Oliver Sacks observed autistic twins who instantly guessed the exact number of match-sticks that had just fallen on the floor, saying in unison “111”. To test the suggestion that normal individuals have the capacity for savant numerosity, we temporarily simulated the savant condition in normal people by inhibiting the left anterior temporal lobe of twelve participants with repetitive transcranial magnetic stimulation (rTMS). This site has been implicated in the savant condition. Ten participants improved their ability to accurately guess the number of discrete items immediately following rTMS and, of these, eight became worse at guessing as the effects of the pulses receded. The probability of as many as eight out of twelve people doing best just after rTMS and not after sham stimulation by chance alone is less than one in one thousand.

A classical test for accessing the potential creativity of an individual is based on ideational fluency, where a person is asked to generate all possible uses for a familiar item like apiece of paper In scoring the results, it is intuitive that the suggested uses should not be weighted equally. Those suggested in radically different categories are "worth more" than those suggested within the same category only. We used information theory to derive a simple mathematical expression for a more objective measure of ideational fluency. We call this the creativity quotient (CQ). This innovative measure was examined using a small sample of participants, and is illustrated by the responses of two typical individuals from an ideational fluency task. The CQ accounts for the number of ideas (fluency), plus the number of categories (flexibility). Ongoing research will examine the independence of CQ from established measures of intelligence and personality.

We advance a dominant neural strategy for facilitating conceptual thought. Concepts are groupings of "object" attributes. Once the brain learns such critical groupings, the "object" attributes are inhibited from conscious awareness. We see the whole, not the parts. The details are inhibited when the concept network is activated, ie. the inhibition is dynamic and can be switched on and off. Autism is suggested to be the state of retarded concept formation. Our model predicts the possibility of accessing nonconscious information by artificially disinhibiting (turning off) the inhibiting networks associated with concept formation, using transcranial magnetic brain stimulation (TMS). For example, this opens the door for the restoration of perfect pitch, for recalling detail, for acquiring accent-free second languages beyond puberty, and even for enhancing creativity. The model further shows how unusual autistic savant skills as well as certain psychopathologies can be due respectively to privileged or inadvertent access to information that is normally inhibited from conscious awareness.

The recognition of the correct solution to a problem after a period when one is not actively searching for an answer is well documented. However, previous research has focused on problems an individual has not yet resolved. We presented a scenario in which 125 participants believed that they had completed a task and so had no reason to seek further solutions. To their surprise, after a period of distraction, we resumed the testing session. This novel method was combined with accurate recording of both response content and timing. The results from the second session displayed a remarkable similarity to those from the first, including an initial burst of ideas, allowing the inference that, even in the absence of a reason to seek solutions, a process of nonconscious idea generation might be operating.

The astonishing skills of savants have been suggested to be latent in everyone, but are not normally accessible without a rare form of brain impairment. We attempted to simulate such brain impairment in healthy people by directing low-frequency magnetic pulses into the left fronto-temporal lobe. Significant stylistic changes in drawing were facilitated by the magnetic pulses in four of our 11 participants. Some of these "facilitated" participants also displayed enhanced proofreading ability. Our conclusions are derived from 11 right-handed male university students, eight of whom underwent placebo stimulation. We examined performance before, during and after exposure to the stimulation.

The nonlinear response of various materials extends beyond the illuminating beam. We present what is to our knowledge the first analytically tractable model for the dynamics of beams in partially nonlocal media. As far as an isolated beam is concerned, propagation is qualitatively the same, independently of the radius of nonlocality.

Unlike the ability to acquire our native language, we struggle to learn multiplication and division. It may then come as a surprise that the mental machinery for performing lightning-fast integer arithmetic calculations could be within us all even though it cannot be readily accessed, nor do we have any idea of its primary function. We are led to this provocative hypothesis by analysing the extraordinary skills of autistic savants. In our view such individuals have privileged access to lower levels of information not normally available through introspection.

