Specifications for a new or remodeled mathematics classroom.

Thesis (Ed.M.)--Boston Universit

Structural correlations in diffusiophoretic colloidal mixtures with nonreciprocal interactions

Nonreciprocal effective interaction forces can occur between mesoscopic particles in colloidal suspensions that are driven out of equilibrium. These forces violate Newton's third law actio  =  reactio on coarse-grained length and time scales. Here we explore the statistical mechanics of Brownian particles with nonreciprocal effective interactions. Our model system is a binary fluid mixture of spherically symmetric, diffusiophoretic mesoscopic particles, and we focus on the time-averaged particle pair- and triplet-correlation functions. Based on the many-body Smoluchowski equation we develop a microscopic statistical theory for the particle correlations and test it by computer simulations. For model systems in two and three spatial dimensions, we show that nonreciprocity induces distinct nonequilibrium pair correlations. Our predictions can be tested in experiments with chemotactic colloidal suspensions

Wave energy localization by self-focusing in large molecular structures: a damped stochastic discrete nonlinear Schroedinger equation model

Wave self-focusing in molecular systems subject to thermal effects, such as thin molecular films and long biomolecules, can be modeled by stochastic versions of the Discrete Self-Trapping equation of Eilbeck, Lomdahl and Scott, and this can be approximated by continuum limits in the form of stochastic nonlinear Schroedinger equations. Previous studies directed at the SNLS approximations have indicated that the self-focusing of wave energy to highly localized states can be inhibited by phase noise (modeling thermal effects) and can be restored by phase damping (modeling heat radiation). We show that the continuum limit is probably ill-posed in the presence of spatially uncorrelated noise, at least with little or no damping, so that discrete models need to be addressed directly. Also, as has been noted by other authors, omission of damping produces highly unphysical results. Numerical results are presented for the first time for the discrete models including the highly nonlinear damping term, and new numerical methods are introduced for this purpose. Previous conjectures are in general confirmed, and the damping is shown to strongly stabilize the highly localized states of the discrete models. It appears that the previously noted inhibition of nonlinear wave phenomena by noise is an artifact of modeling that includes the effects of heat, but not of heat loss.Comment: 22 pages, 13 figures, revision of talk at FPU+50 conference in Rouen, June 200

Towards integrated superconducting detectors on lithium niobate waveguides

Superconducting detectors are now well-established tools for low-light optics, and in particular quantum optics, boasting high-efficiency, fast response and low noise. Similarly, lithium niobate is an important platform for integrated optics given its high second-order nonlinearity, used for high-speed electro-optic modulation and polarization conversion, as well as frequency conversion and sources of quantum light. Combining these technologies addresses the requirements for a single platform capable of generating, manipulating and measuring quantum light in many degrees of freedom, in a compact and potentially scalable manner. We will report on progress integrating tungsten transition-edge sensors (TESs) and amorphous tungsten silicide superconducting nanowire single-photon detectors (SNSPDs) on titanium in-diffused lithium niobate waveguides. The travelling-wave design couples the evanescent field from the waveguides into the superconducting absorber. We will report on simulations and measurements of the absorption, which we can characterize at room temperature prior to cooling down the devices. Independently, we show how the detectors respond to flood illumination, normally incident on the devices, demonstrating their functionality.Comment: 7 pages, 4 figure

A Quasi‐Multinary Composite Coating on a Nickel‐Rich NCM Cathode Material for All‐Solid‐State Batteries

Inorganic solid-state batteries are attracting significant interest as a contender to conventional liquid electrolyte-based lithium-ion batteries but still suffer from several limitations. The search for advanced coatings for protecting cathode materials in solid-state batteries to achieve interfacial stability is a continuing challenge. In the present work, the surface of an industrially relevant Ni-rich LiNi$_x$Co$_y$Mn$_z$O$_2$ cathode material, NCM-851005 (85 % Ni), was modified by applying a coating containing Li, Nb and Zn, aiming at a composition Li$_6$ZnNb$_4$O$_14$, by means of sol-gel chemistry. Detailed characterization using scanning transmission electron microscopy combined with energy-dispersive X-ray spectroscopy and nano-beam electron diffraction showed that the surface layer after heating in O$_2$ at 500 °C contains Li$_3$NbO$_4$ nanocrystals and Li$_2$CO$_3$, with Zn presumably acting as a dopant. The protective coating on the NCM-851005 secondary particles significantly increased the cycling performance (reversible capacity, rate capability etc.) and stability of full cells using argyrodite Li$_6$PS$_5$Cl as solid electrolyte. Interestingly, the level of improvement is superior to that achieved with conventional LiNbO$_3$ coatings

