Optimal Halbach permanent magnet designs for maximally pulling and pushing nanoparticles

Optimization methods are presented to design Halbach arrays to maximize the forces applied on magnetic nanoparticles at deep tissue locations. In magnetic drug targeting, where magnets are used to focus therapeutic nanoparticles to disease locations, the sharp fall off of magnetic fields and forces with distances from magnets has limited the depth of targeting. Creating stronger forces at a depth by optimally designed Halbach arrays would allow treatment of a wider class of patients, e.g. patients with deeper tumors. The presented optimization methods are based on semi-definite quadratic programming, yield provably globally optimal Halbach designs in 2 and 3-dimensions, for maximal pull or push magnetic forces (stronger pull forces can collect nanoparticles against blood forces in deeper vessels; push forces can be used to inject particles into precise locations, e.g. into the inner ear). These Halbach designs, here tested in simulations of Maxwell's equations, significantly outperform benchmark magnets of the same size and strength. For example, a 3-dimensional 36 element 2000 cm³ volume optimal Halbach design yields a 5× greater force at a 10 cm depth compared to a uniformly magnetized magnet of the same size and strength. The designed arrays should be feasible to construct, as they have a similar strength (≤1 T), size (≤2000 cm³), and number of elements (≤36) as previously demonstrated arrays, and retain good performance for reasonable manufacturing errors (element magnetization direction errors ≤5°), thus yielding practical designs to improve magnetic drug targeting treatment depths.     

Poisson Structures Compatible with the Cluster Algebra Structure in Grassmannians

The present paper is a first step toward establishing connections between solutions of the classical Yang–Baxter equations and cluster algebras. We describe all Poisson brackets compatible with the natural cluster algebra structure in the open Schubert cell of the Grassmannian G _k (n) and show that any such bracket endows G _k (n) with a structure of a Poisson homogeneous space with respect to the natural action of SL _n equipped with an R-matrix Poisson–Lie structure. The corresponding R-matrices belong to the simplest class in the Belavin–Drinfeld classification. Moreover, every compatible Poisson structure can be obtained this way.     

BRST Renormalization

We consider the renormalization of general gauge theories on curved space-time background, with the main assumption being the existence of a gauge-invariant and diffeomorphism invariant regularization. Using the Batalin-Vilkovisky (BV) formalism one can show that the theory possesses gauge invariant and diffeomorphism invariant renormalizability at quantum level, up to an arbitrary order of the loop expansion.     

Linear response in the strong field domain

We show that, while it is well-known that first-order perturbation theory leads to linear response (of, e.g., a material system to an external field), the reverse is not true: linear response does not necessarily imply the validity of first-order perturbation theory, nor does it follow from it that the external perturbation is weak. We do so by analyzing the intensity dependence in the photoexcitation followed by dissociation or isomerization of a bound molecular system by a shaped broadband laser pulse. We show that, in certain cases where strong field effects are definitely present, the observed photoexcitation yield as a function of intensity may exhibit linear dependence over a wide range of intensities. The behavior is shown to coexist with a rather extensive range of coherent control over the branching ratios, an effect that was shown in the past to be impossible in the single precursor state (e.g., in the first-order perturbation theory) domain. For example, we demonstrate computationally that when (flat continuum-mediated) Raman transitions are present, appropriate pulse shaping can lead to a linear yield with intensity over a wide range of intensities, while coherent control over the branching ratio is significant. Thus, it is not necessary to invoke external bath effects (as is currently being done) to explain present-day experiments where coherent control is observed in the linear response regime.     

Time-dependent partitioning theory of the control of radiationless transitions in 24-mode pyrazine

We consider the control of internal conversion between the S(2)((1)B(2u)) excited electronic state of pyrazine and the S(1)((1)B(3u)) state. The study is performed both during and after the femtosecond excitation of the ground electronic state S(0)((1)A(g)) to form the S(2) state. The dynamics is examined using the newly developed "effective modes" technique which enables the full computation of quantum dynamics in multi-dimensional spaces. Using this technique, we also investigate the coherent control of population transfer from S(0) to the S(2) and S(1) electronic states. We find that the use of shaped laser pulses enables a significant delay of the internal conversion. For example, after 60 fs, the S(2) population amounts to ～60% of the initial S(0) population, and remains at ～20% after 100 fs, in contrast to the S(0) electronic state which is completely depopulated within 75 fs.     

Overlapping resonances interference-induced transparency: The S(0) → S(2)∕S(1) photoexcitation spectrum of pyrazine

The phenomenon of "overlapping resonances interference-induced transparency" (ORIT) is introduced and studied in detail for the S(0) → S(2)∕S(1) photoexcitation of cold pyrazine (C(4)H(4)N(2)). In ORIT, a molecule becomes transparent at specific wavelengths due to interferences between envelopes of spectral lines displaying overlapping resonances. An example is the S(2)???S(1) internal conversion in pyrazine where destructive interference between overlapping resonances causes the S(0) → S(2)∕S(1) light absorption to disappear at certain wavelengths. ORIT may be of practical importance in multi-component mixtures where it would allow for the selective excitation of some molecules in preference to others. Interference-induced cross section enhancement is also shown.     

Electromagnetically induced transparency spectroscopy

We propose a method based on the electromagnetically induced transparency (EIT) phenomenon for the detection of molecules which exist as a small minority in the presence of a majority of absorbers. The EIT effect we employ effectively eliminates the absorption of the majority species in the spectral region where it overlaps with the absorption of the minority species. The method can also be used to enhance local-modes transitions which overlap spectrally with a background of other local-modes transitions of the same molecule. The general theory is applied to the case of sparse and congested background spectra within the same molecule and to the recording of the spectra of isotopomers (of chlorine and methanol) that are in minority relative to other isotopomers which constitute the majority of molecules present.     

Quasilinearity below the 1st eigenvalue

This paper establishes the existence of two nontrivial weak solutions for a quasilinear Dirichlet problem below the first eigenvalue via the mountain pass theorem.

     

Diffraction Enhancement of the Stern—Gerlach Effect for a Neutron in a Crystal

JETP Letters - The spatial splitting of an unpolarized neutron beam into two spin components in an inhomogeneous magnetic field (an analog of the Stern-Gerlach experiment) with small gradients has...