisttic particles, Norsen, Marian and Otiols
show that in the de Broglie-Bohm interpretation it is possible to replace the
wave function in the configuration space by single-particle wave functions in
physical space. In this paper, we show that this replacment of the wave
function in the configuration space by singl...

This paper presents an effective memetic approach \(HEAD\) designed for coloring difficult graphs. In this algorithm a powerful tabu search is used inside a very specific population of individuals. Indeed, the main characteristic of \(HEAD\) is to work with a population of only two individuals. This provides a very simple algorithm with neither sel...

In the 1927 Solvay conference, three apparently irreconcilable interpretations of the quantum mechanics wave function were presented: the pilot-wave interpretation by de Broglie, the soliton wave interpretation by Schrödinger and the Born statistical rule by Born and Heisenberg. In this paper, we demonstrate the complementarity of these interpretat...

We propose a pedagogical presentation of measurement in the de Broglie-Bohm
interpretation. In this heterodox interpretation, the position of a quantum
particle exists and is piloted by the phase of the wave function. We show how
this position explains determinism and realism in the three most important
experiments of quantum measurement: double-sl...

In this paper we propose a deterministic and realistic quantum mechanics
interpretation which may correspond to Louis de Broglie's "double solution
theory". Louis de Broglie considers two solutions to the Schr\"odinger
equation, a singular and physical wave u representing the particle (soliton
wave) and a regular wave representing probability (stat...

The new OFDMA-based technology is referred to as the Evolved UMTS Terrestrial Radio Access (E-UTRA) through the Long Term Evolution (LTE) system. This paper proposes to add Self-Organizing functionalities on the antenna architecture, so that the network will be more responsive to changes in traffic and environment. This paper also shows the interes...

Some real life problems can be modeled as a graph coloring problem. The main idea consists of partitioning all vertices into k independent sets. The best known approaches consist of hybridize genetic algorithm with a local search in a memetic way. One of the key feature is to find the best balance between intensification and diversification. In thi...

We recently proposed a definition of indiscernability in classical
mechanics for identical particles prepared in the same manner and
without interaction between them [1]. In this paper, we generalize the
indiscernability to identical particles in collision. We first consider
the elastic collision of pairs of classical particles. We then study the
c...

First, we show that there exists in classical mechanics three actions
corresponding to different boundary conditions: two well-known actions, the
Euler-Lagrange classical action S_cl(x,t;x_0), which links the initial position
x_0 and its position x at time t, the Hamilton-Jacobi action S(x,t), which
links a family of particles of initial action S_0...

The currently emerging Long Term Evolution 4G-LTE cellular networks are based on new technique of transmission called the Orthogonal Frequency Division Multiple Access (OFDMA). This paper shows the interest of robust approach due to the uncertainty of traffic distribution. First, we develop and validate the interference model based on SINR metric f...

As acknowledged by the SESAR program, current ATC systems must be drastically improved to accommodate the predicted traffic growth in Europe. This study aims at assessing the performance of 4D-trajectory planning and strategic deconfliction, two of the key concepts identified to meet SESAR capacity objectives. Among the possible degrees of freedom,...

To overcome the traffic growth predicted by current ATM research programs in Europe and the US, we propose a new model to avoid conflicts based on small speed regulations, as depicted in the ERASMUS project [6], with interval conflict constraints as in [2]. After a first conflict detection phase, a centralized solver computes new RTAs to dynamicall...

In quantum information, the qubit is not represented by a full spinor in
space and in time as the z spinor below: Ψ0(z) =
(2πσ20)-12e-z24σ20(cosθ02e-iϕ02sinθ02eiϕ02)
but by a simplified spinor without spatial extension Ψ =
(cosθ02e-iϕ02sinθ02eiϕ02)
This simplification is the basis of our first criticism of the quantum
computer concept. Indeed, the...

