Chiral symmetry analysis and rigid rotational invariance for the lattice dynamics of single-wall carbon nanotubes

We provide a detailed expression of the vibrational potential for the lattice dynamics of single-wall carbon nanotubes (SWCNT's) satisfying the requirements of the exact rigid translational as well as rotational symmetries, which is a nontrivial generalization of the valence force model for the planar graphene sheet. With the model, the low-frequency behavior of the dispersion of the acoustic modes as well as the flexure mode can be precisely calculated. Based upon a comprehensive chiral symmetry analysis, the calculated mode frequencies (including all the Raman- and infrared-active modes), velocities of acoustic modes, and the polarization vectors are systematically fitted in terms of the chiral angle and radius, where the restrictions of various symmetry operations of SWCNT's are fulfilled.

Set invariance in control

The properties of positively invariant sets are involved in many different problems in control theory, such as constrained control, robustness analysis, synthesis and optimization. In this paper we provide an overview of the literature concerning positively invariant sets and their application to the analysis and synthesis of control systems.

Nonlinear Acoustics in Underwater and Biomedical Applications: Array Performance Degradation and Time Reversal Invariance

This dissertation describes a model for acoustic propagation in inhomogeneous flu- ids, and explores the focusing by arrays onto targets under various conditions. The work explores the use of arrays, in particular the time reversal array, for underwater and biomedical applications. Aspects of propagation and phasing which can lead to reduced focusing effectiveness are described. An acoustic wave equation was derived for the propagation of finite-amplitude waves in lossy time-varying inhomogeneous fluid media. The equation was solved numerically in both Cartesian and cylindrical geometries using the finite-difference time-domain (FDTD) method. It was found that time reversal arrays are sensitive to several debilitating factors. Focusing ability was determined to be adequate in the presence of temporal jitter in the time reversed signal only up to about one-sixth of a period. Thermoviscous absorption also had a debilitating effect on focal pressure for both linear and nonlinear propagation. It was also found that nonlinearity leads to degradation of focal pressure through amplification of the received signal at the array, and enhanced absorption in the shocked waveforms. This dissertation also examined the heating effects of focused ultrasound in a tissue-like medium. The application considered is therapeutic heating for hyperther- mia. The acoustic model and a thermal model for tissue were coupled to solve for transient and steady temperature profiles in tissue-like media. The Pennes bioheat equation was solved using the FDTD method to calculate the temperature fields in tissue-like media from focused acoustic sources. It was found that the temperature-dependence of the medium's background prop- erties can play an important role in the temperature predictions. Finite-amplitude effects contributed excess heat when source conditions were provided for nonlinear ef- fects to manifest themselves. The effect of medium heterogeneity was also found to be important in redistributing the acoustic and temperature fields, creating regions with hotter and colder temperatures than the mean by local scattering and lensing action. These temperature excursions from the mean were found to increase monotonically with increasing contrast in the medium's properties.

Probabilistic choice: A simple invariance.

When subjects must choose repeatedly between two or more alternatives, each of which dispenses reward on a probabilistic basis (two-armed bandit ), their behavior is guided by the two possible outcomes, reward and nonreward. The simplest stochastic choice rule is that the probability of choosing an alternative increases following a reward and decreases following a nonreward (reward following ). We show experimentally and theoretically that animal subjects behave as if the absolute magnitudes of the changes in choice probability caused by reward and nonreward do not depend on the response which produced the reward or nonreward (source independence ), and that the effects of reward and nonreward are in constant ratio under fixed conditions (effect-ratio invariance )--properties that fit the definition of satisficing . Our experimental results are either not predicted by, or are inconsistent with, other theories of free-operant choice such as Bush-Mosteller, molar maximization, momentary maximizing, and melioration (matching).

