Dragos-Victor Anghel | Horia Hulubei National Institute for Physics and Nuclear Engineering Bucharest (original) (raw)
Papers by Dragos-Victor Anghel
Physica D: Nonlinear Phenomena, Jul 1, 2022
The parity violation in nuclear reactions led to the discovery of the new class of toroidal multi... more The parity violation in nuclear reactions led to the discovery of the new class of toroidal multipoles. Since then, it was observed that toroidal multipoles are present in the electromagnetic structure of systems at all scales, from elementary particles, to solid state systems and metamaterials. The toroidal dipole T (the lowest order multipole) is the most common. In quantum systems, this corresponds to the toroidal dipole operatorT, with the projectionsTi (i = 1, 2, 3) on the coordinate axes. Here we analyze a quantum particle in a system with cylindrical symmetry, which is a typical system in which toroidal moments appear. We find the expressions for the Hamiltonian, momenta, and toroidal dipole operators in adequate curvilinear coordinates, which allow us to find analytical expressions for the eigenfunctions of the momentum operators. While the toroidal dipole is hermitian, it is not self-adjoint, but in the new set of coordinates the operatorT3 splits into two components, one of which is (only) hermitian, whereas the other one is self-adjoint. The self-adjoint component is the one which is physically significant and represents an observable. Furthermore, we numerically diagonalize the Hamiltonian and the toroidal dipole operator and find their eigenfunctions and eigenvalues. We write the partition function and calculate the thermodynamic quantities for a system of ideal particles on a torus. Beside proving that the toroidal dipole is self-adjoint and therefore an observable (a finding of fundamental relevance) such systems open up the possibility of making metamaterials which exploit the quantization and the quantum properties of the toroidal dipoles.
Physical review, Mar 15, 2022
We investigate reorientation effects under external periodic drive in the nanomagnet dynamics cou... more We investigate reorientation effects under external periodic drive in the nanomagnet dynamics coupled to a Josephson junction. The Kapitsa pendulum is introduced as a mechanical analog to this system and we demonstrate the reorientation of the easy axis of the nanomagnet. The magnetic field generated by the Josephson junction and external drive plays the role of the oscillating force of the suspension point in the Kapitsa pendulum. The high frequency oscillations change the orientation of the magnetic moment. The magnetic field of the quasiparticle current determines the frequency dependence of the magnetic moment's orientation. We obtain simple analytical formulas for the stable position of the magnetic moment, both under the external periodic drive and without it. The influence of external periodic drive on the voltage of complete reorientation have been demonstrated.
Physical review applied, Feb 12, 2020
We investigate theoretically the possibility of using the cold-electron bolometer (CEB) as a coun... more We investigate theoretically the possibility of using the cold-electron bolometer (CEB) as a counter for 1 cm wavelength (30 GHz) photons. To reduce the flux of photons from the environment, which interact with the detector, the bath temperature is assumed to be below 50 mK. At such temperatures, the time interval between two subsequent photons of 30 GHz that hit the detector is more than 100 hours, on average, for a frequency window of 1 MHz. Such temperatures allow the observation of the physically significant photons produced in rare events, like the axions conversion (or Primakoff conversion) in magnetic field. We present the general formalism for the detector's response and noise, together with numerical calculations for proper experimental setups. We observe that the current-biased regime is favorable, due to lower noise, and allows for the photons counting at least below 50 mK. For the experimental setups investigated here, the voltage-biased CEBs may also work as photons counters, but with less accuracy and, eventually, may require smaller volumes of the normal metal island.
arXiv (Cornell University), Jul 20, 2023
We investigate resonance phenomena in a system consisting of a nanomagnet coupled to a Josephson ... more We investigate resonance phenomena in a system consisting of a nanomagnet coupled to a Josephson junction under external periodic drive. The coupling in the system leads to appearance of additional resonance peaks whose properties depend on the periodic signal and Josephson junction dynamics. In the linear regime, we derive an analytical description of the resonance phenomena which is then confirmed by numerical simulations. This analytical method is universal and can be also applied to Josephson junctions with anomalous phase shift in current phase relation. This work provides a new method of controlling the resonances of hybrid structures, which may be interesting for applications.
