We report the observation and quantitative measurements of the parametric resonance of a two-degree-of-freedom harmonic oscillator made of two coupled pendula. When varying the length of one of the pendula, we parametrically excite the whole set. The frequency of this excitation can be tuned and its depth ajusted, enabling us to draw a frequency-depth Cartesian diagram in which the oscillation behaviour, namely finiteness or exponential divergence, can be plotted. As in the well-known case of the one-degree-of-freedom oscillator, the stability and instability domains are demarcated by a tongue centred at twice the oscillator's free frequency. But in the two-degree-of-freedom oscillator case, this tongue has a three-tip fine structure, two tips corresponding to the free oscillator's eigenfrequencies and an extra tip corresponding to the average of both eigenfrequencies. This situation is unravelled theoretically using a classical adaptation of a formalism introduced in quantum optics by Glauber.

We report the first quantitative measurements of the resonance frequencies of a torus of fluid confined in a horizontal Hele-Shaw cell. By using the unwetting property of a metal liquid, we are able to generate a stable torus of fluid with an arbitrary aspect ratio. When subjected to vibrations, the torus displays azimuthal patterns at its outer periphery. These lobes oscillate radially, and their number n depends on the forcing frequency. We report the instability "tongues" of the patterns up to n = 25. These resonance frequencies are well explained by adapting to a fluid torus the usual drop model of Rayleigh. This approach could be applied to the modeling of large-scale structures arisen transiently in vortex rings in various domains.

Clusters of magnetic nanoparticles have received considerable interest in various research fields. Their capacity to generate heat under an alternating magnetic field has recently opened the way to applications such as cancer therapy by hyperthermia. This work is an attempt to investigate the collective effects of interacting dipoles embedded in magnetic nano-particles (MNP) to predict their thermal dissipation with a liquid. We first present a general approach, based on the tracking of the microscopic dipole fluctuations, to access to the dissipation spectra of any spatial distribution of MNPs. Without any other assumption that the linear response regime, it is shown that increasing the particle concentration (dipolar interactions) dramatically diminishes and blueshifts the dissipation processes. This effect originates in a predominance of the coupling energy over the Brownian torques, which create a long-range ordering that saturates the response of the system to an external field. Consequently, the particle density is of fundamental importance to the control of the absorption of electromagnetic energy and its subsequent dissipation in the form of heat.

In its simplest form the magnetoelastic buckling instability refers to the sudden bending transition of an elastic rod experiencing a uniform induction field applied at a normal angle with respect to its long axis. This fundamental physics phenomenon was initially documented in 1968, and, surprisingly, despite many refinements, a gap has always remained between the observations and the theoretical expectations. Here, we first renew the theory with a simple model based on the assumption that the magnetization follows the rod axis as soon as it bends. We demonstrate that the magnetoelastic buckling corresponds to a classical Landau second-order transition. Our model yields a solution for the critical field as well as the shape of the deformed rods which we compare with experiments on flexible ferromagnetic nickel rods at the centimeter scale. We also report this instability at the micrometer scale with specially designed rods made of nanoparticles. We characterized our samples by determining all of the relevant parameters (radius, length, Young modulus, magnetic susceptibility) and, using these values, we found that the theory fits extremely well the experimental results for both systems without any adjustable parameter. The superparamagnetic feature of the microrods also highlights the fact that ferromagnetic systems break the symmetry before the buckling. We propose a magnetic "stick-slip" model to explain this peculiar feature, which was visible in past reports but never detailed.

