Hamiltonian formalism in the equilibrium problem for a plasma with islands

Hamiltonian formalism is applied to the equilibrium problem for a plasma with islands by using an analogy between the equilibrium problem for a plasma with one island and the nonlinear mechanics of a physical pendulum. A relationship is established between magnetic flux coordinates with straightened magnetic field lines and the action-angle variables. The flux and current representations of a magnetic field with islands are obtained, and the solution to the equilibrium problem for a narrow island is presented.     

Hamiltonian formalism in the problem on the modification of the current density profile during the development of tearing instability in a tokamak

The formation of a magnetic island as a result of tearing instability can be interpreted as the bifurcation of an axisymmetric equilibrium configuration at which nested magnetic surfaces are preserved. The modification of the current density profile due to such bifurcation is studied using the Hamiltonian formalism. In the case of a long narrow island, the gradient profile changes to a profile with an extremum on the axis of the magnetic island.     

Islands and ergodicity of the plasma current in toroidal magnetic confinement systems

Magnetic and current structures arising due to resonant perturbations of an equilibrium current-carrying magnetic configuration are analyzed using the Hamiltonian formalism. Special attention is paid to axisymmetric tokamak and pinch configurations. It is shown that, due to the very different dependences of the magnetic and current rotational transforms on the plasma pressure, the resonances (islands) of the magnetic field may not coincide with those of the current. The perturbed force-free equilibrium of a cylindrical pinch in which the field and current islands overlap is analyzed. The long-lived ribbon structures observed in the JET tokamak are explained as a manifestation of a force-free magneto-current island.     

The electronic structure of Fe2+ in reaction centers from Rhodopseudomonas sphaeroides. I. Static magnetization measurements.

We have measured the static magnetization of unreduced and reduced reaction centers that vary in their quinone content. Measurements were performed in the temperature range 0.7 degrees K less than T less than 200 degrees K and magnetic fields of up to 10 kG. The electronic g-value, crystal field parameters D, E, and the exchange interaction, J, between the quinone spin and Fe2+ were determined using the spin Hamiltonian formalism. The effective moment mu eff/Fe2+ of both reduced and unreduced samples were determined to be 5.35 +/- 0.15 Bohr magnetons. This shows, in agreement with previous findings, that Fe2+ does not change its valence state when the reaction centers are reduced. Typical values of D congruent to +5 cm-1 and E/D congruent to 0.27 are consistent with Fe being in an octahedral environment with rhombic distortion. The values of D and E were approximately the same for reaction centers having one and two quinones. These findings imply that quinone is most likely not a ligand of Fe. The Fe2+ and the spin on the quinone in reduced reaction centers were found to be coupled with an exchange interaction 0 less than /J/ less than 1 cm-1. The validity of the spin Hamiltonian was checked by using an orbital Hamiltonian to calculate energy levels of the 25 states of the S = 2, L = 2 manifold and comparing the magnetization of the lowest five states with those obtained from the spin Hamiltonian. Using the orbital Hamiltonian, we calculated the position of the first excited quintet state to be 340 cm-1 above the ground state quintet. This is in good agreement with the temperature dependence of the quadrupole splitting as determined by Mossbauer spectroscopy.     

Crossing of low-lying electronic levels of high-spin ferrous ion in deoxyhemoglobin and deoxymyoglobin.

The electronic structure of high-spin S = 2 ferrous ion in deoxy forms of hemoglobin and myoglobin is considered in terms of spin Hamiltonian formalism. Spin Hamiltonian parameters of the second order B0(2)(D), B2(2)(E) and, for the first time in the available literature, of fourth order B0(4), B2(4) and B4(4), are calculated for the rhombic symmetry case of Fe2+. The Hamiltonian matrix is diagonalized for several sets of Bq(k) parameters compatible with other experimental data. The low-lying Fe2+ levels exhibit crossings in a high magnetic field, applied along the z-axis perpendicular to the heme plane. The cross-over values of the magnetic field are determined to be Hc1 = 46 kOe and Hc2 = 168 kOe for D = 5.2, E = 0.6 cm-1 (close to the magnetic data of Nakano, N., Otsuka, J. and Tasaki, A. (1972) Biochim. Biophys. Acta 278, 355-371) and with B0(4) = 0.037, B2(4) = 0.005, B4(4) = 0.013 cm-1 and gz = 2.028. Experimental techniques for measurement of the crossing effects are discussed.     

