The invariant charges of the Nambu-Goto String and Canonical Quantization

It is shown that the algebra of diffeomorphism-invariant charges of the Nambu-Goto string cannot be quantized in the framework of canonical quantization. The argument is shown to be independent of the dimension of the underlying Minkowski space.Comment: v2: reference adde

Pohlmeyer reduction revisited

A systematic group theoretical formulation of the Pohlmeyer reduction is presented. It provides a map between the equations of motion of sigma models with target-space a symmetric space M=F/G and a class of integrable multi-component generalizations of the sine-Gordon equation. When M is of definite signature their solutions describe classical bosonic string configurations on the curved space-time R_t\times M. In contrast, if M is of indefinite signature the solutions to those equations can describe bosonic string configurations on R_t\times M, M\times S^1_\vartheta or simply M. The conditions required to enable the Lagrangian formulation of the resulting equations in terms of gauged WZW actions with a potential term are clarified, and it is shown that the corresponding Lagrangian action is not unique in general. The Pohlmeyer reductions of sigma models on CP^n and AdS_n are discussed as particular examples of symmetric spaces of definite and indefinite signature, respectively.Comment: 45 pages, LaTeX, more references added, accepted for publication in JHE

W-Infinity Symmetry of the Nambu-Goto String in 4 Dimensions

We consider a bosonic string propagating in 4--dim Minkowski space. We show that in the orthonormal gauge the classical system exhibits a hidden $W_{\infty}$ chiral symmetry, arising from the equivalence of its transverse modes with the $SU(2)/U(1)$ coset model defined on the string world--sheet. Generalizations to other string backgrounds are proposed. We also define a Liouville--like transformation that maps solutions of the $SU(2)/U(1)$ coset model into the solution space of two decoupled Liouville theories. Inverting this transformation, however, remains an open problem.Comment: Latex, 12

Modeling cell proliferation in a perfusion tissue engineering bioreactor

In this dissertation we develop a comprehensive model to simulate a tissue engineering experiment. The experiment takes place in a bioreactor in which a cell seeded porous scaffold is placed, and the scaffold experiences a perfused flow of a nutrient-rich culture medium. The goal of the model is to assist experimentalists in evaluation of different parameter scenarios as the time needed to simulate an experiment is significantly less than the time needed for the experiment itself. We provide the full two-dimensional model development, as well as investigation into possible variations of specific model choices, and we demonstrate the robustness and versatility of the model. Simulation results are presented with different initial cell seeding scenarios which increase in complexity with each simulation. We next model the effect of printing a growth factor onto the scaffold in an attempt to direct cell motility and enhance proliferation via a process known as haptotaxis. While a quantitative representation of these phenomena requires more experimental data than are yet available, qualitative agreement with preliminary experimental studies is obtained, and appears promising. The ultimate goal of such modeling is to ascertain initial conditions (growth factor distribution, initial cell seeding, etc.) that will lead to a final desired outcome. A simplified 2D mathematical model for tissue growth within a cyclically-loaded tissue engineering scaffold is then analyzed. Such cyclic loading has the potential to improve yield and functionality of tissue such as bone and cartilage when grown on a scaffold within a perfusion bioreactor. The cyclic compression affects the flow of the perfused nutrient, leading to flow properties that are inherently unsteady, though periodic, on a timescale short compared with that of tissue proliferation. A two-timescale analysis based on these two well-separated timescales is exploited to derive a closed model for the tissue growth on the long timescale. Some sample numerical results are given for the final model, and the comparison with the unloaded case is discussed. Finally, we simulate to hypothetical extensions to the basic model. We first test the hypothesis of a death rate which varies as a function of the local fluid flow and compare the results to the original model. The second test is the introduction of a channel through the center of the porous scaffold thought to aid in nutrient delivery to the cells in the interior of the scaffold. The last two simulations are presented to illustrate the ability that the model has to incorporate many different supplemental experimental situations, whether they have yet been experimentally considered or not