ABSTRACT After a very brief introduction to the concept of fractional exclusion statistics (FES),... more ABSTRACT After a very brief introduction to the concept of fractional exclusion statistics (FES), introduced by Haldane in Phys. Rev. Lett. 67, 937 (1991), I shall present some recent results regarding the basic properties of this statistics. These properties have been overlooked for almost two decades and because of that, the application of FES to concrete physical systems was, to a certain degree, arbitrary. Essentially, the FES is a generalization of the Pauli Exclusion Principle which allows one to describe systems of interacting particles (bosons or fermions) as systems of "ideal" particles, but which obey a more peculiar type of statistics. In the second part of the paper I shall present some application of FES by analyzing concrete systems of interacting particles.
arXiv (Cornell University), Apr 18, 2012
Journal of physics, Feb 27, 2012
I discuss in parallel two universal phenomena: the independence of statistics of the heat capacit... more I discuss in parallel two universal phenomena: the independence of statistics of the heat capacity and entropy of ideal gases of the same, constant, density of states, on one hand, and the independence of statistics of the heat and entropy transport through one-dimensional channels, on the other hand. I show that there is a close similarity between the microscopic explanations of each of these phenomena.
Physics Letters, Dec 1, 2013
Fractional exclusion statistics (FES) is a generalization of the Bose and Fermi statistics. Typic... more Fractional exclusion statistics (FES) is a generalization of the Bose and Fermi statistics. Typically, systems of interacting particles are described as ideal FES systems and the properties of the FES systems are calculated from the properties of the interacting systems. In this paper I reverse the process and I show that a FES system may be described in general as a gas of quasiparticles which obey Bose or Fermi distributions; the energies of the newly defined quasiparticles are calculated starting from the FES equations for the equilibrium particle distribution. In the end I use a system in the effective mass approximation as an example to show how the procedure works.
Physica D: Nonlinear Phenomena, Mar 1, 2023
arXiv (Cornell University), Dec 8, 2019
We analyze the chain fountain effect-the chain siphoning when falling from a container onto the f... more We analyze the chain fountain effect-the chain siphoning when falling from a container onto the floor. We argue that the main reason for this effect is the inertia of the chain, whereas the momentum received by the beads of the chain from the bottom of the container (typically called "kicks") plays no significant role. The inertia of the chain leads to an effect similar to pulling the chain over a pulley placed up in the air, above the container. In the model used before by the majority of researchers (the so called "scientific consensus"), it was assumed that up to half of the mechanical work done by the tension in the chain may be wasted when transformed into kinetic energy during the pickup process. This prevented the chain to rise unless the energy transfer in the pickup process is improved by "kicks" from the bottom of the container. Here we show that the "kicks" are unnecessary and both, energy and momentum are conserved-as they should be, in the absence of dissipation-if one properly considers the tension and the movement of the chain. By doing so, we conclude that the velocity acquired by the chain is high enough to produce the fountain effect. Simple experiments validate our model and certain configurations produce the highest chain fountain, although "kicks" are impossible.
EPL, Jun 1, 2011
I analyse the transport of particles of arbitrary statistics (Bose, Fermi and fractional exclusio... more I analyse the transport of particles of arbitrary statistics (Bose, Fermi and fractional exclusion statistics) through one-dimensional (1D) channels. Observing that the particle, energy, entropy and heat fluxes through the 1D channel are similar to the particle, internal energy, entropy and heat capacity of a quantum gas in a two-dimensional (2D) flat box, respectively, I write analytical expressions for the fluxes at arbitrary temperatures. Using these expressions, I show that the heat and entropy fluxes are independent of statistics at any temperature, and not only in the low temperature limit, as it was previously known. From this perspective, the quanta of heat conductivity represents only the low temperature limit of the 1D channel heat conductance and is equal (up to a multiplicative constant equal to the Plank constant times the density of states at the Fermi energy) to the universal limit of the heat capacity of quantum gases. In the end I also give a microscopic proof for the universal temperature dependence of the entropy and heat fluxes through 1D channels.
Journal of physics, May 21, 1997
EPL, Apr 1, 2010
I introduce an ansatz for the exclusion statistics parameters of fractional exclusion statistics ... more I introduce an ansatz for the exclusion statistics parameters of fractional exclusion statistics (FES) systems and I apply it to calculate the statistical distribution of particles from both, bosonic and fermionic perspectives. Then, to check the applicability of the ansatz, I calculate the FES parameters in three well-known models: in a Fermi liquid type of system, a one-dimensional quantum systems described in the thermodynamic Bethe ansatz and quasiparticle excitations in the fractional quantum Hall (FQH) systems. The FES parameters of the first two models satisfy the ansatz, whereas those of the third model, although close to the form given by the ansatz, represent an exception. With this ocasion I also show that the general properties of the FES parameters, deduced elsewhere (EPL 87, 60009, 2009), are satisfied also by the parameters of the FQH liquid.