We demonstrate, in both two and three dimensions, how a self-guided beam in a non-Kerr medium is split into two beams on weak illumination. We also provide an elegant physical explanation that predicts the universal character of the observed phenomenon. Possible applications of our findings to guiding light with light are also discussed.

We give what we believe to be the first closed-form exact expression for the dynamic evolution of nonstationary beams of arbitrary intensity and width propagating in a uniform nonlinear medium and in both two and three dimensions. This shows that periodic and quasi-periodic (nonradiating) beams can exist in a non-Kerr nonlinear medium. The Schrödinger equation is solved for Gaussian beams in a saturable medium. For one critical (initial) beam width, the Gaussian is a stable stationary soliton or bullet, independent of its intensity; otherwise, it breathes. New quasi-periodic beams (mighty morphing solitons) and bullets (mighty morphs) of elliptical cross section also exist whose ellipticity changes with propagation.

Dressed ion theory, an exact statistical mechanical formalism for electrolyte systems in the primitive model, is extended to electric double layer systems in various geometries. In this theory an exact equation that has the same form as the linearized Poisson–Boltzmann (PB) equation is set up, in which ‘dressed ions’ take the same role in the exact theory as the bare ions have in the PB approximation. Various distribution functions are expressed in terms of the dressed ion charges. Exact asymptotic results for large particle separations are obtained for the distribution functions, the average electrostatic potential and the interaction free energies in colloid dispersions and for planar double layer systems. A practical method is derived for evaluating the effective surface charge densities of the particles. The question of whether double layer interactions between equally charged colloid particles must be repulsive at large separations (as suggested by the PB approximation) or whether they can be attractive there is treated in some detail.

Solitons are ubiquitous. Their description involves abstruse mathematics and is limited to a two-dimensional idealization. A nonlocal model is presented that provides a radical simplification and allows for an elegant description of soliton collisions, interactions, and deformations in two and three dimensions. The model reveals an intimate connection between solitons and the linear harmonic oscillator. It foreshadows a photonic switch in which a bright beam can steer a distant dim beam, and it predicts the existence of noncircularly symmetric solitons.

The thermodynamics of surfactants in solution has largely been understood in the framework of the flexible surface model. We calculate the bending rigidity for a case where this model might be put to a strong test: ionic surfactant systems with no added salt to screen the electrostatics. In so doing, we present a perturbative solution to the Poisson-Boltzmann equation for the case of two undulating sheets with intervening counterions. The predictions to which this leads for the bending modulus are shown (for a particular choice of undulation mode) to be identical to that of the solution for the geometry of concentric cylinders. This indicates that the curvature free energy is independent of the global aggregate geometry, even in systems with counterions only.

The correlation functions of bulk symmetric electrolytes in the restricted primitive model are analyzed using the formalism of the dressed ion theory of Kjellander and Mitchell [Chem. Phys. Lett. 200, 76 (1992), J. Chem. Phys. 101, 603 (1994)]. An important result of this analysis is that the exact theory for the pair correlation functions can be cast in a form that is virtually identical to that of the Debye–Hückel theory provided one uses the renormalized charges of the ions—‘‘dressed ions’’—instead of bare ion charges. In the current work the (state dependent) charges of these dressed ions are investigated using the HNC approximation. The asymptotic decay of the pair correlation functions are analyzed in terms of the effective point charges of the ions and the effective permittivity of the electrolyte solution, concepts which are given rigorous and physically transparent definitions in the dressed ion theory. Several transitions between regimes with different qualitative behavior of the pair correlation functions are demonstrated, in addition to the well-known transition between monotonic and oscillatory damped decay. By means of an analysis of the singularities of the correlation functions in complex Fourier space, dressed ion theory provides a general method to determine these transitions from numerical pair correlation data and in this paper results are given for symmetric electrolytes with monovalent and divalent ions.

