Dynamical Friction in Nonlocal Gravity

We study dynamical friction in the Newtonian regime of nonlocal gravity (NLG), which is a classical nonlocal generalization of Einstein’s theory of gravitation. The nonlocal aspect of NLG simulates dark matter. The attributes of the resulting effective dark matter are described and the main physical predictions of NLG, which has a characteristic length scale of order 1 kpc, for galactic dynamics are presented. Within the framework of NLG, we derive the analog of Chandrasekhar’s formula for dynamical friction. The astrophysical implications of the results for the apparent rotation of a central bar subject to dynamical friction in a barred spiral galaxy are briefly discussed.

Mandibular rotation during the transitional dentition

Objective: To determine whether dentoalveolar changes or vertical condylar growth is more closely related to the true forward rotation of the mandible during the transition between the late primary and early mixed dentition stages of development. Materials and Methods: The sample included 50 subjects (25 males and 25 females) with Class I (N = 25) and Class II (N = 25) molar relationships. They were selected based on the availability of lateral cephalograms at two developmental stages: T1: last film with complete primary dentition (5.8 ± 0.4 years) and T2: first film with permanent incisors and permanent molars fully erupted (8.0 ± 0.2 years). Seventeen landmarks were identified and 22 measurements were calculated. The mandibles at T1 and T2 were superimposed using natural reference structures in order to measure true mandibular rotation. Results: The mandible underwent −2.4° ± 2.6° of true rotation, 1.9° ± 2.4° of remodeling, and −0.6° ± 1.8° of apparent rotation. There were no significant sex or Class differences in true rotation, remodeling, and apparent rotation. There was a moderate correlation (r = 0.76) between true rotation and remodeling and a moderately low correlation (r = 0.40) between true rotation and apparent rotation. There was a weak correlation between true rotation and SNA (r = 0.28). True rotation was most closely associated with the increases in U1/S-N (r = −0.34), increases in U1/PP (r = −0.36), and decreases in Id-Me (r = 0.36). Conclusions: Independent of sex and Class, the true mandibular rotation that occurred between the late primary and early mixed dentition was mostly masked by angular remodeling, resulting in limited amounts of apparent rotation. True rotation was significantly related to anterior dentoalveolar changes but not to the vertical growth changes that occurred.

Mandibular Rotation and Remodeling Changes during Early Childhood

Objective: To describe the mandibular rotation and remodeling of younger children. Materials and Methods: The sample included 43 males and 43 females who participated in the Bolton-Brush Growth Study at Case Western Reserve University in Ohio. They were chosen on the basis of having Class I (n = 45) or Class II (n = 41) molar relationships and longitudinal lateral cephalograms at three developmental stages of the dentition: late primary (T1: 5.7 ± 0.5 y), early mixed (T2: 8.4 ± 0.6 y), and full permanent dentition (T3: 15.4 ± 0.5 y). Each subject's cephalograms were traced and four landmarks were digitized. Cranial base and mandibular superimpositions were performed with the use of natural reference structures. Results: Yearly rates of true rotation, apparent rotation, and angular remodeling showed significant (P < .05) changes throughout. True rotation was moderately correlated with angular remodeling and apparent rotation. Although no significant sex differences in annual rates of rotation were noted, subjects with Class I molar relationships showed significantly more angular remodeling from T2-T3 than did subjects with Class II molar relationships. Rates of true forward rotation were significantly greater with T1-T2 than with T2-T3 (1.3 and 0.7 degrees/y, respectively). Conclusion: Although significant amounts of true mandibular rotation and angular remodeling occur during childhood and adolescence, true rotation is greatest during the transition from late primary to early mixed dentition. (Angle Orthod. 2009:79; )

Symmetric Parsec-Scale Radio Jets in NGC 4261

VLBA observations of NGC 4261 (3C 270) reveal highly symmetric radio structures at both 1.6 and 8.4 GHz. There is little evidence for free-free absorption in the inner few pc, despite the fact that HST imaging shows this galaxy to contain a nearly edge-on disk of gas and dust in its nucleus. However, at our highest resolution we find a narrow gap in emission just east of the radio core which we interpret as evidence for a small (sub-parsec) nearly edge-on accretion disk which is obscuring the base of the counterjet. The position angle of the pc-scale radio axis agrees with the position angle of the VLA-scale jets, which differs from the apparent rotation axis of the nuclear disk seen by HST.

Conflicts with Extraretinal and Monocular Cues Cause the Small Range of the Induced Effect

A vertical magnifier before one eye causes the induced effect: an apparent rotation of frontal surfaces toward that eye. The rotation required to restore apparent frontoparallelism grows linearly up to ∼4% magnification, but plateaus at 8%. We examined the cause of the plateau. Horizontal disparities (quantified by horizontal size ratios, HSRs) are ambiguous indicators of surface slant. Various retinal and nonretinal signals can allow veridical slant estimation from HSR, sensed eye position, vertical disparities (vertical size ratios, VSRs), and monocular cues. Vertical or horizontal magnification of one eye's image alters the natural relationships among HSR, VSR, eye position, and monocular cues. We argue that the induced-effect plateau is caused by conflicts between these means of estimating slant. A plateau is not observed in the geometric effect because some of the conflicts do not occur with horizontal magnification. Two experiments were designed to test this hypothesis. When strong monocular cues were present, plateaux occurred at ∼8% magnification in the induced, but not the geometric effect. When monocular slant cues were made useless, induced-effect plateaux were abolished. Even with strong monocular cues present, plateaux in the induced effect were eliminated when eye position was consistent with the vertical magnification in the retinal images. The smaller range of the induced effect can only be understood from consideration of all the signals involved in slant estimation.