as shown in Fig. 3, for ∆ < 0 we find that the fixed-points at small γ and V actually become unstable at Hopf bifur- cations  and, in these regimes, limit-cycle oscillations in the phonon dynamics are found at long times. This phenomenon has been observed in trapped ions and is known as phonon lasing . These regions, labelled PL, are shown in Fig. 3, where we also plot two example semi- classical trajectories towards the dark fixed point and the limitcycle. While it appears unphysical that the limit- cycles persist down to V = 0, this feature is destroyed by any finite dissipation on the phonons. Such dissipa- tion inevitably occurs in trapped-ion experiments. We introduce a finite dissipation rate κ/N γ on the mo- tional degrees of freedom by replacing ω → ω − iκ in the mean-field equations (4). Changes to all dynamical phase boundaries by this dissipation are negligible, except for the phonon lasing regime, which becomes suppressed at small V with finite κ (see Fig. 3).
But strong transitions are spectrally broad, which limits the precision of a spectro- scopic experiment at a given signal-to-noise ratio. Another limitation comes from the cumulative back-action of many scattered photons on the motion of an ion. The equilibrium temperature will critically depend on the detuning of the laser frequency with respect to the atomic resonance. Below resonance (red detuning) we expect Doppler cooling to mK temperatures and fluorescence rates up to 100 MHz from a single particle. A laser tuned above resonance (blue detuning) will increase the motional energy, the ion evades the laser beam and no appreciable fluorescence is observed. The resulting line-shape distortions limited the precision of spectroscopy on strong transitions in trapped ions. These problems remained widely unsolved arguably because of additional technical limitations, like the absence of simple and accurate frequency calibration schemes in many laboratories and theoretical limi- tations, which did not allow to push predictions for many electron atoms beyond the precision of early spectroscopic work . Meanwhile the situation has changed. Optical frequency synthesizers  facilitated experiments and basically removed the calibration uncertainty. Transition frequencies in few electron atoms like Li +  and
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that uses a different entanglement mechanism from gate processes. Steady states have balanced inflow and outflow of population due to the system dynamics, and often a pre- pared environmental coupling and other noise sources. Coupling a quantum system to an environment typically causes decoherence: a coherent quantum system is driven towards classical states without distinctively quantum properties. Counterintuitively, one of the methods for combatting the destructive effects of environmental couplings is to engineer dissipation channels, or environments. This quantum reservoir engineering method  has been used to investigate decoherence [31, 32] and to design robust non-classical states  in the motional degrees of freedom of trapped ions. Engineered reservoirs are robust to preexisting natural decoherence sources  and also to variations of parameters and initial conditions. This has led to a number of proposals to engineer many-body quan- tum states [34, 35] and to prepare and stabilise quantum steady-states in a variety of systems [36, 37], including cavity quantum electrodynamics [38, 39], optomechanical sys- tems [40, 41], and superconducting qubits . Although experimentally challenging, en- gineered dissipation has been used to generate entanglement in atomic ensembles , to implement quantum operations in ion traps , and more recently to prepare Bell states in superconducting qubits  and in ion traps .
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This famous quote by Erwin Schr¨ odinger dates back to 1952. Although the extinct aquatic lizard could not be resurrected to date, 26 years later, in 1978, two independent groups simultaneously observed single, trapped, and laser cooled ions [1, 2]. It was Wolfgang Paul’s and others work on the dynamics of particles subject to oscillating electric multipole fields that triggered the evolution from quadrupole mass filters to ion traps and let Hans Dehmelt’s dream of a “single particle floating at rest in free space‘” come true. Radio frequency ion traps (Paul traps) are remarkable devices that allow to confine a sample of atomic or molecular ions extremely well isolated from external perturbations for long times. Modern ion traps can store millions as well as single ions, which can be as hot as ∼ 100’000 K or cooled to the quantum mechanical ground state of motion (corresponding to ∼ µ K). Ultra-high vacuum systems that achieve pressures below 10 nPa have become standard, so that a trapped ion will collide with background gas atoms only about once in five minutes. This allows to store an ion for days. These exciting achievements are not only of aesthetic appeal. Trapped ions are ideal systems for spectroscopy with highest precision. They allow long interactions times and the suppression of many systematic uncertainties, including first and second order Doppler shifts, collisional shifts, etc.. Indeed, the most precise measurements ever made were performed on trapped atomic ions. A recent frequency comparison of the clock transitions of a single aluminum ion and a single mercury ion achieved an accuracy of a few parts in 10 17 . Apart from spectroscopy, the absence of external perturbations make trapped ions ideal systems to study such elusive phenomena as entanglement. Experiments on trapped ions demonstrated quantum gates for the first time and thus paved the way towards quantum computing [4, 5]. The technologies developed along these lines are currently being applied to perform quantum simulations , an idea which goes back to R. Feynman . A rather unexpected but extremely
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The charge density of different test parameters are calculated and shown in Fig. 1(b). The inserted charge density and extracted charge density are calculated from the integration of negative CV curves and positive CV curves, respectively, and the charge density is dependent on not only the CV curve area but scan rate. Although the CV curve area of 0.15 V/s is larger than others, its scan rate is also higher than that of 0.10 V/s and 0.05 V/s. The inserted charge density calculated by equation (2) is 29.70 mC cm -2 , 24.06 mC cm -2 and 17.74 mC cm -2 for the films of 0.05 V/s, 0.10 V/s and 0.15 V/s, respectively. In addition, we can clearly find that there is obvious difference between inserted charge and extracted charge as shown in Fig. 1(b), which means that a part of inserted ions can not be extracted from the film. These ions are defined as trapped ions, and Fig. 1(c) exhibits the relationship between the charge density of trapped ions and scan rates, which demonstrates that the slow scan rate will cause the forming of more trapped ions in film during CV test.