Melanocyte differentiation antigen RAB38/NY-MEL-1 induces frequent antibody responses exclusively in melanoma patients

Expression pattern and immunogenicity are critical issues that define tumor antigens as diagnostic markers and potential targets for immunotherapy. The development of SEREX (serological analysis of recombinant expression libraries) has provided substantial progress in the identification of tumor antigens eliciting both cellular and humoral immune responses in cancer patients. By SEREX, we have previously identified RAB38/NY-MEL-1 as a melanocyte differentiation antigen that is highly expressed in normal melanocytes and melanoma tissues but not in other normal tissues or cancer types. In this study, we further demonstrate that RAB38/NY-MEL-1 is strongly immunogenic, leading to spontaneous antibody responses in a significant proportion of melanoma patients. The immune response occurs solely in malignant melanoma patients and was not detected in patients with other diseases, such as vitiligo, affecting melanocytes. Fine analysis of the spontaneous anti-RAB38/NY-MEL-1 antibody response reveals a polyclonal B cell recognition targeting various epitopes, although a dominant immunogenic region was preferentially recognized. Interestingly, our data indicate that this recognition is not rigid in the course of a patient's response, as the dominant epitope changes during the disease evolution. Implications for the understanding of spontaneous humoral immune responses are discusse

Phase segregation in supramolecular polymers based on telechelics synthesized via multicomponent reactions

The properties of supramolecular polymers in the solid state are strongly dependent on the binding strength of the supramolecular motifs used; however, It has been previously shown that the nanostructure of supramolecular polymers plays an equally important role. Supramolecular polymers are commonly synthesized via end-group functionalization of low-glass transition telechelics with supramolecular units. In these systems, the binding motifs segregate from the soft telechelic backbone and form a hydrogen bonded crystalline hard phase that provides physical cross-links. To date, the reported synthetic approaches do not permit the introduction of a wide variety of supramolecular units with low synthetic effort, which would facilitate studying the structure-property relationships. The use of the Passerini and Ugi multicomponent reactions to synthesize various poly(ethylene-co-butylene) telechelics with diverse amide end-groups is reported. The thermal properties of the supramolecular polymers obtained through their solid-state assembly are investigated and their nanophase- segregation is studied, which is dictated by the end-group volume fraction and the amide–amide hydrogen bonding

Abelian Higgs Hair for Black Holes

We find evidence for the existence of solutions of the Einstein and Abelian Higgs field equations describing a black hole pierced by a Nielsen-Olesen vortex. This situation falls outside the scope of the usual no-hair arguments due to the non-trivial topology of the vortex configuration and the special properties of its energy-momentum tensor. By a combination of numerical and perturbative techniques we conclude that the black hole horizon has no difficulty in supporting the long range fields of the Nielsen Olesen string. Moreover, the effect of the vortex can in principle be measured from infinity, thus justifying its characterization as black hole ``hair".Comment: 31 pages, plain tex, 7 figures included. minor corrections and references adde

Mapping medical careers: Questionnaire assessment of career preferences in medical school applicants and final-year students

BACKGROUND: The medical specialities chosen by doctors for their careers play an important part in the workforce planning of health-care services. However, there is little theoretical understanding of how different medical specialities are perceived or how choices are made, despite there being much work in general on this topic in occupational psychology, which is influenced by Holland's RIASEC (Realistic-Investigative-Artistic-Social-Enterprising-Conventional) typology of careers, and Gottfredson's model of circumscription and compromise. In this study, we use three large-scale cohorts of medical students to produce maps of medical careers. METHODS: Information on between 24 and 28 specialities was collected in three UK cohorts of medical students (1981, 1986 and 1991 entry), in applicants (1981 and 1986 cohorts, N = 1135 and 2032) or entrants (1991 cohort, N = 2973) and in final-year students (N = 330, 376, and 1437). Mapping used Individual Differences Scaling (INDSCAL) on sub-groups broken down by age and sex. The method was validated in a population sample using a full range of careers, and demonstrating that the RIASEC structure could be extracted. RESULTS: Medical specialities in each cohort, at application and in the final-year, were well represented by a two-dimensional space. The representations showed a close similarity to Holland's RIASEC typology, with the main orthogonal dimensions appearing similar to Prediger's derived orthogonal dimensions of 'Things-People' and 'Data-Ideas'. CONCLUSIONS: There are close parallels between Holland's general typology of careers, and the structure we have found in medical careers. Medical specialities typical of Holland's six RIASEC categories are Surgery (Realistic), Hospital Medicine (Investigative), Psychiatry (Artistic), Public Health (Social), Administrative Medicine (Enterprising), and Laboratory Medicine (Conventional). The homology between medical careers and RIASEC may mean that the map can be used as the basis for understanding career choice, and for providing career counselling