Lorentz TEM investigation of the switching behavior in artificial spin ice building blocks

Frustration – the inability to simultaneously satisfy all interactions – occurs in a wide range of systems including neural networks, water ice and magnetic systems. An example of the latter is the so called spin-ice in pyrochlore materials [1] which have attracted a lot of interest not least due to the emergence of magnetic monopole defects when the ‘ice rules’ governing the local ordering breaks down [2]. However it is not possible to directly measure the frustrated property – the direction of the magnetic moments – in such spin ice systems with current experimental techniques. This problem can be solved by instead studying artificial spin-ice systems where the molecular magnetic moments are replaced by nanoscale ferromagnetic islands [3-8]. Two different arrangements of the ferromagnetic islands have been shown to exhibit spin ice behaviour: a square lattice maintaining four moments at each vertex [3,8] and the Kagome lattice which has only three moments per vertex but equivalent interactions between them [4-7]. Magnetic monopole defects have been observed in both types of lattices [7-8]. One of the challenges when studying these artificial spin-ice systems is that it is difficult to arrive at the fully demagnetised ground-state [6-8].
Here we present a study of the switching behaviour of building blocks of the Kagome lattice influenced by the termination of the lattice. Ferromagnetic islands of nominal size 1000 nm by 100 nm were fabricated in five island blocks using electron-beam lithography and lift-off techniques of evaporated 18 nm Permalloy (Ni80Fe20) films. Each block consists of a central island with four arms terminated by a different number and placement of ‘injection pads’, see Figure 1. The islands are single domain and magnetised along their long axis. The structures were grown on a 50 nm thick electron transparent silicon nitride membrane to allow TEM observation, which was back-coated with a 5 nm film of Au to prevent charge build-up during the TEM experiments.
To study the switching behaviour the sample was subjected to a magnetic field strong enough to magnetise all the blocks in one direction, see Figure 1. Each block obeys the Kagome lattice ‘ice-rules’ of “2-in, 1-out” or “1-in, 2-out” in this fully magnetised state. Fresnel mode Lorentz TEM images of the sample were then recorded as a magnetic field of increasing magnitude was applied in the opposite direction. While the Fresnel mode is normally used to image magnetic domain structures [9] for these types of samples it is possible to deduce the direction of the magnetisation from the Lorentz contrast [5]. All images were recorded at the same over-focus judged to give good Lorentz contrast.
The magnetisation was found to switch at different magnitudes of the applied field for nominally identical blocks. However, trends could still be identified: all the blocks with any injection pads, regardless of placement and number, switched the direction of the magnetisation of their central island at significantly smaller magnitudes of the applied magnetic field than the blocks without injection pads. It can therefore be concluded that the addition of an injection pad lowers the energy barrier to switching the connected island, acting as a nucleation site for monopole defects. In these five island blocks the defects immediately propagate through to the other side, but in a larger lattice the monopoles could potentially become trapped at a vertex and observed [10].
References

[1] M J Harris et al, Phys Rev Lett 79 (1997) p.2554.
[2] C Castelnovo, R Moessner and S L Sondhi, Nature 451 (2008) p. 42.
[3] R F Wang et al, Nature 439 (2006) 303.
[4] M Tanaka et al, Phys Rev B 73 (2006) 052411.
[5] Y Qi, T Brintlinger and J Cumings, Phys Rev B 77 (2008) 094418.
[6] E Mengotti et al, Phys Rev B 78 (2008) 144402.
[7] S Ladak et al, Nature Phys 6 (2010) 359.
[8] C Phatak et al, Phys Rev B 83 (2011) 174431.
[9] J N Chapman, J Phys D 17 (1984) 623.
[10] The authors gratefully acknowledge funding from the EPSRC under grant number EP/D063329/1.

MALTS: A Tool to Simulate Lorentz Transmission Electron Microscopy From Micromagnetic Simulations

Here we describe the development of the MALTS software which is a generalized tool that simulates Lorentz Transmission Electron Microscopy (LTEM) contrast of magnetic nanostructures. Complex magnetic nanostructures typically have multiple stable domain structures. MALTS works in conjunction with the open access micromagnetic software Object Oriented Micromagnetic Framework or MuMax. Magnetically stable trial magnetization states of the object of interest are input into MALTS and simulated LTEM images are output. MALTS computes the magnetic and electric phases accrued by the transmitted electrons via the Aharonov-Bohm expressions. Transfer and envelope functions are used to simulate the progression of the electron wave through the microscope lenses. The final contrast image due to these effects is determined by Fourier Optics. Similar approaches have been used previously for simulations of specific cases of LTEM contrast. The novelty here is the integration with micromagnetic codes via a simple user interface enabling the computation of the contrast from any structure. The output from MALTS is in good agreement with both experimental data and published LTEM simulations. A widely-available generalized code for the analysis of Lorentz contrast is a much needed step towards the use of LTEM as a standardized laboratory technique.

