Two simulations are different. Mine V.S. Paper's
You should really try to keep after the example in the paper. Using a capacitor in parallel with a voltage source is not the same as with a current source -- the first simply shorts out the capacitor due to the internal, ideally null resistance, the other forms an integrator.

Looking at your pictures, it looks like you're using a ns scale, while the paper has ms scale. Also, it looks like you'e using a pulsed voltage for the battery(?) instead of a DC. I don't know where did you get the information about the control voltage, but it doesn't look like any of them should be conducting over a whole half-cycle.

So I gave it a try, guessing the values and timings (edit: I accidentally switched the control voltages, reversed them):



The current is a sine, the battery is simplified as a large valued capacitor, precharged to 2V.



I am using LTspice, you are using something different. It doesn't make sense to search for what I used in your library. Whatever voltage controlled switch your library has, that should be used. Additionally, I have plotted controlling waveforms, explained when the switch turns on and off, described the signal of the current source, I am sorry, but you have all you need to build the schematic. The same way you tried to build it from the picture in the pdf, the same way you can see the similarities between my schematic and the picture. I cannot draw things for you, I don't have what you have.

Still, I redid the schematic and I will describe it, maybe LTspice's interface is so unfamiliar to you that you cannot understand what is drawn (but then I don't understand how you managed to understand the picture in the .pdf):


I1 is a current source, set to be a sine waveform with 5uA (micro) amplitude and 50Hz frequency (or 20ms period);
C1 is a 15nF capacitor, with an additional flag which specifies that the initial voltage across it is zero (ic=0);
S1 is a voltage controlled switch with the "on" resistance 1mOhm (milli), "off" resistance 1MegOhm (1e6), threshold voltage Vt=0.5V and Vh=0.5V hysteresis. The switch is turned "on" when the controlling voltage is greater than , or equal to Vt+Vh, and turns off when it's less than, or equal to Vt-Vh;
V1 is the controlling voltage source for S1;
S2 is a voltage controlled switch with the same parameters as S1;
V2 is the controlling voltage source for S2;
L1, together with its parasitic Rser form the series LR as seen in the picture, same values;
C2 is the equivalent of the battery, modeled as a large capacitor precharged at 2V.


The waveforms are:


V(pz) -- the voltage across C1;
V(c1) -- the control voltage for S1, blue waveform: a pulsed waveform from 0V to 1V, 10ms period, and 1% duty-cycle, no delay;
V(c2) -- the control voltage for S2, red waveform, same parameters as V1.