Uncovering GEMS of Mathematics

Gateway to Exploring Mathematical Sciences (GEMS) is an outreach program offered by the six mathematics departments of the Claremont Colleges for eighth, ninth, and tenth graders. In this paper, we describe our program (in terms of format, participants, mathematical activities and topics involved) and share why we are so enthusiastic about it

Compact Modeling for a Double Gate MOSFET

MOSFETs (metal-oxide-silicon field-effect transistors) are an integral part of modern electronics. Improved designs are currently under investigation, and one that is promising is the double gate MOSFET. Understanding device characteristics is critical for the design of MOSFETs as part of design tools for integrated circuits such as SPICE. Current methods involve the numerical solution of PDEs governing electron transport. Numerical solutions are accurate, but do not provide an appropriate way to optimize the design of the device, nor are they suitable for use in chip simulation software such as SPICE. As chips contain more and more transistors, this problem will get more and more acute. There is hence a need for analytic solutions of the equations governing the performance of MOSFETs, even if these are approximate. Almost all solutions in the literature treat the long-channel case (thin devices) for which the PDEs reduce to ODEs. The goal of this problem is to produce analytical solutions based on the underlying PDEs that are rapid to compute (e.g. require solving only a small number of algebraic equations rather than systems of PDEs). Guided by asymptotic analysis, a fast numerical procedure has been developed to obtain approximate solutions of the governing PDEs governing MOSFET properties, namely electron density, Fermi potential and electrostatic potential. The approach depends on the channel’s being long enough, and appears accurate in this limit

Higher D or Li: Probes of Physics beyond the Standard Model

Standard Big Bang Nucleosynthesis at the baryon density determined by the microwave anisotropy spectrum predicts an excess of \li7 compared to observations by a factor of 4-5. In contrast, BBN predictions for D/H are somewhat below (but within ~2 \sigma) of the weighted mean of observationally determined values from quasar absorption systems. Solutions to the \li7 problem which alter the nuclear processes during or subsequent to BBN, often lead to a significant increase in the deuterium abundance consistent with the highest values of D/H seen in absorption systems. Furthermore, the observed D/H abundances show considerable dispersion. Here, we argue that those systems with D/H \simeq 4 \times 10^{-5} may be more representative of the primordial abundance and as a consequence, those systems with lower D/H would necessarily have been subject to local processes of deuterium destruction. This can be accounted for by models of cosmic chemical evolution able to destroy in situ Deuterium due to the fragility of this isotope.Comment: 22 pages, 8 figure

Closing in on Asymmetric Dark Matter I: Model independent limits for interactions with quarks

It is argued that experimental constraints on theories of asymmetric dark matter (ADM) almost certainly require that the DM be part of a richer hidden sector of interacting states of comparable mass or lighter. A general requisite of models of ADM is that the vast majority of the symmetric component of the DM number density must be removed in order to explain the observed relationship $\Omega_B\sim\Omega_{DM}$ via the DM asymmetry. Demanding the efficient annihilation of the symmetric component leads to a tension with experimental limits if the annihilation is directly to Standard Model (SM) degrees of freedom. A comprehensive effective operator analysis of the model independent constraints on ADM from direct detection experiments and LHC monojet searches is presented. Notably, the limits obtained essentially exclude models of ADM with mass 1GeV$\lesssim m_{DM} \lesssim$ 100GeV annihilating to SM quarks via heavy mediator states. This motivates the study of portal interactions between the dark and SM sectors mediated by light states. Resonances and threshold effects involving the new light states are shown to be important for determining the exclusion limits.Comment: 18+6 pages, 18 figures. v2: version accepted for publicatio

Citizen Journalism at the Margins

Amidst burgeoning literature on citizen journalism, we still know relatively little about how and why genuinely marginalised groups seek to use this form of reporting to challenge their exclusion. In this article, we aim to address this gap by analysing two UK citizen journalism initiatives emanating from The Big Issue Foundation, a national homeless organisation, and Access Dorset, a regional charity for disabled and elderly people. These case studies are united by the authors’ involvement in both instances, primarily through designing and delivering bespoke citizen journalism education and mentoring. Based on over 40 hours of interviews with participants of the workshops and 36 hours of participant observation, we analyse the challenges participants faced in their journey to become citizen journalists. This included: low self-esteem, physical health and mental wellbeing, the need for accessible and adaptable technology, and overcoming fear associated with assuming a public voice. We also analyse marginalised groups’ attitudes to professional journalism and education, and its role in shaping journalistic identity and self-empowerment. Whilst demonstrably empowering and esteem building,our participants were acutely aware of societal power relations that were seemingly still beyond their ability to influence. Those who are marginalised are, nevertheless, in the best position to use citizen journalism as a conduit for social change, we argue - though challenges remain even at the grassroots level to foster and sustain participatory practices

Direct detection of dark matter in models with a light Z'

We discuss the direct detection signatures of dark matter interacting with nuclei via a Z' mediator, focussing on the case where both the dark matter and the $Z'$ have mass of a few GeV. Isospin violation (i.e. different couplings to protons and neutrons) arises naturally in this scenario. In particular it is possible to reconcile the preferred parameter regions inferred from the observed DAMA and CoGeNT modulations with the bounds from XENON100, which requires f_n/f_p = -0.7. Moreover, the Z' mediator can also yield a large spin-dependent cross-section which could contribute to the DAMA signal, while the spin-independent cross-section is adequate to explain the CoGeNT signal.Comment: 20 pages, 3 figures. v2: matches published versio

Probing new physics with long-lived charged particles produced by atmospheric and astrophysical neutrinos