The rainbow bridge: Hamiltonian limits and resonance in predator-prey dynamics

 In the presence of seasonal forcing, the intricate topology of non-integrable Hamiltonian predator-prey models is shown to exercise profound effects on the dynamics and bifurcation structure of more realistic schemes which do not admit a Hamiltonian formulation. The demonstration of this fact is accomplished by writing the more general models as perturbations of a Hamiltonian limit, ℋ, in which are contained infinite numbers of periodic, quasiperiodic and chaotic motions. From ℋ, there emanates a surface, Γ, of Nejmark-Sacker bifurcations whereby the annual oscillations induced by seasonality are destabilized. Connecting Γ and ℋ is a bridge of resonance horns within which invariant motions of the Hamiltonian case persist. The boundaries of the resonance horns are curves of tangent (saddle-node) bifurcations corresponding to subharmonics of the yearly cycle. Associated with each horn is a rotation number which determines the dominant frequency, or “color”, of attractors within the horn. When viewed through the necessarily coarse filter of ecological data acquisition, and regardless of their detailed topology, these attractors are often indistinguishable from multi-annual cycles. Because the tips of the horns line up monotonically along Γ, it further follows that the distribution of observable periods in systems subject to fluctuating parameter values induced, for example, by year-to-year variations in the climate, will often exhibit a discernible central tendency. In short, the bifurcation structure is consistent with the observation of multi-annual cycles in Nature. Fundamentally, this is a consequence of the fact that the bridge between ℋ and Γ is a rainbow bridge. While the present analysis is principally concerned with the two species case (one predator and one prey), Hamiltonian limits are also observed in other ecological contexts: 2n-species (n predators, n prey) systems and periodically-forced three level food chain models. Hamiltonian limits may thus be common in models involving the destruction of one species by another. Given the oft-commented upon structural instability of Hamiltonian systems and the corresponding lack of regard in which they are held as useful caricatures of ecological interactions, the pivotal role assigned here to Hamiltonian limits constitutes a qualitative break with the conventional wisdom. Received: 2 November 1998     

The magnetic susceptibility of reduced cytochrome P-450cam

The magnetic susceptibility of singly reduced, camphor-complexed cytochrome P−450 from Pseudomonas putida has been measured at various temperatures. Computer analysis using a spin Hamiltonian gives values of D between 15K and 25K, which agrees with a value of D = 20K found by low-field variable temperature Mössbauer spectroscopy. This result is compared with those from deoxyhemoglobin and deoxy-myoglobin.     

Energy dependence on discharge mode of Izhikevich neuron driven by external stimulus under electromagnetic induction

Energy supply plays a key role in metabolism and signal transmission of biological individuals, neurons in a complex electromagnetic environment must be accompanied by the absorption and release of energy. In this paper, the discharge mode and the Hamiltonian energy are investigated within the Izhikevich neuronal model driven by external signals in the presence of electromagnetic induction. It is found that multiple electrical activity modes can be observed by changing external stimulus, and the Hamiltonian energy is more dependent on the discharge mode. In particular, there is a distinct shift and transition in the Hamiltonian energy when the discharge mode is switched quickly. Furthermore, the amplitude of periodic stimulus signal has a greater effect on the neuronal energy compared to the angular frequency, and the average Hamiltonian energy decreases when the discharge rhythm becomes higher. Based on the principle of energy minimization, the system should choose the minimum Hamiltonian energy when maintaining various trigger states to reduce the metabolic energy of signal processing in biological systems. Therefore, our results give the possible clues for predicting and selecting appropriate parameters, and help to understand the sudden and paroxysmal mechanisms of epilepsy symptoms.     

A high-resolution magnetic tweezer for single-molecule measurements

Magnetic tweezers (MT) are single-molecule manipulation instruments that utilize a magnetic field to apply force to a biomolecule-tethered magnetic bead while using optical bead tracking to measure the biomolecule’s extension. While relatively simple to set up, prior MT implementations have lacked the resolution necessary to observe sub-nanometer biomolecular configuration changes. Here, we demonstrate a reflection-interference technique for bead tracking, and show that it has much better resolution than traditional diffraction-based systems. We enhance the resolution by fabricating optical coatings on all reflecting surfaces that optimize the intensity and contrast of the interference image, and we implement feedback control of the focal position to remove drift. To test the system, we measure the length change of a DNA hairpin as it undergoes a folding/unfolding transition.     

