Comparing data driven and physics inspired models for hopping transport in organic field effect transistors

The past few decades have seen an uptick in the scope and range of device applications of organic semiconductors, such as organic field-effect transistors, organic photovoltaics and light-emitting diodes. Several researchers have studied electrical transport in these materials and proposed physical models to describe charge transport with different material parameters, with most disordered semiconductors exhibiting hopping transport. However, there exists a lack of a consensus among the different models to describe hopping transport accurately and uniformly. In this work, we first evaluate the efficacy of using a purely data-driven approach, i.e., symbolic regression, in unravelling the relationship between the measured field-effect mobility and the controllable inputs of temperature and gate voltage. While the regressor is able to capture the scaled mobility well with mean absolute error (MAE) ~ O(10–2), better than the traditionally used hopping transport model, it is unable to derive physically interpretable input–output relationships. We then examine a physics-inspired renormalization approach to describe the scaled mobility with respect to a scale-invariant reference temperature. We observe that the renormalization approach offers more generality and interpretability with a MAE of the ~ O(10–1), still better than the traditionally used hopping model, but less accurate as compared to the symbolic regression approach. Our work shows that physics-based approaches are powerful compared to purely data-driven modelling, providing an intuitive understanding of data with extrapolative ability.

Optimal renormalization of multiscale systems

While model order reduction is a promising approach in dealing with multiscale time-dependent systems that are too large or too expensive to simulate for long times, the resulting reduced order models can suffer from instabilities. We have recently developed a time-dependent renormalization approach to stabilize such reduced models. In the current work, we extend this framework by introducing a parameter that controls the time decay of the memory of such models and optimally select this parameter based on limited fully resolved simulations. First, we demonstrate our framework on the inviscid Burgers equation whose solution develops a finite-time singularity. Our renormalized reduced order models are stable and accurate for long times while using for their calibration only data from a full order simulation before the occurrence of the singularity. Furthermore, we apply this framework to the three-dimensional (3D) Euler equations of incompressible fluid flow, where the problem of finite-time singularity formation is still open and where brute force simulation is only feasible for short times. Our approach allows us to obtain a perturbatively renormalizable model which is stable for long times and includes all the complex effects present in the 3D Euler dynamics. We find that, in each application, the renormalization coefficients display algebraic decay with increasing resolution and that the parameter which controls the time decay of the memory is problem-dependent.

Interpretable physics-based models compared with symbolic regression for hopping transport in organic field-effect transistors

The past few decades have seen an uptick in the scope and range of device applications of organic semiconductors, such as organic field-effect transistors, organic photovoltaics and light-emitting diodes. Several researchers have studied electrical transport in these materials and proposed physical models to describe charge transport with different material parameters, with most disordered semiconductors exhibiting hopping transport. However, there exists a lack of a consensus among the different models to describe hopping transport accurately and uniformly. In this work, we first evaluate the efficacy of using a purely data-driven approach, i.e., symbolic regression, in unravelling the relationship between the measured field-effect mobility and the controllable inputs of temperature and gate voltage. While the regressor is able to capture the scaled mobility well with mean absolute error (MAE) ~O(10-2), better than the traditionally used hopping transport model, it is unable to derive physically interpretable input-output relationships. We then examine a physics-inspired renormalization approach to describe the scaled mobility with respect to a scale-invariant reference temperature. We observe that the renormalization approach offers more generality and interpretability with a MAE of the ~O(10-1), still better than the traditionally used hopping model, but less accurate as compared to the symbolic regression approach. Our work shows that physics-based approaches are powerful compared to purely data-driven modelling, providing an intuitive understanding of data with extrapolative ability.

Spectral Gap in Mean-Field $${\mathcal {O}}(n)$$-Model

We study the dependence of the spectral gap for the generator of the Ginzburg–Landau dynamics for all $$\mathcal O(n)$$ O ( n ) -models with mean-field interaction and magnetic field, below and at the critical temperature on the number N of particles. For our analysis of the Gibbs measure, we use a one-step renormalization approach and semiclassical methods to study the eigenvalue-spacing of an auxiliary Schrödinger operator.

Renormalization Approach to the Gribov Process: Numerical Evaluation of Critical Exponents in Two Subtraction Schemes

We study universal quantities characterizing the second order phase transition in the Gribov process. To this end, we use numerical methods for the calculation of the renormalization group functions up to two-loop order in perturbation theory in the famous ε-expansion. Within this procedure the anomalous dimensions are evaluated using two different subtraction schemes: the minimal subtraction scheme and the null-momentum scheme. Numerical calculation of integrals was done on the HybriLIT cluster using the Vegas algorithm from the CUBA library. The comparison with existing analytic calculations shows that the minimal subtraction scheme yields more precise results.

Analysis of a fractal ultrasonic transducer with a range of piezoelectric length scales

The transmission and reception sensitivities of most piezoelectric ultrasonic transducers are enhanced by their geometrical structures. This structure is normally a regular, periodic one with one principal length scale, which, due to the resonant nature of the devices, determines the central operating frequency. There is engineering interest in building wide-bandwidth devices, and so it follows that, in their design, resonators that have a range of length scales should be used. This paper describes a mathematical model of a fractal ultrasound transducer whose piezoelectric components span a range of length scales. There have been many previous studies of wave propagation in the Sierpinski gasket but this paper is the first to study its complement. This is a critically important mathematical development as the complement is formed from a broad distribution of triangle sizes, whereas the Sierpinski gasket is formed from triangles of equal size. Within this structure, the electrical and mechanical fields fluctuate in tune with the time-dependent displacement of these substructures. A new set of basis functions is developed that allow us to express this displacement as part of a finite element methodology. A renormalization approach is then used to develop a recursion scheme that analytically describes the key components from the discrete matrices that arise. Expressions for the transducer’s operational characteristics are then derived and analysed as a function of the driving frequency. It transpires that the fractal device has a significantly higher reception sensitivity (18 dB) and a significantly wider bandwidth (3 MHz) than an equivalent Euclidean (standard) device.