46 research outputs found

    Dimensional deformation of sine-Gordon breathers into oscillons

    Full text link
    Oscillons are localized field configurations oscillating in time with lifetimes orders of magnitude longer than their oscillation period. In this paper, we simulate non-travelling oscillons produced by deforming the breather solutions of the sine-Gordon model. Such a deformation treats the dimensionality of the model as a real parameter to produce spherically symmetric oscillons. After considering the post-transient oscillation frequency as a control parameter, we probe the initial parameter space to show how the availability of oscillons depends on the number of spatial dimensions. For small dimensional deformations, our findings are consistent with the lack of a minimal amplitude bound to form oscillons. In D≳2D\gtrsim 2 spatial dimensions, we observe solutions undergoing intermittent phases of contraction and expansion in their cores. Knowing that stable and unstable configurations can be mapped to disjoint regions of the breather parameter space, we find that amplitude modulated solutions are located in the middle of both stability regimes. This displays the dynamics of critical behavior for solutions around the stability limit.Comment: 18+7 pages, 20 figures. Minor typos fixed. Comments are welcom

    On a Bubble algorithm for the cubic Nonlinear Schr{\"o}dinger equation

    Full text link
    Based on very recent and promising ideas, stemming from the use of bubbles, we discuss an algorithm for the numerical simulation of the cubic nonlinear Schr{\"o}dinger equation with harmonic potential (cNLS) in any dimension, that could easily be extended to other polynomial nonlinearities. This algorithm consists in discretizing the initial function as a sum of modulated complex gaussian functions (the bubbles), each one having its own set of parameters, and then updating the parameters according to cNLS. Numerically, we solve exactly the linear part of the equation and use the Dirac-Frenkel-MacLachlan principle to approximate the nonlinear part. We then obtain a grid free algorithm in any dimension whose efficiency compared with spectral methods is illustrated by numerical examples

    Technical Matter Wave Optics - Imaging devices for Bose condensed matter waves - an aberration analysis in space and time

    Get PDF
    Cold atomic gases are the ultimate quantum sensors. Embedded in a matter-wave interferometer, they provide a platform for high-precision sensing of accelerations and rotations probing fundamental physical questions. As in all optical instruments, these devices require careful modeling. Sources of possible aberrations need to be quantified and optimized to guarantee the best possible performance. This applies in particular to high-demanding experiments in microgravity with low repetition rates. In this thesis, we present a theoretical (3+1)d aberration analysis of expanded Bose-Einstein condensates. We demonstrate that the Bogoliubov modes of the scaled mean-field equation serve as good basis states to obtain the corresponding aberration coefficients. Introducing the Stringari polynomials, we describe density and phase variations in terms of a multipole decomposition analogous to the Zernike wavefront analysis in classical optics. We apply our aberration analysis to Bose-Einstein condensates on magnetic chip traps. We obtain the trapping potential using magnetic field simulations with finite wire elements. Using the multipole expansion, we characterize the anharmonic contributions of the Ioffe-Pritchard type Zeeman potential. Used as a matter-wave lens for delta-kick collimation, we determine the wavefront aberrations in terms of \say{Seidel-diagrams}. Supported by (3+1)d Gross-Pitaevskii simulations we study mean-field interactions during long expansion times. Matter-wave interferometry with Bose-Einstein condensates can also be performed in guiding potentials. One of the building blocks are toroidal condensates in a ring-shaped geometry. The required light field patterns are obtained by using the effect of conical refraction or with programmable digital micromirror devices. For the former, we study equilibrium properties and compare them with experimental data. We investigate the collective excitations in the two-dimensional ring-shaped condensate. Our result is compared to the numerical results of the Bogoliubov-de Gennes equations. The latter is used to find signatures in the excitation spectrum during the topological transition from simply connected harmonic to multiply connected ring traps. Changing the topology dynamically leads to radial excitations of the condensate. We propose a damping mechanism based on feedback measurements to control the motion within the toroidal ring

    Uniform L∞L^\infty-bounds for energy-conserving higher-order time integrators for the Gross-Pitaevskii equation with rotation

    Full text link
    In this paper, we consider an energy-conserving continuous Galerkin discretization of the Gross-Pitaevskii equation with a magnetic trapping potential and a stirring potential for angular momentum rotation. The discretization is based on finite elements in space and time and allows for arbitrary polynomial orders. It was first analyzed in [O. Karakashian, C. Makridakis; SIAM J. Numer. Anal. 36(6):1779-1807, 1999] in the absence of potential terms and corresponding a priori error estimates were derived in 2D. In this work we revisit the approach in the generalized setting of the Gross-Pitaevskii equation with rotation and we prove uniform L∞L^\infty-bounds for the corresponding numerical approximations in 2D and 3D without coupling conditions between the spatial mesh size and the time step size. With this result at hand, we are in particular able to extend the previous error estimates to the 3D setting while avoiding artificial CFL conditions

    On the Influence of Trimethylamine-N-oxide (TMAO) and Pressure on Hydrophobic Interactions

