Pauli-Fierz Type Operators with Singular Electromagnetic Potentials on General Domains

We consider Dirichlet realizations of Pauli-Fierz type operators generating the dynamics of non-relativistic matter particles which are confined to an arbitrary open subset of the Euclidean position space and coupled to quantized radiation fields. We find sufficient conditions under which their domains and a natural class of operator cores are determined by the domains and operator cores of the corresponding Dirichlet-Schrödinger operators and the radiation field energy. Our results also extend previous ones dealing with the entire Euclidean space, since the involved electrostatic potentials might be unbounded at infinity with local singularities that can only be controlled in a quadratic form sense, and since locally square-integrable classical vector potentials are covered as well. We further discuss Neumann realizations of Pauli-Fierz type operators on Lipschitz domains.     

Inorganic–organic hybrid compounds exhibiting both magnetic order and non-linear optical properties

Hybrid organic–inorganic framework compounds constitute an important class of materials whose properties, especially paired ones, have not been adequately investigated hitherto. In this communication, we report the non-linear optical properties of hybrid compounds exhibiting interesting magnetic properties.     

Subshifts with slow complexity and simple groups with the Liouville property

We study random walk on topological full groups of subshifts, and show the existence of infinite, finitely generated, simple groups with the Liouville property. Results by Matui and Juschenko-Monod have shown that the derived subgroups of topological full groups of minimal subshifts provide the first examples of finitely generated, simple amenable groups. We show that if the (not necessarily minimal) subshift has a complexity function that grows slowly enough (e.g. linearly), then every symmetric and finitely supported probability measure on the topological full group has trivial Poisson–Furstenberg boundary. We also get explicit upper bounds for the growth of Følner sets.     

The Mass Shell in the Semi-Relativistic Pauli–Fierz Model

We consider the semi-relativistic Pauli–Fierz model for a single free electron interacting with the quantized radiation field. Employing a variant of Pizzo’s iterative analytic perturbation theory we construct a sequence of ground state eigenprojections of infra-red cutoff, dressing transformed fiber Hamiltonians and prove its convergence, as the cutoff goes to zero. Its limit is the ground state eigenprojection of a certain renormalized fiber Hamiltonian. The ground state energy is an exactly twofold degenerate eigenvalue of the renormalized Hamiltonian, while it is not an eigenvalue of the original fiber Hamiltonian unless the total momentum is zero. These results hold true, for total momenta inside a ball about zero of arbitrary radius ${\mathfrak{p} > 0}$ , provided that the coupling constant is sufficiently small depending on ${\mathfrak{p}}$ and the ultra-violet cutoff. Along the way we prove twice continuous differentiability and strict convexity of the ground state energy as a function of the total momentum inside that ball.     

Transfer functions of US transducers for harmonic imaging and bubble responses

Current medical diagnostic echo systems are mostly using harmonic imaging. This means that a fundamental frequency (e.g., 2 MHz) is transmitted and the reflected and scattered higher harmonics (e.g., 4 and 6 MHz), produced by nonlinear propagation, are recorded. The signal level of these harmonics is usually low and a well-defined transfer function of the receiving transducer is required. Studying the acoustic response of a single contrast bubble, which has an amplitude in the order of a few Pascal, is another area where an optimal receive transfer function is important.

We have developed three methods to determine the absolute transfer function of a transducer. The first is based on a well-defined wave generated by a calibrated source in the far field. The receiving transducer receives the calibrated wave and from this the transfer functions can be calculated. The second and third methods are based on the reciprocity of the transducer. The second utilizes a calibrated hydrophone to measure the transmitted field. In the third method, a pulse is transmitted by the transducer, which impinges on a reflector and is received again by the same transducer. In both methods, the response combined with the transducer impedance and beam profiles enables the calculation of the transfer function.

The proposed methods are useful to select the optimal piezoelectric material (PZT, single crystal) for transducers used in reception only, such as in certain 3D scanning designs and superharmonic imaging, and for selected experiments like single bubble behavior.

We tested and compared these methods on two unfocused single element transducers, one commercially available (radius 6.35 mm, centre frequency 2.25 MHz) the other custom built (radius 0.75 mm, centre frequency 4.3 MHz). The methods were accurate to within 15%.     

The Latin-American network of human genetics

The Latin-American Network of Human Genetics (RELAGH) is an internet-based federation of human and medical genetic societies of Latin America constituted in 2001. Member societies include the Mexican Association of Human Genetics, the Brazilian Society of Clinical Genetics, the Human Genetics Section of the Argentinean Society of Genetics, the Colombian Society of Human Genetics and the Panamanian Human Genetics Society. RELAGH is a full member of the steering committee of the International Federation of Human Genetics Societies. A core activity of RELAGH is to become a platform for the integration and collaboration of human geneticists across Latin America regarding training, services and research in medical genetics in the region.     

Additive-free Aqueous Dispersions of Two-Dimensional Materials with Glial Cell Compatibility and Enzymatic Degradability

Water-dispersible two-dimensional (2D) materials are desirable for diverse applications. Aqueous dispersions make processing safer and greener and enable evaluation of these materials on biological and environmental fronts. To evaluate the effects of 2D materials with biological systems, obtaining dispersions without additives is critical and has been a challenge. Herein, a method was developed for obtaining additive-free aqueous dispersions of 2D materials like transition metal dichalcogenides and hexagonal boron nitride (h-BN). The nanosheet dispersions were investigated through spectroscopic and microscopic methods, along with the role of size on stability. The aqueous media enabled investigations on cytocompatibility and enzymatic degradation of molybdenum disulphide (MoS₂) and h-BN. Cytocompatibility with mixed glial cells was observed up to concentrations of 100 μg mL⁻¹, suggesting their plausible usage in bioelectronics. Besides, biodegradation using human myeloperoxidase (hMPO) mediated catalysis was investigated through Raman spectroscopy and electron microscopy. The findings suggested that additive-free 2H-MoS₂ and h-BN were degradable by hMPO, with 2H-phase exhibiting better resistance to degradation than the 1T-phase, while h-BN exhibited slower degradation. The findings pave a path for incorporating 2D materials in the burgeoning field of transient bioelectronics.