Journal of Physics A, Nov 6, 2007
I discuss Haldane's concept of generalised exclusion statistics (Phys. Rev. Lett. 67, 937, 1991) ... more I discuss Haldane's concept of generalised exclusion statistics (Phys. Rev. Lett. 67, 937, 1991) and I show that it leads to inconsistencies in the calculation of the particle distribution that maximizes the partition function. These inconsistencies appear when mutual exclusion statistics is manifested between different subspecies of particles in the system. In order to eliminate these inconsistencies, I introduce new mutual exclusion statistics parameters, which are proportional to the dimension of the Hilbert sub-space on which they act. These new definitions lead to properly defined particle distributions and thermodynamic properties. In another paper (arXiv:0710.0728) I show that fractional exclusion statistics manifested in general systems with interaction have these, physically consistent, statistics parameters.
Physica Scripta, Nov 1, 2012
I show that if the total energy of a system of interacting particles may be written as a sum of q... more I show that if the total energy of a system of interacting particles may be written as a sum of quasiparticle energies, then the system of quasiparticles can be viewed in general as an ideal gas with fractional exclusion statistics (FES). The general method for calculating the FES parameters is also provided. The interacting particle system cannot be described as an ideal gas of Bose and Fermi quasiparticles except in trivial situations.
arXiv (Cornell University), Jan 14, 2021
The quantum operatorT3, corresponding to the projection of the toroidal moment on the z axis, adm... more The quantum operatorT3, corresponding to the projection of the toroidal moment on the z axis, admits several self-adjoint extensions, when defined on the whole R 3 space.T3 commutes withL3 (the projection of the angular momentum operator on the z axis) and they have what we call a natural set of coordinates, denoted (k, u, φ), where φ is the azimuthal angle. The second set of natural coordinates is (k1, k2, u), where k1 = k cos φ, k2 = k sin φ. In both sets these coordinates, the operators get the simple formsT3 ≡ −i ∂/∂u andL3 = −i ∂/∂φ. In both sets,T3 = −i ∂/∂u, so any operator that is a function of k and the partial derivatives with respect to the natural variables (k, u, φ) commute withT3 andL3. Similarly, operators that are functions of k1, k2, and the partial derivatives with respect to k1, k2, and u commute withT3. Therefore, we introduce here the operatorŝ p k ≡ −i ∂/∂k,p (k1) ≡ −i ∂/∂k1, andp (k2) ≡ −i ∂/∂k2 and express them in the (x, y, z) coordinates. One may also invert the relations and write the typical operators, like the momentump ≡ −i ∇ or the kinetic energŷ H0 ≡ 2 ∆/(2m) in terms of the "toroidal" operatorsT3,p (k) ,p (k1) ,p (k2) , and, eventually,L3. The formalism may be applied to specific physical systems, like nuclei, condensed matter systems, or metamaterials. We exemplify it by calculating the momentum operator and the free particle Hamiltonian in terms of natural coordinates in a thin torus, where the general relations get considerably simplified.
Jetp Letters, 2019
The appearance of parametric resonance and the excitation of a longitudinal plasma wave in a syst... more The appearance of parametric resonance and the excitation of a longitudinal plasma wave in a system of coupled Josephson junctions with topologically trivial and nontrivial barriers have been demonstrated. The voltage at resonance as a function of the dissipation parameter has a minimum at which the parametric resonance condition changes from to , where is the Josephson frequency and is the frequency of the formed longitudinal plasma wave. The position of this minimum for the system with nontrivial barriers is shifted from that for the system with trivial barriers. This shift can be used to identify the appearance of Majorana states.