    Get PDF
    Osmolytes are small organic molecules that influence the protein folding equilibrium and biomolecular condensates formed by liquid-liquid phase separation (LLPS). Thereby they can protect the cell from extracellular stress in the form of other molecules or external variables like pressure, temperature and pH, allowing life to flourish at extreme conditions. Trimethylamine-N-oxide (TMAO) is one such osmolyte, which has been studied due to its presence in deep sea organisms living in high pressure environments. Experimentally, it has been found that TMAO can counteract pressure denaturation and the disappearance of LLPS, both crucial in the functioning of the cell. However, there is still no consensus on the molecular mechanism governing the stabilising effect of TMAO and it is still highly controversial in the sense that it is not clear which interactions are responsible for TMAOs stabilising ability. Protein interactions can be manifold, ranging from electrostatic interactions (salt bridge formation between charged side chains), polar interactions, like hydrogen bonds, and hydrophobic interactions. Furthermore, the reason why TMAO is called a "piezolyte'', an osmolyte specialized in its pressure counteracting ability, and whether it is even distinct from other osmolytes at all is unsure. This work focuses on hydrophobic interactions, which are one of the main driving forces for protein folding and biocondensate formation. It proposes molecular mechanisms on the cumulative effect of TMAO and temperature, pressure or molecule size on hydrophobic interactions and hydrophobic hydration. For these studies a combination of structural analysis of the solvent and cosolute distribution, thermodynamic data and statistical mechanics analysis was used. Lastly, the folding equilibrium of a miniprotein has been analyzed to transfer the knowledge gained with hydrophobic molecules to a more complex system. A major problem of computational studies on TMAO effects is the existence of several force fields, which often can not reproduce experimental properties. The results in this work showed that the force field used is capable to capture the general experimentally observed trend of preferential TMAO binding to a small peptide. It is shown that preferential TMAO binding depends on temperature, solute size and charge state (protonation state) of the solute and its functional groups. Generally, the presence of charged groups contribute to TMAO depletion. TMAO is depleted (lowers the solubility of the solute) from small non-polar solutes at low temperatures and switches to preferential binding (increases the solubility of the solute) upon increasing the temperature. Furthermore, TMAO is depleted from small repulsive solutes at all temperatures, but preferentially binds to large repulsive solutes at ambient temperatures. For small solutes TMAO increases hydrophobic interactions independent of preferential TMAO binding, proving that TMAO can increase solute aggregation not only through a depletion mechanism, as is usually proposed in the literature for the stabilising TMAO effect, but also through preferential binding. Intriguingly, preferential TMAO binding to large repulsive solutes drives solute association through a surfactant-like mechanism, dominating at low TMAO concentrations. This leads to a non-monotonic trend in its effect on the association of non-polar solutes, as the contribution of attractive interactions drive solute dissociation, driving the equilibrium to the dissociated state at high TMAO concentrations. Furthermore, this non-monotonic trend prevails at high pressure, but the stabilising TMAO effect of the associated state is enhanced. This effect is due to the enhancement of the TMAO dipole moment upon pressure increase. Force fields which do not take this into account do not exhibit this effect. Thus, in the case of hydrophobic interactions TMAOs piezolytic abilities are caused by its increased dipole moment. Lastly, a protein having hydrophobic, charged and polar interactions was simulated. It has been shown that hydrophobic and electrostatic interactions are strengthened by the presence of TMAO. Additionally, the protein looses protein-solvent hydrogen bonds in the TMAO mixture compared to the pure water case. This destabilizes both the folded and unfolded protein state, but more so the unfolded state as it has a higher solvent accessible surface area. As a result, TMAO drives protein folding due to the loss of favorable protein-solvent hydrogen bonds. This thesis extends the current knowledge of TMAO effects on hydrophobic interactions. Furthermore, it takes collective effects into account, enhancing the knowledge across the temperature-pressure plane and adding knowledge about other functional group effects. Several stabilising effects of TMAO on hydrophobic interactions and protein folding have been discovered, serving to understand the manifold interactions of TMAO with more complex molecules. These findings can be used for a general understanding of cosolute effects on the polymer collapse equilibrium, protein folding equilibrium and the formation of biocondesates via liquid-liquid phase separation (LLPS)

    Pushing the boundaries of lithium battery research with atomistic modelling on different scales

    Get PDF
    Computational modelling is a vital tool in the research of batteries and their component materials. Atomistic models are key to building truly physics-based models of batteries and form the foundation of the multiscale modelling chain, leading to more robust and predictive models. These models can be applied to fundamental research questions with high predictive accuracy. For example, they can be used to predict new behaviour not currently accessible by experiment, for reasons of cost, safety, or throughput. Atomistic models are useful for quantifying and evaluating trends in experimental data, explaining structure-property relationships, and informing materials design strategies and libraries. In this review, we showcase the most prominent atomistic modelling methods and their application to electrode materials, liquid and solid electrolyte materials, and their interfaces, highlighting the diverse range of battery properties that can be investigated. Furthermore, we link atomistic modelling to experimental data and higher scale models such as continuum and control models. We also provide a critical discussion on the outlook of these materials and the main challenges for future battery research

    Development of MQCT Method for Calculations of Collisional Energy Transfer for Astrochemistry and Planetary Atmospheres