Evidence for variable metal-radical spin coupling in oxoferrylporphyrin cation radical complexes

Oxoferrylporphyrin cation radical complexes were generated by m-chloroperoxybenzoic acid oxidation of the chloro and trifluoromethanesulfonato complexes of tetramesitylporphyrinatoiron(III) [(TMP)Fe] and the trifluoromethanesulfonato complex of tetra(2,6-dichlorophenyl)porphyrinatoiron(III) [TPP(2,6-Cl)Fe]. Coupling between ferryl iron (S = 1) and porphyrin radical (S' = 1/2) spin systems was investigated by M?ssbauer and EPR spectroscopy. The oxoferrylporphyrin cation radical systems generated from the TMP complexes show strong ferromagnetic coupling. Analysis of the magnetic M?ssbauer spectra, using a spin Hamiltonian explicitly including a coupling tensor J, suggests an exchange-coupling constant J greater than 80 cm-1. The EPR spectra show non-zero rhombicity, the origin of which is discussed in terms of contributions from the usual zero-field effects of iron and from iron-radical spin-dipolar interaction. A consistent estimate of zero-field splitting parameter D approximately + 6 cm-1 was obtained by EPR and M?ssbauer measurements. EPR and M?ssbauer parameters are shown to be slightly dependent on solvent, but not on the axial ligand in the starting (TMP)Fe complex. In contrast to the TMP complex, the oxoferrylporphyrin cation radical system generated from [TPP(2,6-Cl)FeOSO2CF3] exhibits M?ssbauer and EPR spectra consistent with weak iron-porphyrin radical coupling of magnitude of J approximately 1 cm-1.     

Low-lying electronic states of the ferrous high-spin (S=2) heme in deoxy-Mb and deoxy-Hb studied by highly-sensitive multi-frequency EPR

The low-lying electronic states of the ferrous high-spin heme in deoxy-myoglobin (deoxy-Mb) and deoxy-hemoglobin (deoxy-Hb) were probed by multi-frequency electron paramagnetic resonance (MFEPR) spectroscopy. An unexpected broad EPR signal was measured at the zero magnetic field using cavity resonators at 34-122 GHz that could not be simulated using any parameter sets for the S = 2 spin Hamiltonian assuming spin quintet states in the ⁵B₂ ground state. Furthermore, we have observed novel, broad EPR signals measured at 70-220 GHz and 1.5 K using a single pass transmission probe. These signals are attributed to the ferrous high-spin heme in deoxy-Mb and deoxy-Hb. The resonant peaks shifted to a higher magnetic field with increasing frequency. The energy level separation between the ground singlet and the first excited state at the zero magnetic field was directly estimated to be 3.5 cm^− 1 for deoxy-Hb. For deoxy-Mb, the first two excited singlet states are separated by 3.3 cm^− 1 and 6.5 cm^− 1, respectively, from the ground state. The energy gap at the zero magnetic field is directly derived from our MFEPR for deoxy-Mb and deoxy-Hb and strongly supports the theoretical analyses based on the Mössbauer and magnetic circular dichroism experiments.     

Fe(II)-substituted horse liver alcohol dehydrogenase, a model for non-heme iron enzymes. Various states of iron-dioxygen interaction investigated by M?ssbauer and EPR spectroscopy

The catalytic Zn(II) ion of horse liver alcohol dehydrogenase (EE isozyme) was replaced by Fe(II), providing a novel iron protein with the unusual coordination of Fe(II) to two cysteines residues, one histine residue and water. The electronic structure of iron in this system was characterized by M?ssbauer spectroscopy at various temperatures as well as applied magnetic fields and analysed in terms of the spin Hamiltonian formalism. The novelty we found is an unusually weak spin coupling (/J/ less than 0.1 cm-1) of a paramagnet (S = 1) with iron (S = 2). From EPR and biochemical studies we conclude that the corresponding chemical species is triplet oxygen (O2). The quantitative determination of the coupling energy was possible utilizing the competition between Zeemann interaction and spin coupling at weak magnetic fields and low temperature. Oxidation experiments followed by M?ssbauer spectroscopy showed that the spin-coupled system is an outer-sphere Fe(II) . (O2)aq complex occurring as an intermediate during a Fe(II)-catalyzed dioxygen activation. We observed two additional Fe(II) species after treatment with O2 and dithionite. The spin Hamiltonian parameters of iron in the coupled system are presented. The results are compared with those of iron in other non-heme iron proteins.     

The electronic structure of Fe2+ in reaction centers from Rhodopseudomonas sphaeroides. III. EPR measurements of the reduced acceptor complex.