Epj Web of Conferences, 2016
Physica D: Nonlinear Phenomena, Jul 1, 2022
The parity violation in nuclear reactions led to the discovery of the new class of toroidal multi... more The parity violation in nuclear reactions led to the discovery of the new class of toroidal multipoles. Since then, it was observed that toroidal multipoles are present in the electromagnetic structure of systems at all scales, from elementary particles, to solid state systems and metamaterials. The toroidal dipole T (the lowest order multipole) is the most common. In quantum systems, this corresponds to the toroidal dipole operatorT, with the projectionsTi (i = 1, 2, 3) on the coordinate axes. Here we analyze a quantum particle in a system with cylindrical symmetry, which is a typical system in which toroidal moments appear. We find the expressions for the Hamiltonian, momenta, and toroidal dipole operators in adequate curvilinear coordinates, which allow us to find analytical expressions for the eigenfunctions of the momentum operators. While the toroidal dipole is hermitian, it is not self-adjoint, but in the new set of coordinates the operatorT3 splits into two components, one of which is (only) hermitian, whereas the other one is self-adjoint. The self-adjoint component is the one which is physically significant and represents an observable. Furthermore, we numerically diagonalize the Hamiltonian and the toroidal dipole operator and find their eigenfunctions and eigenvalues. We write the partition function and calculate the thermodynamic quantities for a system of ideal particles on a torus. Beside proving that the toroidal dipole is self-adjoint and therefore an observable (a finding of fundamental relevance) such systems open up the possibility of making metamaterials which exploit the quantization and the quantum properties of the toroidal dipoles.
Physical review, Mar 15, 2022
We investigate reorientation effects under external periodic drive in the nanomagnet dynamics cou... more We investigate reorientation effects under external periodic drive in the nanomagnet dynamics coupled to a Josephson junction. The Kapitsa pendulum is introduced as a mechanical analog to this system and we demonstrate the reorientation of the easy axis of the nanomagnet. The magnetic field generated by the Josephson junction and external drive plays the role of the oscillating force of the suspension point in the Kapitsa pendulum. The high frequency oscillations change the orientation of the magnetic moment. The magnetic field of the quasiparticle current determines the frequency dependence of the magnetic moment's orientation. We obtain simple analytical formulas for the stable position of the magnetic moment, both under the external periodic drive and without it. The influence of external periodic drive on the voltage of complete reorientation have been demonstrated.
Physical review applied, Feb 12, 2020
We investigate theoretically the possibility of using the cold-electron bolometer (CEB) as a coun... more We investigate theoretically the possibility of using the cold-electron bolometer (CEB) as a counter for 1 cm wavelength (30 GHz) photons. To reduce the flux of photons from the environment, which interact with the detector, the bath temperature is assumed to be below 50 mK. At such temperatures, the time interval between two subsequent photons of 30 GHz that hit the detector is more than 100 hours, on average, for a frequency window of 1 MHz. Such temperatures allow the observation of the physically significant photons produced in rare events, like the axions conversion (or Primakoff conversion) in magnetic field. We present the general formalism for the detector's response and noise, together with numerical calculations for proper experimental setups. We observe that the current-biased regime is favorable, due to lower noise, and allows for the photons counting at least below 50 mK. For the experimental setups investigated here, the voltage-biased CEBs may also work as photons counters, but with less accuracy and, eventually, may require smaller volumes of the normal metal island.
arXiv (Cornell University), Jul 20, 2023
We investigate resonance phenomena in a system consisting of a nanomagnet coupled to a Josephson ... more We investigate resonance phenomena in a system consisting of a nanomagnet coupled to a Josephson junction under external periodic drive. The coupling in the system leads to appearance of additional resonance peaks whose properties depend on the periodic signal and Josephson junction dynamics. In the linear regime, we derive an analytical description of the resonance phenomena which is then confirmed by numerical simulations. This analytical method is universal and can be also applied to Josephson junctions with anomalous phase shift in current phase relation. This work provides a new method of controlling the resonances of hybrid structures, which may be interesting for applications.
ABSTRACT After a very brief introduction to the concept of fractional exclusion statistics (FES),... more ABSTRACT After a very brief introduction to the concept of fractional exclusion statistics (FES), introduced by Haldane in Phys. Rev. Lett. 67, 937 (1991), I shall present some recent results regarding the basic properties of this statistics. These properties have been overlooked for almost two decades and because of that, the application of FES to concrete physical systems was, to a certain degree, arbitrary. Essentially, the FES is a generalization of the Pauli Exclusion Principle which allows one to describe systems of interacting particles (bosons or fermions) as systems of "ideal" particles, but which obey a more peculiar type of statistics. In the second part of the paper I shall present some application of FES by analyzing concrete systems of interacting particles.
arXiv (Cornell University), Apr 18, 2012
Journal of physics, Feb 27, 2012
I discuss in parallel two universal phenomena: the independence of statistics of the heat capacit... more I discuss in parallel two universal phenomena: the independence of statistics of the heat capacity and entropy of ideal gases of the same, constant, density of states, on one hand, and the independence of statistics of the heat and entropy transport through one-dimensional channels, on the other hand. I show that there is a close similarity between the microscopic explanations of each of these phenomena.
