Inverse problem for the wave equation : partial data and novel boundary sources

An inverse problem for the wave equation is a mathematical formulation of the problem to convert measurements of sound waves to information about the wave speed governing the propagation of the waves. This doctoral thesis extends the theory on the inverse problems for the wave equation in cases with partial measurement data and also considers detection of discontinuous interfaces in the wave speed. A possible application of the theory is obstetric sonography in which ultrasound measurements are transformed into an image of the fetus in its mother's uterus. The wave speed inside the body can not be directly observed but sound waves can be produced outside the body and their echoes from the body can be recorded. The present work contains five research articles. In the first and the fifth articles we show that it is possible to determine the wave speed uniquely by using far apart sound sources and receivers. This extends a previously known result which requires the sound waves to be produced and recorded in the same place. Our result is motivated by a possible application to reflection seismology which seeks to create an image of the Earth s crust from recording of echoes stimulated for example by explosions. For this purpose, the receivers can not typically lie near the powerful sound sources. In the second article we present a sound source that allows us to recover many essential features of the wave speed from the echo produced by the source. Moreover, these features are known to determine the wave speed under certain geometric assumptions. Previously known results permitted the same features to be recovered only by sequential measurement of echoes produced by multiple different sources. The reduced number of measurements could increase the number possible applications of acoustic probing. In the third and fourth articles we develop an acoustic probing method to locate discontinuous interfaces in the wave speed. These interfaces typically correspond to interfaces between different materials and their locations are of interest in many applications. There are many previous approaches to this problem but none of them exploits sound sources varying freely in time. Our use of more variable sources could allow more robust implementation of the probing.

Effect of long-wave UV radiation on mouse melanoma: an in vitro and in vivo study

The skin cancer incidence has increased substantially over the past decades and the role of ultraviolet (UV) radiation in the etiology of skin cancer is well established. Ultraviolet B radiation (280-320 nm) is commonly considered as the more harmful part of the UV-spectrum due to its DNA-damaging potential and well-known carcinogenic effects. Ultraviolet A radiation (320-400 nm) is still regarded as a relatively low health hazard. However, UVA radiation is the predominant component in sunlight, constituting more than 90% of the environmentally relevant solar ultraviolet radiation. In the light of the recent scientific evidence, UVA has been shown to have genotoxic and immunologic effects, and it has been proposed that UVA plays a significant role in the development of skin cancer. Due to the popularity of skin tanning lamps, which emit high intensity UVA radiation and because of the prolonged sun tanning periods with the help of effective UVB blockers, the potential deleterious effects of UVA has emerged as a source of concern for public health. The possibility that UV radiation may affect melanoma metastasis has not been addressed before. UVA radiation can modulate various cellular processes, some of which might affect the metastatic potential of melanoma cells. The aim of the present study was to investigate the possible role of UVA irradiation on the metastatic capacity of mouse melanoma both in vitro and in vivo. The in vitro part of the study dealt with the enhancement of the intercellular interactions occurring either between tumor cells or between tumor cells and endothelial cells after UVA irradiation. The use of the mouse melanoma/endothelium in vitro model showed that a single-dose of UVA to melanoma cells causes an increase in melanoma cell adhesiveness to non-irradiated endothelium after 24-h irradiation. Multiple-dose irradiation of melanoma cells already increased adhesion at a 1-h time-point, which suggests the possible cumulative effect of multiple doses of UVA irradiation. This enhancement of adhesiveness might lead to an increase in binding tumor cells to the endothelial lining of vasculature in various internal organs if occurring also in vivo. A further novel observation is that UVA induced both decline in the expression of E-cadherin adhesion molecule and increase in the expression of the N-cadherin adhesion molecule. In addition, a significant decline in homotypic melanoma-melanoma adhesion (clustering) was observed, which might result in the reduction of E-cadherin expression. The aim of the in vivo animal study was to confirm the physiological significance of previously obtained in vitro results and to determine whether UVA radiation might increase melanoma metastasis in vivo. The use of C57BL/6 mice and syngeneic melanoma cell lines B16-F1 and B16-F10 showed that mice, which were i.v. injected with B16-F1 melanoma cells and thereafter exposed to UVA developed significantly more lung metastases when compared with the non-UVA-exposed group. To study the mechanism behind this phenomenon, the direct effect of UVA-induced lung colonization capacity was examined by the in vitro exposure of B16-F1 cells. Alternatively, the UVA-induced immunosuppression, which might be involved in increased melanoma metastasis, was measured by standard contact hypersensitivity assay (CHS). It appears that the UVA-induced increase of metastasis in vivo might be caused by a combination of UVA-induced systemic immunosuppression, and to the lesser extent, it might be caused by the increased adhesiveness of UVA irradiated melanoma cells. Finally, the UVA effect on gene expression in mouse melanoma was determined by a cDNA array, which revealed UVA-induced changes in the 9 differentially expressed genes that are involved in angiogenesis, cell cycle, stress-response, and cell motility. These results suggest that observed genes might be involved in cellular response to UVA and a physiologically relevant UVA dose have previously unknown cellular implications. The novel results presented in this thesis offer evidence that UVA exposure might increase the metastatic potential of the melanoma cells present in blood circulation. Considering the wellknown UVA-induced deleterious effects on cellular level, this study further supports the notion that UVA radiation might have more potential impact on health than previously suggested. The possibility of the pro-metastatic effects of UVA exposure might not be of very high significance for daily exposures. However, UVA effects might gain physiological significance following extensive sunbathing or solaria tanning periods. Whether similar UVA-induced pro-metastatic effects occur in people sunbathing or using solaria remains to be determined. In the light of the results presented in this thesis, the avoidance of solaria use could be well justified.