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This article is organized as follows. In Sec. II, we describe the scheme based on quasi-periodic drivings that leads to an effective XYZ model for a trapped-ion crystal. We analyze the suitability of this scheme with respect to experimentally- available tools in Sec. III, and test its validity by compar- ing the analytical predictions to numerical simulations in Sec. IV. In Sec. V, we derive an effective quantum field the- ory to describe the low-energy properties of the effective long- range XYZ model in the SU(2) symmetric regime, and tests some of its predictions using numerical algorithms based on Matrix-Product-States. Finally, we present our conclusions in Sec. VI. Details of the different derivations in these sections are given in the Appendixes.
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Abstract. We present theoretical and numerical studies of the acceleration of monoenergetic protons in a double layer formed by the laser irradiation of an ultra-thin film. The ponderomotive force of the laser light pushes the electrons forward, and the induced space charge electric field pulls the ions and makes the thin foil accelerate as a whole. The ions trapped by the combined electric field and inertial force in the accelerated frame, together with the electrons trapped in the well of the ponderomotive and ion electric field, form a stable double layer. The trapped ions are accelerated to monoenergetic energies up to 100 MeV and beyond, making them suitable for cancer treatment. We present an analytic theory for the laser-accelerated ion energy and for the amount of trapped ions as functions of the laser intensity, foil thickness and the plasma number density. We also discuss the underlying physics of the trapped and untrapped ions in a double layer. The analytical results are compared with those obtained from direct Vlasov simulations of the fully nonlinear electron and ion dynamics that is controlled by the laser light.
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A Lighthill’s airfoil with a cavity and strong steady suc- tion is capable of stabilising a large-scale vortex thereby enhancing its aerodynamic performance. However, this is only possible up to a critical suction rate. The alter- native of unsteady suction provides stabilisation with a reduced suction rate but may be limited in practice by actuator performance. The trapped vortex stability, defined with respect to large-scale vortex shedding, was proved using a simple exponential decaying model. The use of a linear feedback controller based on a stabilis- ing parameter 7 was effective in retaining the trapped
In summary, the temperature of an optically trapped upconverting particle has been mea- sured by studying its internal and external degrees of freedom. The internal degree of freedom has been experimentally assessed through the temperature-dependent luminescence of the particle, while the rotational and translational degrees of freedom were analyzed through the rotation rate and the trap stiffness of the particle, respectively. The higher thermal resolution in comparison with former studies has allowed a detailed study between these three independent methods. Both the internal and rotational degrees of freedom yielded the same effective temperature, while the translational motion exhibited a lower temperature in the non-thermal equilibrium state. These results are in good agreement with the hot Brow- nian motion to which the particle is subjected. Moreover, we note that any non-spherical particle will present non-zero off-diagonal terms in its hydrodynamic friction tensor that couples translational and rotational motion. 36 This is a minor effect not considered in the 3
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Once the nanodiamond is trapped in the potential, it is very likely that the orientation of the NV center quanti- zation axis, with respect to which the splitting D is com- puted, is randomly orientated with respect to the trap axis. Measuring the optically-detected magnetic reso- nance spectrum of the NV electron spin in an applied magnetic field will reveal the orientation of the NV cen- ter with respect to the applied magnetic field and hence the trap axis. This orientation could be controlled in x-y plane by adjusting the linear polarization of the trapping light because the nanodiamonds are not spherical. Us- ing rod-shaped diamonds would increase this control . Alternatively, the birefringence of diamond  might be used to control the orientation with circularly polarized light .