Physics Letters, Dec 1, 2013
Fractional exclusion statistics (FES) is a generalization of the Bose and Fermi statistics. Typic... more Fractional exclusion statistics (FES) is a generalization of the Bose and Fermi statistics. Typically, systems of interacting particles are described as ideal FES systems and the properties of the FES systems are calculated from the properties of the interacting systems. In this paper I reverse the process and I show that a FES system may be described in general as a gas of quasiparticles which obey Bose or Fermi distributions; the energies of the newly defined quasiparticles are calculated starting from the FES equations for the equilibrium particle distribution. In the end I use a system in the effective mass approximation as an example to show how the procedure works.
Physica D: Nonlinear Phenomena, Mar 1, 2023
arXiv (Cornell University), Dec 8, 2019
We analyze the chain fountain effect-the chain siphoning when falling from a container onto the f... more We analyze the chain fountain effect-the chain siphoning when falling from a container onto the floor. We argue that the main reason for this effect is the inertia of the chain, whereas the momentum received by the beads of the chain from the bottom of the container (typically called "kicks") plays no significant role. The inertia of the chain leads to an effect similar to pulling the chain over a pulley placed up in the air, above the container. In the model used before by the majority of researchers (the so called "scientific consensus"), it was assumed that up to half of the mechanical work done by the tension in the chain may be wasted when transformed into kinetic energy during the pickup process. This prevented the chain to rise unless the energy transfer in the pickup process is improved by "kicks" from the bottom of the container. Here we show that the "kicks" are unnecessary and both, energy and momentum are conserved-as they should be, in the absence of dissipation-if one properly considers the tension and the movement of the chain. By doing so, we conclude that the velocity acquired by the chain is high enough to produce the fountain effect. Simple experiments validate our model and certain configurations produce the highest chain fountain, although "kicks" are impossible.
EPL, Jun 1, 2011
I analyse the transport of particles of arbitrary statistics (Bose, Fermi and fractional exclusio... more I analyse the transport of particles of arbitrary statistics (Bose, Fermi and fractional exclusion statistics) through one-dimensional (1D) channels. Observing that the particle, energy, entropy and heat fluxes through the 1D channel are similar to the particle, internal energy, entropy and heat capacity of a quantum gas in a two-dimensional (2D) flat box, respectively, I write analytical expressions for the fluxes at arbitrary temperatures. Using these expressions, I show that the heat and entropy fluxes are independent of statistics at any temperature, and not only in the low temperature limit, as it was previously known. From this perspective, the quanta of heat conductivity represents only the low temperature limit of the 1D channel heat conductance and is equal (up to a multiplicative constant equal to the Plank constant times the density of states at the Fermi energy) to the universal limit of the heat capacity of quantum gases. In the end I also give a microscopic proof for the universal temperature dependence of the entropy and heat fluxes through 1D channels.
Journal of physics, May 21, 1997
EPL, Apr 1, 2010
I introduce an ansatz for the exclusion statistics parameters of fractional exclusion statistics ... more I introduce an ansatz for the exclusion statistics parameters of fractional exclusion statistics (FES) systems and I apply it to calculate the statistical distribution of particles from both, bosonic and fermionic perspectives. Then, to check the applicability of the ansatz, I calculate the FES parameters in three well-known models: in a Fermi liquid type of system, a one-dimensional quantum systems described in the thermodynamic Bethe ansatz and quasiparticle excitations in the fractional quantum Hall (FQH) systems. The FES parameters of the first two models satisfy the ansatz, whereas those of the third model, although close to the form given by the ansatz, represent an exception. With this ocasion I also show that the general properties of the FES parameters, deduced elsewhere (EPL 87, 60009, 2009), are satisfied also by the parameters of the FQH liquid.