As acknowledged by the SESAR program, current ATC systems must be drastically improved to accommodate the predicted traffic growth in Europe. This study aims at assessing the performance of 4Dtrajectory planning and strategic deconfliction, two of the key concepts identified to meet SESAR capacity objectives. Among the possible degrees of freedom,...

La demande en trafic dans les réseaux de radiocommunication a augmenté d'une manière vertigineuse ces dernières années [3]. Dans les réseaux LTE (Long Term Evolution), plusieurs recherches sur le paramétrage des antennes [1, 2] ont été effectuées pour répondre aux besoins des utilisateurs et augmenter les performances du système. Diverses combinais...

The Long Term Evolution (LTE) cellular network is based on Orthogonal Frequency Division Multiple Access (OFDMA) to meet several services and performance requirement. This paper shows the interest of robustness approach due to the uncertainty of traffic distribution while evaluating some antenna parameters. We use a greedy algorithm with different...

We present an analytical solution to the decoherence time for the spin measurement and the diagonalization of the density matrix of spin variables in the Stern-Gerlach experiment. This solution requires the calculation of the Pauli spinor with a spatial extension, which is not found in quantum mechanics
textbooks. With this full spinor and the mea...

The purpose of this paper is to evaluate the impact of frequency parameter settings while evaluating interference model in LTE (Long Term Evolution); the work is applied on a network. We develop and validate the interference model based on SINR which is used by 3GPP (3rd Group Partnership Project) to estimate the quality of signal received by UE (U...

We study, in the semi-classical approximation, the convergence of the quantum
density and the quantum action, solutions to the Madelung equations, when the
Planck constant h tends to 0. We find two different solutions which depend to
the initial density . In the first case where the initial quantum density is a
classical density rho_0(x), the quant...

Les réseaux de communication mobile doivent écouler un trafic de plus en plus important. Pour ce faire, les réseaux auto-organisés SON (Self Organizing Networks) proposent des solutions qui visent à augmenter leur capacité en s'adaptant le mieux possible à la demande des clients. Dans ce cadre, la future norme de téléphonie mobile LTE [1] inclut de...

We introduce into classical mechanics the concept of non-discerned particles for particles that are identical, non-interacting and prepared in the same way. The non-discerned particles correspond to an action and a density which satisfy the statistical Hamilton-Jacobi equations and allow to explain the Gibbs paradox. On the other hand, a discerned...

In this paper we present a study of mobile connectivity for vehicular network in urban environment. The considered area is a real map divided into equally sized cells, each characterized by a set of information including the type of structure in the cell, cell altitude and cell attraction for vehicles. These characteristics are taken into account i...

We introduce into classical mechanics the concept of non-discerned particles for particles that are identical, non-interacting and prepared in the same way. The non-discerned particles correspond to an action and a density which satisfy the statistical Hamilton-Jacobi equations and allow to explain the Gibbs paradox in a simple manner. On the other...

In this paper we attempt to answer the following question : how to deploy a WLAN in order to guarantee the requested Quality of Service (QoS) while reducing the location error ? Such a problem includes two aspects : WLAN planning and positioning error reduction. To provide users an optimal wireless access to their local network, WLAN planning not o...

We show how energy flow lines answer the question about diffraction phenomena
presented in 1818 by the French Academy: "deduce by mathematical induction, the
movements of the rays during their crossing near the bodies". This provides a
complementary answer to Fresnel's wave theory of light. A numerical simulation
of these energy flow lines proves t...

RÉSUMÉ. On montre que la faisabilité de l'ordinateur quantique dépend de l'interprétation de la mécanique quantique: faisable dans l'interprétation de Copenhague où la mécanique quantique est com-plète et où le qubit suffit à décrire complètement le système quantique; infaisable dans l'interprétation de Broglie-Bohm où la mécanique quan-tique est i...

Frequency assignment is one of the main issues in radio networks planning. The multiple interferences are seldom taken into account in literature. There is not a framework with their modeling. A hypergraph modeling of the network gives a more realistic representation of this phenomenon. We generalize the T -coloring problem for graphs to hypergraph...

