Time-Response Functions of Mechanical Networks with Inerters and Causality

This paper derives the causal time-response functions of three-parameter mechanical networks that have been reported in the literature and involve the inerter-a two-node element in which the force-output is proportional to the relative acceleration of its end-nodes. This two-terminal device is the mechanical analogue of the capacitor in a force-current/velocity-voltage analogy. The paper shows that all frequency-response functions that exhibit singularities along the real frequency axis need to be enhanced with the addition of a Dirac delta function or with its derivative depending on the strength of the singularity. In this way the real and imaginary parts of the enhanced frequency response functions are Hilbert pairs; therefore, yielding a causal time-response function in the time domain. The integral representation of the output signals offers an attractive computational alternative given that the constitutive equations of the three-parameter networks examined herein involve the third derivative of the nodal displacement which may challenge the numerical accuracy of a state-space formulation when the input signal is only available in digital form as in the case of recorded seismic accelerograms

Administrative Bureaus with Standard Operating Procedures

We investigate the terms of exchange between the legislative branch of the government and an administrative bureau with standard operating procedures. An administrative bureau is a not-for-profit public organisation responsible for the production of a non-marketable good. Such a bureau is tax-financed and the budget appropriations can be linked directly to a verifiable measure of the agency's performance. Also, the tax-financed transfer must not be less than the monetary cost of running the public agency. When standard operating procedures are central to the workings of the bureau, the agency is unencumbered by moral hazard. Yet, such agency is likely to have superior information over its production technology relative to the legislature. In such an information environment, we focus on how the legislature could minimise its welfare losses. Our results come in striking contrast to those in the literature on bureaucracies and to the received adverse selection findings. In a setting where the agency can be either of two cost-types, the principal finds it optimal in most cases to distort the production performance of the beureau regardless of its cost-type. Also the distortions are not of the same direction.bureaucracy, non profit organisations, adverse selection

Seignorage and Capital Taxation: Tax Competition Revisited

We re-examine the standard view that capital taxes are too low when capital is mobile across tax jurisdictions. We do so by emphasising a previously neglected implication of non-cooperative capital tax setting in a world with national currencies. Namely, capital taxes also affect foreign seignorage. This horizontal externality may lead, ceteris paribus, to too high national capital taxes, and may more than o set the usual effects of tax competition. In this case, and contrary to conventional wisdom, national capital taxes will be too high. Conditions under which the latter is indeed the case are derived and discussed.Tax Competition, Seignorage.

Complementarities and Macroeconomics: Poisson Games

In many situations in macroeconomics strategic complementarities arise, and agents face a coordination problem. An important issue, from both a theoretical and a policy perspective, is equilibrium uniqueness. We contribute to this literature by focusing on the macroeconomic aspect of the problem: the number of potential innovators, speculators e.t.c. is large. In particular, we follow Myerson (1998, 2000) that in large games “a more realistic model should admit some uncertainty about the number of players in the game”. In more detail, we model the coordination problem as a Poisson game, and investigate the conditions under which unique equilibrium selection is obtained.Strategic Complementarities, Coordination Games, Poisson Games, Currency Crises, Innovation.

Probing Transverse-Momentum Dependent Evolution With Groomed Jets

We propose an observable which involves measuring the properties (transverse momentum $p_{h\perp}$ and energy fraction $z_h$) of an identified hadron inside a groomed jet. The jet is identified with an anti-kT/CA algorithm and is groomed by implementing the modified mass drop procedure with an energy cut-off parameter $z_{cut}$. The transverse momentum of the hadron inside the jet is measured with respect to the groomed jet axis. We obtain a factorization theorem in the framework of Soft Collinear Effective Theory (SCET), to define a Transverse Momentum Dependent Fragmenting Jet Function (TMDFJF). The TMDFJF is factorized into collinear and collinear soft modes by matching onto SCET$_+$. We resum large logarithms in $E_J/p_{h\perp}$, where $E_J$ is the ungroomed jet energy, to NLL accuracy and apply this formalism for computing the shape of the $p_{h\perp}$ distribution of a pion produced in an $e^+ +e^-$ collision. We observe that the introduction of grooming makes this observable insensitive to non-global logarithms and particularly sensitive to non-perturbative physics of the transverse momentum dependent evolution at low values of $p_{h\perp}$, which can be probed in the variation of the cut-off parameter $z_{cut}$ of the groomer. We discuss how this observable can be used to distinguish between non-perturbative models that describe universal TMD evolution and provide a window into the three dimensional structure of hadrons.Comment: 23 pages, 4 figure