Journal of Physics A, Nov 6, 2007
I discuss Haldane's concept of generalised exclusion statistics (Phys. Rev. Lett. 67, 937, 1991) ... more I discuss Haldane's concept of generalised exclusion statistics (Phys. Rev. Lett. 67, 937, 1991) and I show that it leads to inconsistencies in the calculation of the particle distribution that maximizes the partition function. These inconsistencies appear when mutual exclusion statistics is manifested between different subspecies of particles in the system. In order to eliminate these inconsistencies, I introduce new mutual exclusion statistics parameters, which are proportional to the dimension of the Hilbert sub-space on which they act. These new definitions lead to properly defined particle distributions and thermodynamic properties. In another paper (arXiv:0710.0728) I show that fractional exclusion statistics manifested in general systems with interaction have these, physically consistent, statistics parameters.
Physica Scripta, Nov 1, 2012
I show that if the total energy of a system of interacting particles may be written as a sum of q... more I show that if the total energy of a system of interacting particles may be written as a sum of quasiparticle energies, then the system of quasiparticles can be viewed in general as an ideal gas with fractional exclusion statistics (FES). The general method for calculating the FES parameters is also provided. The interacting particle system cannot be described as an ideal gas of Bose and Fermi quasiparticles except in trivial situations.
arXiv (Cornell University), Jan 14, 2021
The quantum operatorT3, corresponding to the projection of the toroidal moment on the z axis, adm... more The quantum operatorT3, corresponding to the projection of the toroidal moment on the z axis, admits several self-adjoint extensions, when defined on the whole R 3 space.T3 commutes withL3 (the projection of the angular momentum operator on the z axis) and they have what we call a natural set of coordinates, denoted (k, u, φ), where φ is the azimuthal angle. The second set of natural coordinates is (k1, k2, u), where k1 = k cos φ, k2 = k sin φ. In both sets these coordinates, the operators get the simple formsT3 ≡ −i ∂/∂u andL3 = −i ∂/∂φ. In both sets,T3 = −i ∂/∂u, so any operator that is a function of k and the partial derivatives with respect to the natural variables (k, u, φ) commute withT3 andL3. Similarly, operators that are functions of k1, k2, and the partial derivatives with respect to k1, k2, and u commute withT3. Therefore, we introduce here the operatorŝ p k ≡ −i ∂/∂k,p (k1) ≡ −i ∂/∂k1, andp (k2) ≡ −i ∂/∂k2 and express them in the (x, y, z) coordinates. One may also invert the relations and write the typical operators, like the momentump ≡ −i ∇ or the kinetic energŷ H0 ≡ 2 ∆/(2m) in terms of the "toroidal" operatorsT3,p (k) ,p (k1) ,p (k2) , and, eventually,L3. The formalism may be applied to specific physical systems, like nuclei, condensed matter systems, or metamaterials. We exemplify it by calculating the momentum operator and the free particle Hamiltonian in terms of natural coordinates in a thin torus, where the general relations get considerably simplified.
Jetp Letters, 2019
The appearance of parametric resonance and the excitation of a longitudinal plasma wave in a syst... more The appearance of parametric resonance and the excitation of a longitudinal plasma wave in a system of coupled Josephson junctions with topologically trivial and nontrivial barriers have been demonstrated. The voltage at resonance as a function of the dissipation parameter has a minimum at which the parametric resonance condition changes from to , where is the Josephson frequency and is the frequency of the formed longitudinal plasma wave. The position of this minimum for the system with nontrivial barriers is shifted from that for the system with trivial barriers. This shift can be used to identify the appearance of Majorana states.
Epj Web of Conferences, 2016
Research Square, 2020
We analyze the evolution of the COVID19 pandemics and show that the basic compartmental SIR model... more We analyze the evolution of the COVID19 pandemics and show that the basic compartmental SIR model cannot explain the data, some characteristic time series being by more than an order of magnitude different from the fit function over significant parts of the documented time interval. To correct this large discrepancy, we amend the SIR model by assuming that there is a relatively large population that was infected but was not tested and confirmed. This assumption qualitatively changes the fitting possibilities of the model and, despite its simplicity, in most cases, all the time series can be quite well reproduced. Nevertheless, in some cases (i.e., countries or regions) the estimated susceptible population decreases too fast. In such a case, the observed dynamic is only due to the transitions between the two infected compartments–the confirmed infected and the unconfirmed infected –and the rate of closing the cases (by recovery or death) in the confirmed infected compartment. Our analysis proves that the number of infected people is significantly larger than the one recorded and we provide a method to estimate it. We also discuss some relevant extensions of this model, to improve the interpretation and the fitting of the data.