Recent developments in magnetic resonance imaging (MRI) have led the community to consider more complex nanostructures than the regular superparamagnetic iron oxide nanoparticles (NPs) as potential efficient contrast agents. These nanostructures present a magnetic dynamical behavior that may stand beyond the superparamagnetic regime and then affect the proton relaxation in a way that is not described by the existing models. Here, we focus on the longitudinal relaxation rate R-1 = 1/T-1 and revisit the seminal model of relaxation in order to consider any dynamical behavior of the NP magnetic moment. Our new model is validated experimentally, reproducing the nuclear magnetic relaxation dispersion (NMRD) profiles of colloidal NPs in the two extreme dynamical regimes, the superparamagnetic one and the rigid dipole one. In particular, it predicts an unexpected low field contribution of the transverse component of the NP magnetic moment to the proton relaxation. This new contribution accounts for the disappearance of the high field R-1 maximum when the dynamics of the magnetic moment slows down

Cellular processing of nanomaterials may affect their physical properties at the root of various biomedical applications. When nanoparticles interact with living cells, their spatial distribution is progressively modified by cellular activity, which tends to concentrate them into intracellular compartments, changing in turn their responsivity to physical stimuli. In this paper, we investigate the consequences of cellular uptake on the related magnetic properties and NMR relaxivity of iron oxide nanoparticles. The superparamagnetic behavior (field-dependent and temperature-dependent magnetization curves investigated by SQUID (Superconducting Quantum Interference Device) measurements) and nuclear magnetic relaxation dispersion (NMRD) R(1) profiles of citrate-coated maghemite nanoparticles (mean diameter 8 nm) were characterized in colloidal suspension and after being uptaken by several types of cells (tumor cells, stem cells and macrophages). The temperature-dependent magnetization as well as the NMRD profile were changed following cellular uptake depending on the stage of endocytosis process while the field-dependent magnetization at room temperature remained unchanged. Magnetic coupling between nanoparticles confined in cell lysosomes accounts for the modification in magnetic behavior, thereby reflecting the local organization of nanoparticles. NMR longitudinal relaxivity was directly sensitive to the intracellular distribution of nanoparticles, in line with Transmission Electron Microscopy TEM observations. This study is the first attempt to link up magnetic properties and NMR characterization of iron oxide nanoparticles before and after their cell processing.

There are very few methods to investigate how nanoparticles (NPs) are taken up and processed by cells in the organism in the short and long terms. We propose a nanomagnetism approach, in combination with electron microscopy, to document the magnetic outcome of iron oxide-based P904 NPs injected intravenously into mice. The NP superparamagnetic properties are shown to be modified by cell internalization, due to magnetic interactions between NPs sequestered within intracellular organelles. These modifications of magnetic behaviour are observed in vivo after NP uptake by resident macrophages in spleen and liver or by inflammatory macrophages in adipose tissue as well as in vitro in monocyte-derived macrophages. The dynamical magnetic response of cell-internalized NPs is theoretically and experimentally evidenced as a global signature of their local organization in the intracellular compartments. The clustering of NPs and their magnetism become dependent on the targeted organ, on the dose administrated and on the time elapsed since their injection. Nanomagnetism probes the intracellular clustering of iron-oxide NPs and sheds light on the impact of cellular metabolism on their magnetic responsivity.

Biomedical applications based on superparamagnetic nanoparticles injected in vivo may be affected by the cellular uptake of these nanoparticles. Living cells indeed capture and internalize nanoparticles, concentrating them into intracellular vesicles called lysosomes. As a consequence, nanoparticles interact magnetically with each other, modifying their magnetic properties. The effects of cellular uptake can be observed on the temperature dependence of zero-field cooled (ZFC) magnetization, which is known to be sensitive to magnetic interactions. In this paper, a theoretical model is proposed to account for weak magnetic interactions between nanoparticles aggregated into spherical compartments. This model suggests a new interpretation of the maximum of the ZFC curve, uncorrelated with the nanoparticle relaxation time but with the extent of interaction effects. It focuses on the local field felt by each nanoparticle, which is the sum of the applied magnetic field and the field created by all the other nanoparticles. For the considered organization of nanoparticles, only the field created by touching neighbors has to be taken into account, setting up the local nanoparticle volume fraction as the unique parameter of the model. This parameter relates the global magnetization measurements to the local distribution of nanoparticles in cells and tissues or in other complex media with aggregated organization.

It has already been shown that, with the simplest classical device, namely two coupled pendula, one can simulate the movement of a free quantum two-level system, as for instance a one-half spin in a static magnetic field. We now show that, with a hardly more sophisticated device, one can simulate the latter system undergoing outer perturbation. In the case of sinusoidal excitation, we present an experimental mechanical illustration of the transition of the system between its two eigenstates, known as the Rabi precession. Abstract theoretical concepts of absorption and stimulated emission of energy are thus provided with intuitive support.