Jet Shapes in Dijet Events at the LHC in SCET

We consider the class of jet shapes known as angularities in dijet production at hadron colliders. These angularities are modified from the original definitions in e+e- collisions to be boost invariant along the beam axis. These shapes apply to the constituents of jets defined with respect to either k_T-type (anti-k_T, C/A, and k_T) algorithms and cone-type algorithms. We present an SCET factorization formula and calculate the ingredients needed to achieve next-to-leading-log (NLL) accuracy in kinematic regions where non-global logarithms are not large. The factorization formula involves previously unstudied "unmeasured beam functions," which are present for finite rapidity cuts around the beams. We derive relations between the jet functions and the shape-dependent part of the soft function that appear in the factorized cross section and those previously calculated for e+e- collisions, and present the calculation of the non-trivial, color-connected part of the soft-function to O(\alpha_s). This latter part of the soft function is universal in the sense that it applies to any experimental setup with an out-of-jet p_T veto and rapidity cuts together with two tagged jets and it is independent of the choice of jet (sub-)structure measurement. In addition, we implement the recently introduced soft-collinear refactorization to resum logarithms of the jet size, valid in the region of non-enhanced non-global logarithm effects. While our results are valid for all 2 \to 2 channels, we compute explicitly for the qq' \to qq' channel the color-flow matrices and plot the NLL resummed differential dijet cross section as an explicit example, which shows that the normalization and scale uncertainty is reduced when the soft function is refactorized. For this channel, we also plot the jet size R dependence, the p_T^{\rm cut} dependence, and the dependence on the angularity parameter a.Comment: 41 pages, 4 figure

Interface solitons in two-dimensional photonic lattices

We analyze localization of light at the interface separating square and hexagonal photonic lattices, as recently realized experimentally in two-dimensional laser-written waveguide arrays in silica glass with self-focusing nonlinearity [A. Szameit {\em et al.}, Opt. Lett. {\bf 33}, 663 (2008)]. We reveal the conditions for the existence of {\em linear} and {\em nonlinear} surface states substantially influenced by the lattice topology, and study the effect of the different symmetries and couplings on the stability of two-dimensional interface solitons.Comment: 3 pages, 4 figures, submitted to Opt. Let

Nonlinear dynamics of wave packets in PT-symmetric optical lattices near the phase transition point

Nonlinear dynamics of wave packets in PT-symmetric optical lattices near the phase-transition point are analytically studied. A nonlinear Klein-Gordon equation is derived for the envelope of these wave packets. A variety of novel phenomena known to exist in this envelope equation are shown to also exist in the full equation including wave blowup, periodic bound states and solitary wave solutions.Comment: 4 pages, 2 figure

Quantum Zeno effect by indirect measurement: The effect of the detector

We study the quantum Zeno effect in the case of indirect measurement, where the detector does not interact directly with the unstable system. Expanding on the model of Koshino and Shimizu [Phys. Rev. Lett., 92, 030401, (2004)] we consider a realistic Hamiltonian for the detector with a finite bandwidth. We also take explicitly into account the position, the dimensions and the uncertainty in the measurement of the detector. Our results show that the quantum Zeno effect is not expected to occur, except for the unphysical case where the detector and the unstable system overlap.Comment: 4 pages, 4 figure

Transverse Vetoes with Rapidity Cutoff in SCET

We consider di-jet production in hadron collisions where a transverse veto is imposed on radiation for (pseudo-)rapidities in the central region only, where this central region is defined with rapidity cutoff. For the case where the transverse measurement (e.g., transverse energy or min $p_T$ for jet veto) is parametrically larger relative to the typical transverse momentum beyond the cutoff, the cross section is insensitive to the cutoff parameter and is factorized in terms of collinear and soft degrees of freedom. The virtuality for these degrees of freedom is set by the transverse measurement, as in typical transverse-momentum dependent observables such as Drell-Yan, Higgs production, and the event shape broadening. This paper focuses on the other region, where the typical transverse momentum below and beyond the cutoff is of similar size. In this region the rapidity cutoff further resolves soft radiation into (u)soft and soft-collinear radiation with different rapidities but identical virtuality. This gives rise to rapidity logarithms of the rapidity cutoff parameter which we resum using renormalization group methods. We factorize the cross section in this region in terms of soft and collinear functions in the framework of soft-collinear effective theory, then further refactorize the soft function as a convolution of the (u)soft and soft-collinear functions. All these functions are calculated at one-loop order. As an example, we calculate a differential cross section for a specific partonic channel, $q q' \to q q'$, for the jet shape angularities and show that the refactorization allows us to resum the rapidity logarithms and significantly reduce theoretical uncertainties in the jet shape spectrum