Elastic cavitation, tube hollowing, and differential growth in plants and biological tissues

Elastic cavitation is a well-known physical process by which elastic materials under stress can open cavities. Usually, cavitation is induced by applied loads on the elastic body. However, growing materials may generate stresses in the absence of applied loads and could induce cavity opening. Here, we demonstrate the possibility of spontaneous growth-induced cavitation in elastic materials and consider the implications of this phenomenon to biological tissues and in particular to the problem of schizogenous aerenchyma formation

Generation of directional, coherent matter beams through dynamical instabilities in Bose-Einstein condensates

We present a theoretical analysis of a coupled, two-state Bose-Einstein condensate with non-equal scattering lengths, and show that dynamical instabilities can be excited. We demonstrate that these instabilities are exponentially amplified resulting in highly-directional, oppositely-propagating, coherent matter beams at specific momenta. To accomplish this we prove that the mean field of our system is periodic, and extend the standard Bogoliubov approach to consider a time-dependent, but cyclic, background. This allows us to use Floquet's theorem to gain analytic insight into such systems, rather than employing the usual Bogoliubov-de Gennes approach, which is usually limited to numerical solutions. We apply our theory to the metastable Helium atom laser experiment of Dall et al. [Phys. Rev. A 79, 011601(R) (2009)] and show it explains the anomalous beam profiles they observed. Finally we demonstrate the paired particle beams will be EPR-entangled on formation.Comment: Corrected reference

Bostonia. Volume 4

Founded in 1900, Bostonia magazine is Boston University's main alumni publication, which covers alumni and student life, as well as university activities, events, and programs

Dynamical derivation of Bode's law

In a planetary or satellite system, idealized as n small bodies in initially coplanar, concentric orbits around a large central body, obeying Newtonian point-particle mechanics, resonant perturbations will cause dynamical evolution of the orbital radii except under highly specific mutual relationships, here derived analytically apparently for the first time. In particular, the most stable situation is achieved (in this idealized model) only when each planetary orbit is roughly twice as far from the Sun as the preceding one, as observed empirically already by Titius (1766) and Bode (1778) and used in both the discoveries of Uranus (1781) and the Asteroid Belt (1801). ETC.Comment: 27 page

Development and validation of a self-report measure of mentalizing: The Reflective Functioning Questionnaire

Reflective functioning or mentalizing is the capacity to interpret both the self and others in terms of internal mental states such as feelings, wishes, goals, desires, and attitudes. This paper is part of a series of papers outlining the development and psychometric features of a new self-report measure, the Reflective Functioning Questionnaire (RFQ), designed to provide an easy to administer self-report measure of mentalizing. We describe the development and initial validation of the RFQ in three studies. Study 1 focuses on the development of the RFQ, its factor structure and construct validity in a sample of patients with Borderline Personality Disorder (BPD) and Eating Disorder (ED) (n=108) and normal controls (n=295). Study 2 aims to replicate these findings in a fresh sample of 129 patients with personality disorder and 281 normal controls. Study 3 addresses the relationship between the RFQ, parental reflective functioning and infant attachment status as assessed with the Strange Situation Procedure (SSP) in a sample of 136 community mothers and their infants. In both Study 1 and 2, confirmatory factor analyses yielded two factors assessing Certainty (RFQ_C) and Uncertainty (RFQ_U) about the mental states of self and others. These two factors were relatively distinct, invariant across clinical and non-clinical samples, had satisfactory internal consistency and test–retest stability, and were largely unrelated to demographic features. The scales discriminated between patients and controls, and were significantly and in theoretically predicted ways correlated with measures of empathy, mindfulness and perspective-taking, and with both self-reported and clinician-reported measures of borderline personality features and other indices of maladaptive personality functioning. Furthermore, the RFQ scales were associated with levels of parental reflective functioning, which in turn predicted infant attachment status in the SSP. Overall, this study lends preliminary support for the RFQ as a screening measure of reflective functioning. Further research is needed, however, to investigate in more detail the psychometric qualities of the RFQ

Low thrust propulsion in a coplanar circular restricted four body problem

This paper formulates a circular restricted four body problem (CRFBP), where the three primaries are set in the stable Lagrangian equilateral triangle configuration and the fourth body is massless. The analysis of this autonomous coplanar CRFBP is undertaken, which identies eight natural equilibria; four of which are close to the smaller body, two stable and two unstable, when considering the primaries to be the Sun and two smaller bodies of the solar system. Following this, the model incorporates `near term' low-thrust propulsion capabilities to generate surfaces of articial equilibrium points close to the smaller primary, both in and out of the plane containing the celestial bodies. A stability analysis of these points is carried out and a stable subset of them is identied. Throughout the analysis the Sun-Jupiter-Asteroid-Spacecraft system is used, for conceivable masses of a hypothetical asteroid set at the libration point L4. It is shown that eight bounded orbits exist, which can be maintained with a constant thrust less than 1:5 10􀀀4N for a 1000kg spacecraft. This illustrates that, by exploiting low-thrust technologies, it would be possible to maintain an observation point more than 66% closer to the asteroid than that of a stable natural equilibrium point. The analysis then focusses on a major Jupiter Trojan: the 624-Hektor asteroid. The thrust required to enable close asteroid observation is determined in the simplied CRFBP model. Finally, a numerical simulation of the real Sun-Jupiter-624 Hektor-Spacecraft is undertaken, which tests the validity of the stability analysis of the simplied model

Analytical solutions of a class of optimum orbit modifications

This paper presents the complete analytical solution of several fundamental problems in orbital correction. The initial orbit is represented by a given point in the phase space, while the final orbit is constrained to stay in a given curve which can be bounded, unbounded, or composed of a finite number of segments of different curves. The inclusion of atmospheric maneuver as part of the optimum process is discussed; its analytical treatment can be carried out by modifying the final state to include the set of orbits having their perigee at the boundary of the atmosphere.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45226/1/10957_2004_Article_BF00927715.pd

Periodic orbits in the restricted three-body problem and Arnold's J+J^+-invariant

We apply Arnold's theory of generic smooth plane curves to Stark-Zeeman systems. This is a class of Hamiltonian dynamical systems that describes the dynamics of an electron in an external electric and magnetic field, and includes many systems from celestial mechanics. Based on Arnold's $J^+$-invariant, we introduce invariants of periodic orbits in planar Stark-Zeeman systems and study their behaviour.Comment: 36 Pages, 16 Figure