arXiv:1912.08682v3, 2019
We analyse the chain fountain effect-the chain siphoning when falling from a container onto the f... more We analyse the chain fountain effect-the chain siphoning when falling from a container onto the floor. We argue that the main reason for this effect are the inertial forces that appear in the chain and not the momentum received by the beads of the chain from the bottom of the container, as it was considered before. The inertia of the chain leads to an effect similar to pulling the chain over a pulley placed up in the air, above the container. This effect have been overlooked until now because of the method of calculating the chain velocity. In the method used before, the momentum conservation was apparently imposed, which led to the apparent dissipa-tion of half of the energy of the chain. Because of this large "dissipation", this approach cannot explain the formation of the fountain effect unless part of the "wasted" energy is recovered in the form of "kicks" from the bottom of the container. Here we show that in a correct approach, if there is no explicit dissipation, then both the momentum and the energy are conserved and therefore the velocity of the chain is high enough to produce the fountain effect without relying on eventually unimportant effects, such as "kicks" from the container. We propose an experiment, which may validate our model by producing the highest fountain chain, while eliminating the kicks the previous model relied upon. We also analyse the equations of motion and observe that the stationary solution is unstable. For this reason, the stationary solution is not expected to be formed in an experiment, but the trajectory of the chain should rather fluctuate around it. Whether the fluctuating trajectory averages to the stationary solution or not, remains to be studied.
arXiv:1912.08682, 2019
We analyse the chain fountain effect -- the chain siphoning, when falling from a container onto t... more We analyse the chain fountain effect -- the chain siphoning, when falling from a container onto the floor.
We argue that the main reason for this effect are the inertial forces that appear in the chain (like the centrifugal forces) and not the momentum received by the beads of the chain from the bottom of the container. The centrifugal force leads to an effect similar to pulling the chain over a pulley placed up in the air, above the beaker. We also analyse the equations of motion and the stationary solution. We conclude that the stationary solution is unstable and any disturbance tends to be amplified -- until it is constrained by the lateral rigidity of the chain and the geometry of the experiment, in general. For this reason, the stationary solution is not expected to be formed in an experiment, but the chain should rather have a fluctuating trajectory. Whether the fluctuating trajectory averages to the stationary solution is not clear and remains to be studied.
arXiv, 2019
We analyse the chain fountain effect-the chain siphoning, when falling from a container onto the ... more We analyse the chain fountain effect-the chain siphoning, when falling from a container onto the floor. We argue that the main reason for this effect are the inertial forces that appear in the chain (like the centrifugal forces) and not the momentum received by the beads of the chain from the bottom of the container. The centrifugal force leads to an effect similar to pulling the chain over a pulley placed up in the air, above the beaker. We also analyse the equations of motion and the stationary solution. We conclude that the stationary solution is unstable and any disturbance tends to be amplified-until it is constrained by the lateral rigidity of the chain and the geometry of the experiment, in general. For this reason, the stationary solution is not expected to be formed in an experiment, but the chain should rather have a fluctuating trajectory. Whether the fluctuating trajectory averages to the stationary solution is not clear and remains to be studied.
We examine the equilibrium solutions of the BCS theory of superconductivity in the low temperatur... more We examine the equilibrium solutions of the BCS theory of superconductivity in the low temperature limit, allowing the attraction band to be asymmetric with respect to the chemical potential of the system µR. If we denote by µ the middle of the attraction band, we observe that the super-conducting phase is formed only if |µR − µ| < 2∆0, where ∆0 is the energy gap at zero temperature in the standard BCS theory. If |µR − µ| < 2∆0, the system of equations which give the energy gap has two solutions for each value of µR − µ: one with ∆(T = 0) = ∆0 and another one, with ∆(T = 0) < ∆0 (∆(T = 0) is the energy gap at 0 K). If 0 < |µR − µ| < 2∆0, a quasiparticle imbalance appears in equilibrium. In the " standard BCS limit, " which is µR → µ, beside the standard solution ∆(T = 0) = ∆0, we find another one, with ∆(T = 0) = ∆0/3 and nonzero quasiparticle population. The formalism takes into account in a consistent way the variation of the total number of particles with the population of the quasiparticle states.