It is often difficult to understand nonlinear guided wave effects because our intuition is built upon linear phenomena. We wish here to show that nonlinear phenomena can be approached from a linear perspective. This is not a new technique for solving nonlinear equations. Rather, we show that the linear perspective (1) anticipates the possible classes of nonlinear waves and their characteristics. It thus predicts novel phenomena, such as solitons with internal dynamics, and it facilitates previously unforeseen generalizations, such as those necessary for the universal criterion for stability. By imparting physical insight, it (2) offers a powerful predictive tool, for example one which foreshadows the phase shift and the radiation free nature of soliton collisions. Further, it (3) shows how the mathematical foundation for nonlinear waves is borrowed from the literature of linear waves. Finally, it (4) allows for closed form solutions of illustrative examples to be lifted directly from the pages of linear physics. This powerful approach is demonstrated here through the vehicle of spatial guided wave optics, embracing such phenomena as guiding and manipulating light by light itself 1-7 .

Periodic (second order) solitons exist in an idealized saturating medium. We give a physical explanation for why they result from scaling up a fundamental soliton.

A detailed derivation of the dressed-ion theory—a formally exact theory for primitive model Coulomb fluids—is presented for the case of bulk electrolyte solutions. It is shown that the exact average electrostatic potential, ψ av(r), in the ion atmosphere around each ion satisfies a linear Poisson–Boltzmann (PB) equation for ‘‘dressed ions,’’ each of which consists of a central ion together with a specific part of the surrounding ion cloud. The dressed-ion charge distribution—a renormalized charge for each ion—takes the role that the bare ionic charge has in the usual PB equation. Apart from this, virtually the only difference between the exact dressed-ion and the approximate Debye–Hückel (DH) theories for the pair distribution function is that the former theory is nonlocal; the spread-out nature of the dressed-ion charge distribution gives rise to a nonlocal polarization response to the average potential. The linear response function relating the polarization and the average potential is investigated in the general case and is found to be intimately related to the dressed-ion charge distributions. A close relationship is also demonstrated between these charge distributions and the electrostatic susceptibility of the electrolyte solution. The theory gives a rigorous definition of the concept of effective point charges for ions. Except at high coupling, the long-range asymptotic behavior of the pair distribution functions is of the Debye–Hückel form, but with effective values of the ionic charges (qi*) and a decay length (κ−1) different from the Debye length (κ−1D). A simple formula relating qi* and κ is derived. Explicit formulae for qi* and κ in terms of κD are given in the limit of low electrolyte concentrations. The long range asymptotic behaviors of the bridge function and the short range parts of the direct and total correlation functions are analyzed in some detail.

We consider the expanded class of one- and two-dimensional spatial solitons that exist when the soliton is a compound entity composed of two orthogonal beams [1-3]. These solitons propagate in a homogeneous isotropic medium whose refractive index has an arbitrary dependence on intensity. As with classical solitons, their intensity profile remains axially uniform but, in addition, their polarization state now changes continuously with propagation. We refer to this new class of self-guided waves as ‘dynamic solitons’ because of their internal field dynamics. Dynamic solitons can have an arbitrary number of intensity peaks and thus exhibit novel intensity profiles. Their common salient property is that they are composed of two orthogonal beams, neither of which is, in general, a soliton on its own. Each beam is, however, a mode of the (axially uniform) linear optical waveguide induced by the dynamic soliton.

It is shown that the exact theory for electrolyte solutions and colloid dispersions in the primitive model can be reformulated in terms of quasiparticles, constituting “dressed” ions or colloid particles, where parts of the ion cloud around each bare particle are included in the quasiparticle. The resulting exact theory for the dressed particles is virtually identical to the linear Poisson—Boltzmann (PB) theory, where the bare particle charges in the PB theory are replaced by the internal charge distributions of the quasiparticles. Nonlinearities and many-body correlations only contribute to the internal charge distributions of the quasiparticles. The long-range asymptotic behaviour of the pair correlations is analyzed.

The ‘modes’ of triple core nonlinear couplers are used to construct a bifurcation diagram from which the novel physics is revealed. Amplification is possible for arbitrarily low power, even for touching cores, where the third core acts as a ‘parasitic’ element