183,881 research outputs found
Physically Interacting With Four Dimensions
Thesis (Ph.D.) - Indiana University, Computer Sciences, 2009People have long been fascinated with understanding the fourth
dimension. While making pictures of 4D objects by projecting them to 3D can help reveal basic geometric features, 3D graphics images by themselves are of limited value. For example, just as 2D shadows of 3D curves may have lines crossing one another in the shadow, 3D graphics projections of smooth 4D topological surfaces can be interrupted where one surface intersects another.
The research presented here creates physically realistic models for
simple interactions with objects and materials in a virtual 4D world.
We provide methods for the construction, multimodal exploration, and interactive manipulation of a wide variety of 4D objects. One basic achievement of this research is to exploit the free motion of a
computer-based haptic probe to support a continuous motion that
follows the \emph{local continuity\/} of a 4D surface, allowing collision-free exploration in the 3D projection. In 3D, this interactive probe follows the full local continuity of the surface as though we were in fact \emph{physically touching\/} the actual static 4D object.
Our next contribution is to support dynamic 4D objects that can move, deform, and collide with other objects as well as with themselves. By combining graphics, haptics, and collision-sensing physical modeling, we can thus enhance our 4D visualization experience. Since we cannot actually place interaction devices in 4D, we develop fluid methods for interacting with a 4D object in its 3D shadow image using adapted reduced-dimension 3D tools for manipulating objects embedded in 4D. By physically modeling the correct properties of 4D surfaces, their bending forces, and their collisions in the 3D interactive or haptic controller interface, we can support full-featured physical exploration of 4D mathematical objects in a manner that is otherwise far beyond the real-world experience accessible to human beings
Bosonization and Fermion Liquids in Dimensions Greater Than One
(Revised, with postscript figures appended, corrections and added comments.)
We develop and describe new approaches to the problem of interacting Fermions
in spatial dimensions greater than one. These approaches are based on
generalizations of powerful tools previously applied to problems in one spatial
dimension. We begin with a review of one-dimensional interacting Fermions. We
then introduce a simplified model in two spatial dimensions to study the role
that spin and perfect nesting play in destabilizing Fermion liquids. The
complicated functional renormalization group equations of the full problem are
made tractable in our model by replacing the continuum of points that make up
the closed Fermi line with four Fermi points. Despite this drastic
approximation, the model exhibits physically reasonable behavior both at
half-filling (where instabilities occur) and away from half-filling (where a
Luttinger liquid arises). Next we implement the Bosonization of higher
dimensional Fermi surfaces introduced by Luther and advocated most recently by
Haldane. Bosonization incorporates the phase space and small-angle scattering
.... (7 figures, appended as a postscript file at the end of the TeX file).Comment: 48 text pages, plain TeX, BUP-JBM-
Bootstrapping Vector Models in
We use the conformal bootstrap to study conformal field theories with
global symmetry in and spacetime dimensions that have a scalar
operator transforming as an vector. The crossing symmetry of
the four-point function of this vector operator, along with unitarity
assumptions, determine constraints on the scaling dimensions of conformal
primary operators in the OPE. Imposing a lower bound on
the second smallest scaling dimension of such an -singlet conformal
primary, and varying the scaling dimension of the lowest one, we obtain an
allowed region that exhibits a kink located very close to the interacting
-symmetric CFT conjectured to exist recently by Fei, Giombi, and
Klebanov. Under reasonable assumptions on the dimension of the second lowest
singlet in the OPE, we observe that this kink
disappears in for small enough , suggesting that in this case an
interacting CFT may cease to exist for below a certain critical
value.Comment: 24 pages, 5 figures; v2 minor improvement
General Properties of Multiscalar RG Flows in
Fixed points of scalar field theories with quartic interactions in
dimensions are considered in full generality. For such
theories it is known that there exists a scalar function of the couplings
through which the leading-order beta-function can be expressed as a gradient.
It is here proved that the fixed-point value of is bounded from below by a
simple expression linear in the dimension of the vector order parameter, .
Saturation of the bound requires a marginal deformation, and is shown to arise
when fixed points with the same global symmetry coincide in coupling space.
Several general results about scalar CFTs are discussed, and a review of known
fixed points is given.Comment: 29 pages, 4 figures; see section 3 for a prize problem. v2: small
correction in appendix, typos fixed. v3: minor additions. v4: some
next-to-leading order results added, typos fixe
EVAPORATION OF QUARK DROPS DURING THE COSMOLOGICAL Q-H TRANSITION
We have carried out a study of the hydrodynamics of disconnected quark
regions during the final stages of the cosmological quark-hadron transition. A
set of relativistic Lagrangian equations is presented for following the
evaporation of a single quark drop and results from the numerical solution of
this are discussed. A self-similar solution is shown to exist and the formation
of baryon number density inhomogeneities at the end of the drop contraction is
discussed.Comment: 12 pages Phys. Rev. format, uuencoded postscript file including 12
figure
Charged Dual String Vacua from Interacting Rotating Black Holes Via Discrete and Nonlinear Symmetries
Using the stationary formulation of the toroidally compactified heterotic
string theory in terms of a pair of matrix Ernst potentials we consider the
four-dimensional truncation of this theory with no U(1) vector fields excited.
Imposing one time-like Killing vector permits us to express the stationary
effective action as a model in which gravity is coupled to a matrix Ernst
potential which, under certain parametrization, allows us to interpret the
matter sector of this theory as a double Ernst system. We generate a web of
string vacua which are related to each other via a set of discrete symmetries
of the effective action (some of them involve S-duality transformations and
possess non-perturbative character). Some physical implications of these
discrete symmetries are analyzed and we find that, in some particular cases,
they relate rotating black holes coupled to a dilaton with no Kalb--Ramond
field, static black holes with non-trivial dilaton and antisymmetric tensor
fields, and rotating and static naked singularities. Further, by applying a
nonlinear symmetry, namely, the so-called normalized Harrison transformation,
on the seed field configurations corresponding to these neutral backgrounds, we
recover the U(1)^n Abelian vector sector of the four-dimensional action of the
heterotic string, charging in this way the double Ernst system which
corresponds to each one of the neutral string vacua, i.e., the stationary and
the static black holes and the naked singularities.Comment: 19 pages in latex, added referenc
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