Electron paramagnetic resonance (EPR) spectra of the reduced quinone-iron acceptor complex in reaction centers were measured in a variety of environments and compared with spectra calculated from a theoretical model. Spectra were obtained at microwave frequencies of 1, 9, and 35 GHz and at temperatures from 1.4 to 30 K. The spectra are characterized by a broad absorption peak centered at g = 1.8 with wings extending from g approximately equal to 5 to g less than 0.8. The peak is split with the low-field component increasing in amplitude with temperature. The theoretical model is based on a spin Hamiltonian, in which the reduced quinone, Q-, interacts magnetically with Fe2+. In this model the ground manifold of the interacting Q-Fe2+ system has two lowest doublets that are separated by approximately 3 K. Both perturbation analyses and exact numerical calculations were used to show how the observed spectrum arises from these two doublets. The following spin Hamiltonian parameters optimized the agreement between simulated and observed spectra: the electronic g tensor gFe, x = 2.16, gFe, y = 2.27, gFez = 2.04, the crystal field parameters D = 7.60 K and E/D = 0.25, and the antiferromagnetic magnetic interaction tensor, Jx = -0.13 K, Jy = -0.58 K, Jz = -0.58 K. The model accounts well for the g value (1.8) of the broad peak, the observed splitting of the peak, the high and low g value wings, and the observed temperature dependence of the shape of the spectra. The structural implications of the value of the magnetic interaction, J, and the influence of the environment on the spin Hamiltonian parameters are discussed. The similarity of spectra and relaxation times observed from the primary and secondary acceptor complexes Q-AFe2+ and Fe2+Q-B leads to the conclusion that the Fe2+ is approximately equidistant from QA and QB.     

Examples of high-frequency EPR studies in bioinorganic chemistry

Low-temperature EPR spectroscopy with frequencies between 95 and 345 GHz and magnetic fields up to 12 T has been used to study metal sites in proteins or inorganic complexes and free radicals. The high-field EPR method was used to resolve g-value anisotropy by separating it from overlapping hyperfine couplings. The presence of hydrogen bonding interactions to the tyrosyl radical oxygens in ribonucleotide reductases were detected. At 285 GHz the g-value anisotropy from the rhombic type 2 Cu(II) signal in the enzyme laccase has its g-value anisotropy clearly resolved from slightly different overlapping axial species. Simple metal site systems with S>1/2 undergo a zero-field splitting, which can be described by the spin Hamiltonian. From high-frequency EPR, the D values that are small compared to the frequency (high-field limit) can be determined directly by measuring the distance of the outermost signal to the center of the spectrum, which corresponds to (2 S-1)* mid R: Dmid R: For example, D values of 0.8 and 0.3 cm(-1) are observed for S=5/2 Fe(III)-EDTA and transferrin, respectively. When D values are larger compared to the frequency and in the case of half-integer spin systems, they can be obtained from the frequency dependence of the shifts of g(eff), as observed for myoglobin in the presence ( D=5 cm(-1)) or absence ( D=9.5 cm(-1)) of fluoride. The 285 and 345 GHz spectra of the Fe(II)-NO-EDTA complex show that it is best described as a S=3/2 system with D=11.5 cm(-1), E=0.1 cm(-1), and g(x)= g(y)= g(z)=2.0. Finally, the effects of HF-EPR on X-band EPR silent states and weak magnetic interactions are demonstrated.     

Dynamical and Static Spin Susceptibilities of Doped Gapped Graphene Nanoribbon Due to Local Electronic Interaction

We present the behaviors of both dynamical and static spin susceptibilities of doped gapped armchair graphene nanoribbon using the Green’s function approach in the context of Hubbard model Hamiltonian. Specially, the effects of spin polarization and gap parameter on the spin excitation modes of armchair graphene nanoribbon are investigated via calculating correlation function of spin density operators. Our results show the increase of electron concentration leads to disappear low frequency spin excitation mode for gapless case. We also show that low frequency excitation mode for both gapped and gapless nanoribbon disappears under spin full polarization condition. Finally, the electron density dependence of static charge structure factor of armchair graphene nanoribbon is studied. The effects of both gap parameter and magnetic ordering on the static structure factor are discussed in details.     