As suggested by some extensions of the Standard Model of particle physics, dark matter may be a super-weakly interacting lightest stable particle, while the next-to-lightest particle (NLP) is charged and meta-stable. One could test such a possibility with neutrino telescopes, by detecting the charged NLPs produced in high-energy neutrino collisions with Earth matter. We study the production of charged NLPs by both atmospheric and astrophysical neutrinos; only the latter, which is largely uncertain and has not been detected yet, was the focus of previous studies. We compute the resulting fluxes of the charged NLPs, compare those of different origins, and analyze the dependence on the underlying particle physics setup. We point out that even if the astrophysical neutrino flux is very small, atmospheric neutrinos, especially those from the prompt decay of charmed mesons, may provide a detectable flux of NLP pairs at neutrino telescopes such as IceCube. We also comment on the flux of charged NLPs expected from proton-nucleon collisions, and show that, for theoretically motivated and phenomenologically viable models, it is typically sub-dominant and below detectable rates.Comment: 27 pages, 6 figures; accepted for publication in JCA

The New Look pMSSM with Neutralino and Gravitino LSPs

The pMSSM provides a broad perspective on SUSY phenomenology. In this paper we generate two new, very large, sets of pMSSM models with sparticle masses extending up to 4 TeV, where the lightest supersymmetric particle (LSP) is either a neutralino or gravitino. The existence of a gravitino LSP necessitates a detailed study of its cosmological effects and we find that Big Bang Nucleosynthesis places strong constraints on this scenario. Both sets are subjected to a global set of theoretical, observational and experimental constraints resulting in a sample of \sim 225k viable models for each LSP type. The characteristics of these two model sets are briefly compared. We confront the neutralino LSP model set with searches for SUSY at the 7 TeV LHC using both the missing (MET) and non-missing ET ATLAS analyses. In the MET case, we employ Monte Carlo estimates of the ratios of the SM backgrounds at 7 and 8 TeV to rescale the 7 TeV data-driven ATLAS backgrounds to 8 TeV. This allows us to determine the pMSSM parameter space coverage for this collision energy. We find that an integrated luminosity of \sim 5-20 fb^{-1} at 8 TeV would yield a substantial increase in this coverage compared to that at 7 TeV and can probe roughly half of the model set. If the pMSSM is not discovered during the 8 TeV run, then our model set will be essentially void of gluinos and lightest first and second generation squarks that are \lesssim 700-800 GeV, which is much less than the analogous mSUGRA bound. Finally, we demonstrate that non-MET SUSY searches continue to play an important role in exploring the pMSSM parameter space. These two pMSSM model sets can be used as the basis for investigations for years to come.Comment: 54 pages, 22 figures; typos fixed, references adde

Factors associated with spontaneous stone passage in a contemporary cohort of patients presenting with acute ureteric colic. Results from the MIMIC Study (A Multi-centre cohort study evaluating the role of Inflammatory Markers in patients presenting with acute ureteric Colic)

Objectives There is conflicting data on the role of white blood cell count (WBC) and other inflammatory markers in spontaneous stone passage in patients with acute ureteric colic. The aim of the study was to assess the relationship of WBC and other routinely collected inflammatory and clinical markers including stone size, stone position and Medically Expulsive Therapy use (MET) with spontaneous stone passage (SSP) in a large contemporary cohort of patients with acute ureteric colic. Subjects and Methods Multi‐centre retrospective cohort study coordinated by the British Urology Researchers in Surgical Training (BURST) Research Collaborative at 71 secondary care hospitals across 4 countries (United Kingdom, Republic of Ireland, Australia and New Zealand). 4170 patients presented with acute ureteric colic and a computer tomography confirmed single ureteric stone. Our primary outcome measure was SSP as defined by the absence of need for intervention to assist stone passage. Multivariable mixed effects logistic regression was used to explore the relationship between key patient factors and SSP. Results 2518 patients were discharged with conservative management and had further follow up with a SSP rate of 74% (n = 1874/2518). Sepsis after discharge with conservative management was reported in 0.6% (n = 16/2518). On multivariable analysis neither WBC, Neutrophils or CRP were seen to predict SSP, with an adjusted OR of 0.97 [95% CI 0.91 to 1.04, p = 0.38], 1.06 [95% CI 0.99 to 1.13, p = 0.1] and 1.00 [95% CI 0.99 to 1.00, p = 0.17], respectively. Medical expulsive therapy (MET) also did not predict SSP [adjusted OR 1.11 [95% CI 0.76 to 1.61]). However, stone size and stone position were significant predictors. SSP for stones 7mm. For stones in the upper ureter the SSP rate was 52% [95% CI 48 to 56], middle ureter was 70% [95% CI 64 to 76], and lower ureter was 83% [95% CI 81 to 85]. Conclusion In contrast to the previously published literature, we found that in patients with acute ureteric colic who are discharged with initial conservative management, neither WBC, Neutrophil count or CRP help determine the likelihood of spontaneous stone passage. We also found no overall benefit from the use of MET. Stone size and position are important predictors and our findings represent the most comprehensive stone passage rates for each mm increase in stone size from a large contemporary cohort adjusting for key potential confounders. We anticipate that these data will aid clinicians managing patients with acute ureteric colic and help guide management decisions and the need for intervention

Explicit Solutions for LBIC Signals in Semiconductors by Asymptotic Method

A non-destructive testing technique to obtain information on the electrical structure in semiconductor materials involves traversing the material surface with a laser beam, and measuring induced currents generated by the beam\u27s interaction with the electrical field. A mathematical model has been established, and the inverse problem of reconstructing the electrical structure from the current image has been studied. Here we obtain explicit solutions for simple structures (p-n and p-n-p junctions) in the asymptotic limit of strong doping. Comparison with numerical results shows that the asymptotic solutions are quite accurate. These solutions may provide a quick way to identify the doping profile by matching actual current signals to a class of simple functions