The Force Between Giant Magnons

We compute the force and torque between well-separated, slowly-moving Giant Magnons with arbitrary orientations on S^5. We propose an effective Hamiltonian for Giant Magnons in this regime

Gauging kinematical and internal symmetry groups for extended systems: the Galilean one-time and two-times harmonic oscillators

The possible external couplings of an extended non-relativistic classical system are characterized by gauging its maximal dynamical symmetry group at the center-of-mass. The Galilean one-time and two-times harmonic oscillators are exploited as models. The following remarkable results are then obtained: 1) a peculiar form of interaction of the system as a whole with the external gauge fields; 2) a modification of the dynamical part of the symmetry transformations, which is needed to take into account the alteration of the dynamics itself, induced by the {\it gauge} fields. In particular, the Yang-Mills fields associated to the internal rotations have the effect of modifying the time derivative of the internal variables in a scheme of minimal coupling (introduction of an internal covariant derivative); 3) given their dynamical effect, the Yang-Mills fields associated to the internal rotations apparently define a sort of Galilean spin connection, while the Yang-Mills fields associated to the quadrupole momentum and to the internal energy have the effect of introducing a sort of dynamically induced internal metric in the relative space.Comment: 32 pages, LaTex using the IOP preprint macro package (ioplppt.sty available at: http://www.iop.org/). The file is available at: http://www.fis.unipr.it/papers/1995.html The file is a uuencoded tar gzip file with the IOP preprint style include

Design for subjective well-being in interior architecture

Can interior environments engage people in pleasurable and meaningful experiences and thereby have a positive influence on their happiness? This paper discusses why and how interior architects might want to consider implementing ideas in relation to ‘design for subjective well-being’. Despite of people being the ingredients that bring life to the built environment, it tends to be designed in such a way for them to predominantly only passively absorb the surrounding. Up to date, when designing interior environments, (interior) architects are mainly concerned about the fulfillment of various rather objective considerations. Typical reflections in this respect are: is there enough daylight, how are the acoustics, how is the accessibility and the organization of the inner space? Starting from such premises, the atmosphere of the inner space is given substance. However, empirical studies have shown that long-term happiness is less a matter of one’s circumstances than of the activities that a person engages in. Hence, one could go one step further from viewing the built environment as a static entity, to designing spaces that facilitate desirable activities. In other words, inner environments could aim to stimulate experiences that provide pleasure and meaning to its inhabitants. Subjective well-being (SWB) is an emerging research topic in the field of design sciences. Design models and strategies are being developed in an effort to increase users’ well-being. However, a detailed understanding of how these insights apply to interior architecture still needs to be refined. For this reason, this paper will firstly outline why interior environments could have the potential to contribute to people’s SWB and thereby to become platforms for the full spectrum of human well-being. The second section of the paper reflects on how a deliberate focus on SWB will affect the process of designing interior environments. The Positive Design Framework, developed by Desmet & Pohlmeyer (2013), will be introduced to the (interior) architectural community. Interior architects can use this framework as a guide to assist them in the design process of interior environments that aim to contribute to people’s happiness. A number of examples will demonstrate in an interior architectural vocabulary the value that this framework can have for this discipline

Particle versus Field Structure in Conformal Quantum Field Theories

I show that a particle structure in conformal field theory is incompatible with interactions. As a substitute one has particle-like exitations whose interpolating fields have in addition to their canonical dimension an anomalous contribution. The spectra of anomalous dimension is given in terms of the Lorentz invariant quadratic invariant (compact mass operator) of a conformal generator $R_{\mu}$ with pure discrete spectrum. The perturbative reading of $R_{0\text{}}$as a Hamiltonian in its own right i.e. associated with an action in a functional integral setting naturally leads to the AdS formulation. The formal service role of AdS in order to access CQFT by a standard perturbative formalism (without being forced to understand first massive theories and then taking their scale-invariant limit) vastly increases the realm of conventionally accessible 4-dim. CQFT beyond those for which one had to use Lagrangians with supersymmetry in order to have a vanishing Beta-function.Comment: 9 pages tcilatex, reference added, some typos correcte