In this paper we study a two-step version of EPR-B experiment, the Bohm version of the Einstein-Podolsky-Rosen experiment. Its theoretical resolution in space and time enables us to refute the classic "impossibility" to decompose a pair of entangled atoms into two distinct states, one for each atom. We propose a new causal interpretation of the EPR...

In this article we address the frequency management during WLAN planning. Frequency management refers to channels interference and SINR computation. We propose a new approach where location selection and frequency assignment are tackled together during WLAN planning process. Two steps characterize this approach. Firstly we use all the available cha...

L'affectation de fréquences est un problème majeur pour la planification de réseaux radio. Il a pour objectif de limiter les interférences qui dégradent la Qualité de Service du réseau en limitant sa couverture et sa capacité. Cependant, il n'est souvent pas possible d'éviter les interférences, le but est donc de les répartir au mieux dans l'espace...

We present a numerical simulation of the double slit interference experiment realized by F. Shimizu, K. Shimizu and H. Takuma with ultracold atoms. We show how the Feynman path integral method enables the calculation of the time-dependent wave function. Because the evolution of the probability density of the wave packet just after it exits the slit...

Le problème de planification de réseaux WLAN consiste d'une part à positionner et à paramétrer des antennes dans un bâtiment et d'autre part à leur affecter une fréquence afin d'offrir aux clients un accès sans fil au réseau local. Le réseau ainsi construit doit répondre à des critères de couverture et de qualité de service, tout en minimisant le c...

We are looking for the answers to some questions which naturally arise when one starts to think about possible influence of the size of a particle on the transmission, diffraction and interference pattern behind an interference grating.

Optimal planning of wireless networks is one of the most fundamental problems in WLAN design. This paper discusses the organisation of BSS in WLAN extended service set planning for large-scale deployment. We take advantage of a new geometric criterion to evaluate the coverage quality and apply them to WLAN planning. The obtained results show that u...

The two relevant stages in cellular network planning process arc the location selection of the transmitters and the frequency assignment. In the literature WLAN planning approach treats successively those two stages. In this article we propose a new approach where location selection and frequency assignment are tackled together during WLAN planning...

Experiment{Fabre_1983} shows that Rydberg atoms do not pass through 1
micronmeter width slits if their principal quantum number is rather large(n >
60). Thus, the particle density measured after the slits is null while the wave
function calculated after the slits is not. This experiment is in contradiction
with the Born interpretation (the square o...

The Wireless Local Area Networks (WLAN) large-scale deployment is a difficult parameterisation work and it requires automatic planning process with formal models. This paper proposes a solution to this matter and provides a model integrating all useful parameters to estimate the location and parameter settings of such network while optimising netwo...

The standard quantum theory has not taken into account the size of quantum particles, the latter being implicitly treated as material points. The recent interference experiments of Zeilinger [3] with large molecules like fullerenes and the thought experiments of Bozic et al [7] with asymmetrical Young slits make it possible today to take into accou...

The Stern-Gerlach experiment is the fundamental experiment in order to exhibit the quantization of spin and understand the measurement problem in quantum mechanics. However, although the Stern-Gerlach experiment plays an essential role in the teaching of quantum mechanics, no complete analysis of this experiment using Pauli spinors is presented in...

We revisit the definition of the probability current for the Schrodinger equation. First, we prove that the Dirac probability currents of stationary wave functions of the hydrogen atom and of the isotrop harmonic oscillator are not nil and correspond to a circular rotation of the probability. Then, we recall how it is necessary to add to classical...

La planification de réseaux WLAN nécessite d'optimiser conjointement le placement des émetteurs ( Access Point ) et l'affectation des fréquences. Cet article s'intéresse à l'impact de la planification des fréquences sur la capacité d'un réseau IEEE 802.11. La distrib ution des clients d'un AP selon leurs débits physiques détermine la capacité de l'...