Measuring math anxiety in Italian college and high school students: Validity, reliability and gender invariance of the Abbreviated Math Anxiety Scale (AMAS)

Given that the ability to manage numbers is essential in a modern society, mathematics anxiety – which has been demonstrated to have unfortunate consequences in terms of mastery of math – has become a subject of increasing interest, and the need to accurately measure it has arisen. One of the widely employed scales to measure math anxiety is the Abbreviated Math Anxiety Scale (AMAS) (Hopko, Mahadevan, Bare & Hunt, 2003). The first aim of the present paper was to confirm the factor structure of the AMAS when administered to Italian high school and college students, and to test the invariance of the scale across educational levels. Additionally, we assessed the reliability and validity of the Italian version of the scale. Finally, we tested the invariance of the AMAS across genders. The overall findings provide evidence for the validity and reliability of the AMAS when administered to Italian students.

Sex-related invariance across cultures in an online role-playing game

This study examines the Social Dominance Orientation of players of the online roleplaying game World of Warcraft. The World of Warcraft offers an opportunity to investigate social dominance and biological sex differences in an environment where there is no cultural dominance of one sex over another. Social Dominance Orientation has been found to be different between males and females, with males scoring higher. However, this might be the consequence of social context. To this end sex differences between male and female players were investigated in the World of Warcraft environment, as well as the effects of chosen character sex. Player sex and character sex were found to have effects on Social Dominance Orientation. These results add further support to claims that Social Dominance Orientation has the characteristics of a sexually selected disposition to acquire resources and out-compete rival groups.

Spacelike maximal surfaces in 3D Lorentz-Minkowski space

We investigate spacelike maximal surfaces in 3-dimensional Lorentz-Minkowski space, give an Enneper-Weierstrass representation of such surfaces and classify those with a Lorentzian or Euclidian rotation symmetry.

A Detailed Look at Scale and Translation Invariance in a Hierarchical Neural Model of Visual Object Recognition

The HMAX model has recently been proposed by Riesenhuber & Poggio as a hierarchical model of position- and size-invariant object recognition in visual cortex. It has also turned out to model successfully a number of other properties of the ventral visual stream (the visual pathway thought to be crucial for object recognition in cortex), and particularly of (view-tuned) neurons in macaque inferotemporal cortex, the brain area at the top of the ventral stream. The original modeling study only used ``paperclip'' stimuli, as in the corresponding physiology experiment, and did not explore systematically how model units' invariance properties depended on model parameters. In this study, we aimed at a deeper understanding of the inner workings of HMAX and its performance for various parameter settings and ``natural'' stimulus classes. We examined HMAX responses for different stimulus sizes and positions systematically and found a dependence of model units' responses on stimulus position for which a quantitative description is offered. Interestingly, we find that scale invariance properties of hierarchical neural models are not independent of stimulus class, as opposed to translation invariance, even though both are affine transformations within the image plane.

Translation Invariance in Object Recognition, and Its Relation to Other Visual Transformations

Human object recognition is generally considered to tolerate changes of the stimulus position in the visual field. A number of recent studies, however, have cast doubt on the completeness of translation invariance. In a new series of experiments we tried to investigate whether positional specificity of short-term memory is a general property of visual perception. We tested same/different discrimination of computer graphics models that were displayed at the same or at different locations of the visual field, and found complete translation invariance, regardless of the similarity of the animals and irrespective of direction and size of the displacement (Exp. 1 and 2). Decisions were strongly biased towards same decisions if stimuli appeared at a constant location, while after translation subjects displayed a tendency towards different decisions. Even if the spatial order of animal limbs was randomized ("scrambled animals"), no deteriorating effect of shifts in the field of view could be detected (Exp. 3). However, if the influence of single features was reduced (Exp. 4 and 5) small but significant effects of translation could be obtained. Under conditions that do not reveal an influence of translation, rotation in depth strongly interferes with recognition (Exp. 6). Changes of stimulus size did not reduce performance (Exp. 7). Tolerance to these object transformations seems to rely on different brain mechanisms, with translation and scale invariance being achieved in principle, while rotation invariance is not.