Heavy-light mesons on a lattice

Several excited states of Ds and Bs mesons have been discovered in the last six years: BaBar, Cleo and Belle discovered the very narrow states D(s0)*(2317)+- and D(s1)(2460)+- in 2003, and CDF and DO Collaborations reported the observation of two narrow Bs resonances, B(s1)(5830)0 and B*(s2)(5840)0 in 2007. To keep up with experiment, meson excited states should be studied from the theoretical aspect as well. The theory that describes the interaction between quarks and gluons is quantum chromodynamics (QCD). In this thesis the properties of the meson states are studied using the discretized version of the theory - lattice QCD. This allows us to perform QCD calculations from first principles, and "measure" not just energies but also the radial distributions of the states on the lattice. This gives valuable theoretical information on the excited states, as we can extract the energy spectrum of a static-light meson up to D wave states (states with orbital angular momentum L=2). We are thus able to predict where some of the excited meson states should lie. We also pay special attention to the order of the states, to detect possible inverted spin multiplets in the meson spectrum, as predicted by H. Schnitzer in 1978. This inversion is connected to the confining potential of the strong interaction. The lattice simulations can also help us understand the strong interaction better, as the lattice data can be treated as "experimental" data and used in testing potential models. In this thesis an attempt is made to explain the energies and radial distributions in terms of a potential model based on a one-body Dirac equation. The aim is to get more information about the nature of the confining potential, as well as to test how well the one-gluon exchange potential explains the short range part of the interaction.

Tsoi Yuen Resistance and Post-80s Generation: A new wave of domestic social movement

Hong Kong was once a British colony and has been under the sovereignty of People’s Republic of China (PRC) since 1997. However, some of the unjust practices and colonial legacies are infiltrated into the development ideology as well as the social structures. The construction of intercity express railway project announced in 2008 causing the demolishment of Tsoi Yuen Tsuen, a “non-indigenous” agricultural village in Hong Kong, was one of the current examples. Tsoi Yuen village was established under the former colonial sovereignty sixty years ago. Approximately 450 populations were affected that they had to relocate their homeland involuntarily. However, these villagers were very attached to their homelands and were unwilling to move, and meanwhile they found that they were absent in the government’s consultation and decision-making process. Soon they began their resistance and demanded for “No Move! No Demolish!”. Their movement was strongly supported by a group of “Post-80s generation” and turned into the most important social movement of the city in recent years. In fact, demolition of Tsoi Yuen Village for city development is not an isolated case in the city. Meanwhile the situation is getting worse in Mainland China. I chose the case study of Tsoi Yuen Resistance from 2008 to 2011 for revelation of the complicated colonial history and postcolonial era of Hong Kong. I focused on discussing the Tsoi Yuen Resistance and the Post-80s movement, and how they have exposed the tension between top-down urban planning and development and public movements fighting for a more democratic process in choosing their way of living. Through the study of a village movement which as well as the rationale behind the Post-80s’ support, I hoped to illustrate how this movement has awaken a different sense of living for the new generations in the midst of the high-sounding urban development. It is an opportunity to examine Hong Kong’s colonial epoch in a different perspective: through studying the Tsoi Yuen Village, let them (subalterns) speak for themselves. Furthermore, the significance of this resistance, taking place eleven years after the handover to the PRC, is an important fact that I shall not miss in later discussion. Last but not least, during the resistance, advanced technology and social networks such as Facebook, Twitter, iPhone were used by Post 80s generation to spread the latest information in order to attract public’s concern and participation. Therefore, apart from studying Tsoi Yuen Resistance as a local social movement, I also regard it as a part of the global movement in perusing ecological lifestyle and civil society. How Post 80s’ generation manipulates the global idea in a local context will also be examined.

Tuning and stability of a singly resonant continuous-wave optical parametric oscillator close to degeneracy

Wavelength tuning and stability characteristics of a singly resonant continuous-wave optical parametric oscillator (cw OPO) in the proximity of signal-idler degeneracy have been studied. The OPO is made singly resonant by using a Bragg grating as a spectral filter in the OPO cavity. The signal-idler frequency difference can be tuned from 0.5 to 7 THz, which makes the OPO suitable for cw THz generation by optical heterodyning. The operation of the OPO within this singly-resonant regime is characterized by a strong self-stabilization effect. A gradual transition to an unstable, doubly-resonant regime is observed for a signal-idler detuning smaller than ~ 0.5 THz.

Paradoxical reflection in quantum mechanics

This article concerns a phenomenon of elementary quantum mechanics that is quite counter-intuitive, very non-classical, and apparently not widely known: a quantum particle can get reflected at a downward potential step. In contrast, classical particles get reflected only at upward steps. The conditions for this effect are that the wave length is much greater than the width of the potential step and the kinetic energy of the particle is much smaller than the depth of the potential step. This phenomenon is suggested by non-normalizable solutions to the time-independent Schroedinger equation, and we present evidence, numerical and mathematical, that it is also indeed predicted by the time-dependent Schroedinger equation. Furthermore, this paradoxical reflection effect suggests, and we confirm mathematically, that a quantum particle can be trapped for a long time (though not forever) in a region surrounded by downward potential steps, that is, on a plateau.