Galilean limit of equilibrium relativistic mass distribution for indistinguishable events

The relativistic distribution for indistinguishable events is considered in the mass-shell limit $m^2\cong M^2,$ where $M$ is a given intrinsic property of the events. The characteristic thermodynamic quantities are calculated and subject to the zero-mass and the high-temperature limits. The results are shown to be in agreement with the corresponding expressions of an on-mass-shell relativistic kinetic theory. The Galilean limit $c\rightarrow \infty ,$ which coincides in form with the low-temperature limit, is considered. The theory is shown to pass over to a nonrelativistic statistical mechanics of indistinguishable particles.Comment: Report TAUP-2136-9

Generalized Boltzmann Equation in a Manifestly Covariant Relativistic Statistical Mechanics

We consider the relativistic statistical mechanics of an ensemble of $N$ events with motion in space-time parametrized by an invariant ``historical time'' $\tau .$ We generalize the approach of Yang and Yao, based on the Wigner distribution functions and the Bogoliubov hypotheses, to find the approximate dynamical equation for the kinetic state of any nonequilibrium system to the relativistic case, and obtain a manifestly covariant Boltzmann-type equation which is a relativistic generalization of the Boltzmann-Uehling-Uhlenbeck (BUU) equation for indistinguishable particles. This equation is then used to prove the $H$-theorem for evolution in $\tau .$ In the equilibrium limit, the covariant forms of the standard statistical mechanical distributions are obtained. We introduce two-body interactions by means of the direct action potential $V(q),$ where $q$ is an invariant distance in the Minkowski space-time. The two-body correlations are taken to have the support in a relative $O( 2,1)$-invariant subregion of the full spacelike region. The expressions for the energy density and pressure are obtained and shown to have the same forms (in terms of an invariant distance parameter) as those of the nonrelativistic theory and to provide the correct nonrelativistic limit

Equilibrium Relativistic Mass Distribution for Indistinguishable Events

A manifestly covariant relativistic statistical mechanics of the system of $N$ indistinguishable events with motion in space-time parametrized by an invariant ``historical time'' $\tau$ is considered. The relativistic mass distribution for such a system is obtained from the equilibrium solution of the generalized relativistic Boltzmann equation by integration over angular and hyperbolic angular variables. All the characteristic averages are calculated. Expressions for the pressure and the density of events are found and the relativistic equation of state is obtained. The Galilean limit is considered; the theory is shown to pass over to the usual nonrelativistic statistical mechanics of indistinguishable particles.Comment: TAUP-2115-9

Matrix Microarchitecture and Myosin II Determine Adhesion in 3D Matrices

SummaryBackgroundReports of adhesions in cells growing in 3D vary widely—from nonexistent to very large and elongated—and are often in apparent conflict, due largely to our minimal understanding of the underlying mechanisms that determine 3D cell phenotype. We address this problem directly by systematically identifying mechanisms that determine adhesion in 3D matrices and, from our observations, develop principles widely applicable across 2D and 3D substrates.ResultsWe demonstrate that nonmuscle myosin II activity guides adhesion phenotype in 3D as it does in 2D; however, in contrast to 2D, decreasing bulk matrix stiffness does not necessarily inhibit the formation of elongated adhesions. Even in soft 3D matrices, cells can form large adhesions in areas with appropriate local matrix fiber alignment. We further show that fiber orientation, apart from influencing local stiffness, modulates the available adhesive area and thereby determines adhesion size.ConclusionsThus adhesion in 3D is determined by both myosin activity and the immediate microenvironment of each adhesion, as defined by the local matrix architecture. Important parameters include not only the resistance of the fiber to pulling (i.e., stiffness) but also the orientation and diameter of the fiber itself. These principles not only clarify conflicts in the literature and point to adhesion modulating factors other than stiffness, but also have important implications for tissue engineering and studies of tumor cell invasion

Covariant Equilibrium Statistical Mechanics

A manifest covariant equilibrium statistical mechanics is constructed starting with a 8N dimensional extended phase space which is reduced to the 6N physical degrees of freedom using the Poincare-invariant constrained Hamiltonian dynamics describing the micro-dynamics of the system. The reduction of the extended phase space is initiated forcing the particles on energy shell and fixing their individual time coordinates with help of invariant time constraints. The Liouville equation and the equilibrium condition are formulated in respect to the scalar global evolution parameter which is introduced by the time fixation conditions. The applicability of the developed approach is shown for both, the perfect gas as well as the real gas. As a simple application the canonical partition integral of the monatomic perfect gas is calculated and compared with other approaches. Furthermore, thermodynamical quantities are derived. All considerations are shrinked on the classical Boltzmann gas composed of massive particles and hence quantum effects are discarded.Comment: 22 pages, 1 figur

Approximate resonance states in the semigroup decomposition of resonance evolution

The semigroup decomposition formalism makes use of the functional model for $C_{.0}$ class contractive semigroups for the description of the time evolution of resonances. For a given scattering problem the formalism allows for the association of a definite Hilbert space state with a scattering resonance. This state defines a decomposition of matrix elements of the evolution into a term evolving according to a semigroup law and a background term. We discuss the case of multiple resonances and give a bound on the size of the background term. As an example we treat a simple problem of scattering from a square barrier potential on the half-line.Comment: LaTex 22 pages 3 figure

Relativistic mass distribution in event-anti-event system and ``realistic'' equation of state for hot hadronic matter

We find the equation of state $p,\rho \propto T^6,$ which gives the value of the sound velocity $c^2=0.20,$ in agreement with the ``realistic'' equation of state for hot hadronic matter suggested by Shuryak, in the framework of a covariant relativistic statistical mechanics of an event--anti-event system with small chemical and mass potentials. The relativistic mass distribution for such a system is obtained and shown to be a good candidate for fitting hadronic resonances, in agreement with the phenomenological models of Hagedorn, Shuryak, {\it et al.} This distribution provides a correction to the value of specific heat 3/2, of the order of 5.5\%, at low temperatures.Comment: 19 pages, report TAUP-2161-9

Positive and Negative Expectations of Hopelessness as Longitudinal Predictors of Depression, Suicidal Ideation, and Suicidal Behavior in High‐Risk Adolescents

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/136513/1/sltb12273.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/136513/2/sltb12273_am.pd

Adult Manifestation of Milder Forms of Autism Spectrum Disorder; Autistic and Non-autistic Psychopathology

We compared the presence of autistic and comorbid psychopathology and functional impairments in young adults who received a clinical diagnosis of Pervasive Developmental Disorders Not Otherwise Specified or Asperger's Disorder during childhood to that of a referred comparison group. While the Autism Spectrum Disorder group on average scored higher on a dimensional ASD self- and other-report measure than clinical controls, the majority did not exceed the ASD cutoff according to the Autism Diagnostic Observation Schedule. Part of the individuals with an ASD diagnosis in their youth no longer show behaviors that underscribe a clinical ASD diagnosis in adulthood, but have subtle difficulties in social functioning and a vulnerability for a range of other psychiatric disorders