We propose an ab initio introduction to the well-known Minnaert pulsating bubble at graduate level. After a brief recall of the standard stuff, we begin with a detailed discussion of the radial movements of an air bubble in water. This discussion is managed from an acoustic point of view, and using the Lagrangian rather than the Eulerian variables. In unbounded water, the air-water system has a continuum of eigenmodes, some of them correspond to regular Fabry Perot resonances. A singular resonance, the lowest one, is shown to coincide with that of Minnaert. In bounded water, the eigenmodes spectrum is discrete, with a finite fundamental frequency. A spectacular quasi-locking of the latter occurs if it happens to exceed the Minnaert frequency, which provides an unforeseen one-bubble alternative version of the famous 'hot chocolate effect'. In the ( low) frequency domain in which sound propagation inside the bubble reduces to a simple 'breathing' (i.e. inflation/deflation), the light air bubble can be 'dressed' by the outer water pressure forces, and is turned into the heavy Minnaert bubble. Thanks to this unexpected renormalization process, we demonstrate that the Minnaert bubble definitely behaves like a true harmonic oscillator of the spring-bob type, but with a damping term and a forcing term in apparent disagreement with those commonly admitted in the literature. Finally, we underline the double role played by the water. In order to tell the water motion associated with water compressibility (i.e. the sound) from the simple incompressible accompaniment of the bubble breathing, we introduce a new picture analogous to the electromagnetic radiative picture in Coulomb gauge, which naturally leads us to split the water displacement in an instantaneous and a retarded part. The Minnaert renormalized mass of the dressed bubble is then automatically recovered.

In this theoretical paper, we propose a general derivation of the adiabatic invariant of the n-degree-of-freedom harmonic oscillator, available whichever the physical nature of the oscillator and of the parametrical excitation it undergoes. This derivation is founded on the use of the classical Glauber variables and ends up with this simplest result: the oscillator's adiabatic invariant is just the sum of all the semiclassical quanta numbers associated with its different eigenmodes.

It is recalled how the nonlinear interaction between a gas bubble and an external extra pressure can yield phase conjugation. Using the Glauber representation, we show that the effect of the latter is formally analogous to that of a pi pulse in nuclear magnetic resonance, so that the acoustic equivalent of spin echoes may be expected in a bubble cloud. An experimental attempt to observe phase conjugation is reported in the single-bubble case.

Anionic iron oxide nanoparticles are efficiently internalized into macrophages where they concentrate within micrometric endosomes, conferring on them a high magnetic susceptibility. The uptake of anionic maghemite nanoparticles by macrophages was quantified by an electron spin resonance (ESR) experiment. MR spin‐echo sequences were performed with various TEs and TRs. The contrast enhancement was compared between two types of agarose phantoms with the same equivalent ferrite concentrations but containing either dispersed isolated nanoparticles or magnetically labeled macrophages. It is shown that the intracellular confinement of maghemite nanoparticles within micrometric endosomes results in a significant decrease of the longitudinal relaxivity and a moderate decrease of the transverse relaxivity compared to the relaxivities of the dispersed isolated nanoparticles. As a consequence, the signature of endosomal magnetic labeling consists of a negative contrast on T1‐weighted images in the whole ferrite concentration range, whereas the presence of extracellular isolated nanoparticles can result in a positive enhancement. Magn Reson Med 49:646–654, 2003. © 2003 Wiley‐Liss, Inc.

We discuss a series of easily reproducible experiments with one and two air bubbles immersed in water, and we show that these systems can be analyzed in terms of harmonic oscillators.

: The acoustic coupling between two air bubbles immersed in water is clearly demonstrated. The system is acoustically forced, and its response is detected. The experimental results confirm that both theoretically predicted eigenmodes, respectively symmetrical and antisymmetrical, do exist. Their frequencies, measured as a function of the bubbles spacing, follow theoretical estimations within a 10% accuracy.