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A number of alternative paths for the transformation of the vicinal silanol pair defect can be envisaged which do not include its direct oxydation. Two patterns can be recognised in the configuration of the resulting species: the formation of the defects of the first kind involves the breaking of the ring structure whilst the second does not. The simplest example of the ring breaking mechanism is the dehydration of the vicinal silanol pair defect which restores an intact Si-O-Si linkage, i.e. this process reverses the formation of the vicinal silanol pair defect in the high silica materials. In the presence of water in the pores of the zeolite, the site deprotonation can also occur: the protons are transferred to the adjacent bridging oxygens by water molecules form ing the transient hydroxonium ions. It has been of a particular interest to us to investigate the stability of the ring structure of the defect towards such a process since it could lead to the formation of the ^ i- 0 -...H O - S i= species proposed in the work H. Koller, R.F, Lobo et al (1995), as discussed previously. Moreover, the attachment of a proton to one o f the adjacent oxygens can be the source of the isolated silanol groups and their derivatives in the zeolite bulk, the existence of which has been frequently doubted in the experimental literature (see our review in Chapter 1). On the other hand, the iso valent substitution into the vicinal silanol pair presents a separate interesting issue since it leads to a further stabilisation of the dioxygen species as well as can clear up the situation with the introduction of the fluoride ions into the zeolite lattice. Therefore both mechnisms have been studied and are discussed next.
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The results of this study were demonstrated that the species Tatera indica is the highest trapped type; this finding was in agreement with other studies . Generally, M. musculus mean numbers were lowest than R. rattus mean numbers on both sites of the study, this result was supported by another study . In addition, the results of the study noticed that the abundance of rodents in summer were more than in winter. Many factors have effect on the prevalence of rodents. Other researchers studied these factors. Rainfall, food available, competition unavailable suitable habitats, climate are the most effect factors to the prevalence of rodents. Our results were in agreement with other studies, which found that the seasonal variations have effect on population of small mammals. In general, the factors that determine population dynamics can be varied over the months of the year (McMillan et al., 2005).
In the laboratory, both Grue et al. 13 and Carr et al. 14 have observed unstable ISWs with trapped cores. Grue et al. 13 observed trapped cores in which small vortices took place in the leading part of the wave. In Carr et al. 14 larger amplitudes than in Grue et al. 13 were considered and in addition to observing small scale vortices, shear instability was seen. No laboratory evidence of stable (mode one) ISWs with trapped cores has been presented. Hence all numerical and laboratory studies to date seem to suggest that ISWs with trapped cores are inherently unstable. Unfortunately, it is not possible to check this conjecture from presently available field data 8–12 due to a lack of resolution in the core measurements.
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TL intensity increases with increasing the concentration of activator (Eu) and attains a maximum value for 0.05 mol% concentration of Eu and decreases for higher concentrations of Eu. The drop in Peak TL intensity for higher doping concentration of Eu can be explained by the fact that the trapping probability is reduced if the density of the activator ion is increased due to the statistical reduced spatial distance between the activator ions and the excitons formed after band absorption.
In recent years, with interest in large transport aircraft, actively controlled trapped vortices were studied within the VortexCell2050 project (6), with positive outcomes. Tutty et al. (7) were able to stabilise a vortex trapped in a cavity using suction. Bouferrouk (8) showed that stabilisation of a vortex trapped in a nearly circular cavity required minimum mass flow rate with unsteady suction, but only in a limited range of flow conditions. Lasagna et al. (9) found that distributed suction required less energy input compared with localised suction, similar to the findings of Bouferrouk (8). It was also established that the drag curve exhibited a hysteresis loop. Other studies had looked into using fences for trapping vortices on wings, e.g. (5). It is worth noting that all studies agree that a trapped vortex can only improve the aerodynamic performance if the flow remains stable at all times, otherwise perturbations cause the vortex to shed downstream, leading to the situation in Figure 1 (a). Therefore, there is a need for effective flow control strategies, advanced aerodynamic design, and intelligent use of sensors and actuators that achieve vortex stabilisation with minimum energy expenditure.