Comparing recovering efficiency of immunomagnetic separation and centrifugation of mycobacteria in metalworking fluids

The accurate detection and enumeration of Mycobacterium immunogenum in metalworking fluids (MWFs) is imperative from an occupational health and industrial fluids management perspective. We report here a comparison of immunomagnetic separation (IMS) coupled to flow-cytometric enumeration, with traditional centrifugation techniques for mycobacteria in a semisynthetic MWF. This immunolabeling involves the coating of laboratory-synthesized nanometer-scale magnetic particles with protein A, to conjugate a primary antibody (Ab), specific to Mycobacterium spp. By using magnetic separation and flow-cytometric quantification, this approach enabled much higher recovery efficiency and fluorescent light intensities in comparison to the widely applied centrifugation technique. This IMS technique increased the cell recovery efficiency by one order of magnitude, and improved the fluorescence intensity of the secondary Ab conjugate by 2-fold, as compared with traditional techniques. By employing nanometer-scale magnetic particles, IMS was found to be compatible with flow cytometry (FCM), thereby increasing cell detection and enumeration speed by up to two orders of magnitude over microscopic techniques. Moreover, the use of primary Ab conjugated magnetic nanoparticles showed better correlation between epifluorescent microscopy counts and FCM analysis than that achieved using traditional centrifugation techniques. The results strongly support the applicability of the flow-cytometric IMS for microbial detection in complex matrices.     

Analysis and Optimization of Pulse Dynamics for Magnetic Stimulation

Magnetic stimulation is a standard tool in brain research and has found important clinical applications in neurology, psychiatry, and rehabilitation. Whereas coil designs and the spatial field properties have been intensively studied in the literature, the temporal dynamics of the field has received less attention. Typically, the magnetic field waveform is determined by available device circuit topologies rather than by consideration of what is optimal for neural stimulation. This paper analyzes and optimizes the waveform dynamics using a nonlinear model of a mammalian axon. The optimization objective was to minimize the pulse energy loss. The energy loss drives power consumption and heating, which are the dominating limitations of magnetic stimulation. The optimization approach is based on a hybrid global-local method. Different coordinate systems for describing the continuous waveforms in a limited parameter space are defined for numerical stability. The optimization results suggest that there are waveforms with substantially higher efficiency than that of traditional pulse shapes. One class of optimal pulses is analyzed further. Although the coil voltage profile of these waveforms is almost rectangular, the corresponding current shape presents distinctive characteristics, such as a slow low-amplitude first phase which precedes the main pulse and reduces the losses. Representatives of this class of waveforms corresponding to different maximum voltages are linked by a nonlinear transformation. The main phase, however, scales with time only. As with conventional magnetic stimulation pulses, briefer pulses result in lower energy loss but require higher coil voltage than longer pulses.     

Bioinspired magnetic reception and multimodal sensing

Several animals use Earth’s magnetic field in concert with other sensor modes to accomplish navigational tasks ranging from local homing to continental scale migration. However, despite extensive research, animal magnetic reception remains poorly understood. Similarly, the Earth’s magnetic field offers a signal that engineered systems can leverage to navigate in environments where man-made positioning systems such as GPS are either unavailable or unreliable. This work uses a behavioral strategy inspired by the migratory behavior of sea turtles to locate a magnetic goal and respond to wind when it is present. Sensing is performed using a number of distributed sensors. Based on existing theoretical biology considerations, data processing is performed using combinations of circles and ellipses to exploit the distributed sensing paradigm. Agent-based simulation results indicate that this approach is capable of using two separate magnetic properties to locate a goal from a variety of initial conditions in both noiseless and noisy sensory environments. The system’s ability to locate the goal appears robust to noise at the cost of overall path length.     

Magnetic particles for the separation and purification of nucleic acids

Nucleic acid separation is an increasingly important tool for molecular biology. Before modern technologies could be used, nucleic acid separation had been a time- and work-consuming process based on several extraction and centrifugation steps, often limited by small yields and low purities of the separation products, and not suited for automation and up-scaling. During the last few years, specifically functionalised magnetic particles were developed. Together with an appropriate buffer system, they allow for the quick and efficient purification directly after their extraction from crude cell extracts. Centrifugation steps were avoided. In addition, the new approach provided for an easy automation of the entire process and the isolation of nucleic acids from larger sample volumes. This review describes traditional methods and methods based on magnetic particles for nucleic acid purification. The synthesis of a variety of magnetic particles is presented in more detail. Various suppliers of magnetic particles for nucleic acid separation as well as suppliers offering particle-based kits for a variety of different sample materials are listed. Furthermore, commercially available manual magnetic separators and automated systems for magnetic particle handling and liquid handling are mentioned.