    Get PDF
    A mixed quantum/classical methodology and an efficient computer code, named MQCT, were developed to model molecular energy transfer processes relevant to astrochemical environments and planetary atmospheres and applied to several real systems. In particular, the rotational energy transfer in N2 + Na collisions was studied with the focus on quantum phase, differential cross-sections, and scattering resonances, and excellent agreement with full quantum results was found. For H2O + H2, detailed calculations were carried out with the focus on allowed vs. forbidden transitions between the ortho/para states of both collision partners. Again, excellent agreement with full quantum calculations was achieved. Calculations of rotational energy transfer in a collision of two asymmetric-top rotors, a unique capability of this code, were tested using H2O + H2O system where the full-quantum calculations are unfeasible. To make MQCT calculations practical, an approximate, very efficient version of the method was developed, in which the classical-like equations of motion for the translational degrees of freedom (scattering) are decoupled from the quantum-like equations for time-evolution of the internal molecular states (rotational, vibrational). The code MQCT was made publicly available to serve as an efficient computational tool for other members of the community. It can perform scattering calculations on larger molecules and at higher collision energy than it is currently possible with full quantum methods and codes. To study the rotational quenching of isotopically substituted sulfur molecules, such as 32S32S, 32S34S, and 34S34S, a new accurate potential energy surface was developed for S2+Ar system. Rotational state-to-state transition cross sections were computed using MQCT, and the master equation modeling of energy transfer kinetics was carried out. It is found that isotopically substituted asymmetric molecules such as 32S34S promote energy transfer due to symmetry breaking and transitions with odd ∆j that become allowed. This process may be responsible for mass-independent isotopic fractionation of sulfur isotopes, typical to the Archean surface deposits

    Aberrations of atomic diffraction - From ultracold atoms to hot ions

    Get PDF
    Atomic diffraction is the central concept of matter-wave interferometers, which provide the opportunity of high-precision rotation and acceleration sensing. Ultracold atoms are the ultimate quantum sensors for this purpose. Transferring photon momentum from two counterpropagating laser beams to atomic wavepackets prepares coherent superpositions in the momentum space, realising atomic beamsplitters and mirrors. Like classical optical systems, these matter-wave devices require exact specifications and ubiquitous imperfections need to be quantified. Therefore, in this thesis, the performance of (3+1)D atomic beamsplitters in the quasi-Bragg regime is studied numerically as well as analytically and is confirmed by experimental data [1]. Ideally, the incoming wavepacket can be split exactly into two parts or reflected perfectly with unit response, independent of its spatial and velocity distribution. However, the velocity selectivity of the Bragg diffraction, as well as losses into undesired diffraction orders in the quasi-Bragg regime, constitute aberrations, which cannot be neglected. The non-ideal behaviour due to spatial variations of the laser beam profiles and wavefront curvatures, regarding realistic Laguerre-Gaussian laser beams instead of ideal plane waves, reduces the diffraction efficiency and leads to rogue momentum components, just like misaligned lasers. In contrast, smooth temporal envelopes improve the beamsplitter performance. Different pulse shapes are taken into account, where some are amenable for closed analytical solutions. The realistic modelling and exhausting aberration studies characterises in detail atomic Bragg beamsplitters and demonstrate pathways for improvements, both required by challenging experiments. For hot ions in accelerator beams the atomic diffraction is used contrary to generate a velocity filter. Two counterpropagating far-detuned lasers transfer a narrow velocity class of ions from an initially broad distribution via a stimulated Raman transition between the ground states of a Λ-system. This colder subensemble prepares optimal initial conditions for precision collinear laser spectroscopy on fast ion beams. The efficiency of the filter is diminished by aberrations like the spontaneous emission from the two single-photon resonances, as well as the ground-state decoherence induced by laser noise. Spatial intensity variations of the ion and laser beams are considered, whereas wavefront curvature is negligible. A comprehensive master equation leads to conditions for the optimal frequency pair of lasers. The time-resolved population transfer characterises the filter performance and is evaluated numerically as well as analytically. Derived models match the numerical results, keeping the computational effort small. Taking into account the mentioned aberrations, the possible use of Raman transition as velocity filter for hot ions is demonstrated. Velocity classes with widths as low as 0.2 m/s can be transferred, achieving a significant population proportion from per mill to percent. Applying the analysis to current 40-Ca+ ion experiments, a sensitivity for measuring high ion acceleration voltages on the ppm level or below is substantiated

    Aspects of Today's Cosmology

    Get PDF
    This book presents some aspects of the cosmological scientific odyssey that started last century. The chapters vary with different particular works, giving a versatile picture. It is the result of the work of many scientists in the field of cosmology, in accordance with their expertise and particular interests. Is a collection of different research papers produced by important scientists in the field of cosmology. A sample of the great deal of efforts made by the scientific community, trying to understand our universe. And it has many challenging subjects, like the possible doomsday to be confirmed by the next decade of experimentation. May be we are now half way in the life of the universe. Many more challenging subjects are not present here: they will be the result of further future work. Among them, we have the possibility of cyclic universes, and the evidence for the existence of a previous universe
    corecore