If for a particular vibration frequency the problem has a non-trivial solution decaying at infinity, we shall say that we have a trapped mode. As pointed out in Evans, Levitin & Vassiliev (1994), Roitberg, Vassiliev & Weidl (1998) and Davies & Parnovski (1998) the existence of trapped modes is usually related to certain symmetries in the problem. In this paper we deal with the most basic type of symmetry, namely when the obstacle is symmetric about the centreline. We restrict ourselves to the study of antisymmetric modes, and search for trapped mode eigenvalues below the first antisymmetric cutoff.
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Dust-ion-acoustic solitary waves in a multi-component unmagnetized dusty plasma containing negatively charged dust particles, nonisothermal electrons and nonthermal ions, have been investigated. The Sagdeev potential approach is applied to study the large amplitude solitary waves. The intermediate integral forms of Korteweg-de Vries (KdV) and modified Korteweg-de Vries (mKdV) equations are derived under different approximations to obtain the solutions of small amplitude solitary waves of different forms. Spiky and Explosive solitary waves as well as double layers are found to exist. The parameters , , M , , a n d , representing the population of nonthermal ions, ratio of free and trapped electron’s temperatures, Mach number, temperature ratio of ion and free electrons, and the density ratio respectively, are found to play a very important role in the formation of solitary waves.
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states of C and Si were evaluated by X-ray photoelectron spectroscopy (XPS). The deuterium desorption and retention were also analyzed by thermal desorption spectroscopy (TDS). The deuterium desorption behavior for SiC was compared to that for Si and graphite, and it was found that deuterium is preferentially trapped by C and, after the saturation of the C-D bond, it is trapped by Si in SiC. Deuterium desorption was found to consist of two stages, namely deuterium desorptions bound to Si and C. Their trapping mechanisms were inﬂuenced by the damaged structures produced by the D 2 þ ion implantation. Finally, deuterium retention in SiC at temperatures above 700 K was higher than that in graphite,
Additionally, most protocols assume perfect detectors while in practice they are generally not available. This problem is compounded by the fact that in a number of setups for optical cavities the mirrors possess consider- able absorption which can be as high as 50% of the pho- tons that are not reflected from the cavity . There- fore, any proposed scheme aimed to be demonstrated with current technology needs to be highly insensitive to detector inefficiencies. Many of the above problems, such as weak coupling, poor detector efficiencies or absorption in the mirrors, also occur, if one wishes to entangle two ions in a single optical cavity by detecting photons as they leak out of the mirrors. For this setting a number of schemes have been put forward recently, see e.g. [13, 14]. In  an entangled state between the ions is prepared conditional on the failure to detect a photon leaking from the cavity. In practice the fidelity of the state decreases very rapidly when one enters the weak coupling limit or when one has imperfect detectors or absorption in the mirrors. The second scheme  is more robust within the weak coupling regime, but requires single photons pulses and suffers strong loss of fidelity when faced with imperfect detectors or absorption in the mirrors .
ABSTRACT Polysaccharides are ubiquitous components of the Gram-positive bacte- rial cell wall. In Lactococcus lactis, a polysaccharide pellicle (PSP) forms a layer at the cell surface. The PSP structure varies among lactococcal strains; in L. lactis MG1363, the PSP is composed of repeating hexasaccharide phosphate units. Here, we report the presence of an additional neutral polysaccharide in L. lactis MG1363 that is a rh- amnan composed of ␣ - L -Rha trisaccharide repeating units. This rhamnan is still pres- ent in mutants devoid of the PSP, indicating that its synthesis can occur indepen- dently of PSP synthesis. High-resolution magic-angle spinning nuclear magnetic resonance (HR-MAS NMR) analysis of whole bacterial cells identiﬁed a PSP at the sur- face of wild-type cells. In contrast, rhamnan was detected only at the surface of PSP- negative mutant cells, indicating that rhamnan is located underneath the surface- exposed PSP and is trapped inside peptidoglycan. The genetic determinants of rhamnan biosynthesis appear to be within the same genetic locus that encodes the PSP biosynthetic machinery, except the gene tagO encoding the initiating glycosyltrans- ferase. We present a model of rhamnan biosynthesis based on an ABC transporter- dependent pathway. Conditional mutants producing reduced amounts of rhamnan ex- hibit strong morphological defects and impaired division, indicating that rhamnan is essential for normal growth and division. Finally, a mutation leading to reduced expres- sion of lcpA, encoding a protein of the LytR-CpsA-Psr (LCP) family, was shown to se- verely affect cell wall structure. In lcpA mutant cells, in contrast to wild-type cells, rham- nan was detected by HR-MAS NMR, suggesting that LcpA participates in the attachment of rhamnan to peptidoglycan.
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